id
stringlengths 9
16
| vector
listlengths 1.02k
1.02k
| title
stringlengths 2
382
| abstract
stringlengths 16
3.07k
| authors
stringlengths 3
128
| categories
stringlengths 5
125
| month
stringclasses 12
values | year
int64 1.99k
2.01k
| url
stringlengths 31
38
|
|---|---|---|---|---|---|---|---|---|
hep-lat/9207034
|
[
0.4298630952835083,
0.11967015266418457,
-0.014527101069688797,
0.2754417657852173,
0.043573252856731415,
-0.26464250683784485,
-0.1430065780878067,
-0.48501843214035034,
-0.7340145111083984,
1.2917861938476562,
0.18235430121421814,
0.11495469510555267,
0.16779370605945587,
-0.49288803339004517,
-0.28332242369651794,
0.4531536102294922,
0.13070791959762573,
-0.7809514403343201,
-1.163678526878357,
0.5789240002632141,
0.4355175197124481,
0.11407160758972168,
-1.1526525020599365,
-0.2832636833190918,
-0.3284948766231537,
0.953557550907135,
0.4085325598716736,
0.43278923630714417,
1.1061246395111084,
0.7268581390380859,
-0.1902039498090744,
-0.34473729133605957,
-0.31395769119262695,
-0.2996428310871124,
-0.5628149509429932,
-0.3069942891597748,
-0.4942469894886017,
0.17226967215538025,
0.4118039309978485,
-0.3172772526741028,
0.9670426845550537,
-0.4183119833469391,
0.04703668877482414,
0.24405090510845184,
-0.3196542263031006,
0.10164841264486313,
-0.1794869303703308,
-0.20409490168094635,
0.4372546672821045,
-1.1825544834136963,
0.028849035501480103,
0.5558698177337646,
-0.09940847754478455,
-0.5205651521682739,
-0.3581532835960388,
0.44671630859375,
0.321562260389328,
-0.1641339510679245,
-0.4072895050048828,
-0.5282350182533264,
0.5374002456665039,
-0.09567779302597046,
0.5601381659507751,
-1.1665374040603638,
0.07397718727588654,
0.879679262638092,
0.06616948544979095,
0.65505450963974,
0.33882707357406616,
-0.11339346319437027,
-0.19771155714988708,
0.03052796795964241,
-1.0397663116455078,
-0.3103049099445343,
-1.0282195806503296,
0.176831915974617,
0.23114441335201263,
0.10853378474712372,
-0.6422494053840637,
0.20620845258235931,
0.12818580865859985,
0.2159096747636795,
-0.12088458240032196,
0.32005685567855835,
-0.867251455783844,
-0.0002209209487773478,
0.40668782591819763,
-0.2754814028739929,
0.09414016455411911,
0.527715265750885,
-0.5613117218017578,
0.36950334906578064,
-0.4909575283527374,
0.31222158670425415,
0.10734181106090546,
0.14914926886558533,
-0.13800083100795746,
0.441182017326355,
-0.13028426468372345,
-0.056239254772663116,
0.17657330632209778,
0.431352436542511,
-0.4324844479560852,
0.13558246195316315,
-0.9738914370536804,
0.40962034463882446,
-0.15413407981395721,
0.19669821858406067,
0.024522380903363228,
-0.7486085891723633,
0.4557790458202362,
-0.5813223123550415,
0.1392868012189865,
0.47872188687324524,
0.4220059812068939,
0.582606852054596,
-0.6585163474082947,
0.2687954306602478,
-1.0004947185516357,
-0.29353389143943787,
0.7007198333740234,
0.3645138442516327,
0.6609397530555725,
0.8784754276275635,
0.29559382796287537,
-0.18807700276374817,
0.09907115995883942,
0.7123352289199829,
-0.2510097622871399,
0.8576772809028625,
0.12792330980300903,
-0.2676263451576233,
-0.5524601340293884,
1.0108481645584106,
-0.9586268067359924,
0.24186666309833527,
-0.5311448574066162,
0.5161368250846863,
0.2812921702861786,
-0.15033791959285736,
0.8554378151893616,
-0.2935533821582794,
-0.08175962418317795,
1.2009775638580322,
-0.06592898815870285,
0.26662689447402954,
-0.21380293369293213,
-0.16179734468460083,
-0.10769137740135193,
0.22661305963993073,
-0.14342965185642242,
-0.2997936010360718,
-0.3708360195159912,
0.4272822439670563,
-0.3504072427749634,
0.7695131897926331,
-0.39926397800445557,
-0.2881476581096649,
-0.3733283579349518,
-0.24985718727111816,
0.6502504944801331,
0.04444556310772896,
-0.3588789105415344,
0.2952979803085327,
-0.3568100929260254,
0.4229431450366974,
-0.5981591939926147,
-0.15272650122642517,
-0.04785395413637161,
-0.7397040724754333,
-0.04292086884379387,
0.27463433146476746,
-0.16851089894771576,
0.6891034841537476,
0.7694435119628906,
0.148690328001976,
0.6876386404037476,
-0.6862936019897461,
-0.27654117345809937,
0.46247127652168274,
-0.6518533825874329,
-0.12139329314231873,
0.25394150614738464,
-0.04228546470403671,
-0.9052615761756897,
-0.5673046112060547,
0.5285645127296448,
-0.09857887029647827,
0.005299237556755543,
0.27702340483665466,
-0.6906399130821228,
-0.21604937314987183,
-0.11538626253604889,
0.6302695274353027,
-0.8185354471206665,
0.2602941691875458,
-1.0762730836868286,
-0.051883768290281296,
-0.8346952795982361,
0.09320761263370514,
0.06797916442155838,
0.4057254493236542,
-0.8153667449951172,
0.33990466594696045,
-1.3039199113845825,
-0.0667380690574646,
0.662218451499939,
0.16006311774253845,
-0.6588586568832397,
0.2898934483528137,
0.38850897550582886,
-0.41161659359931946,
0.3578219711780548,
-0.7943657040596008,
0.06399296224117279,
-0.1918545514345169,
0.22662992775440216,
0.531233549118042,
-0.22383596003055573,
0.16916491091251373,
0.9569106101989746,
0.18124422430992126,
0.2777244448661804,
1.0067780017852783,
0.16306130588054657,
-0.2670503258705139,
-0.28038308024406433,
0.15333391726016998,
0.182972714304924,
-0.3620152473449707,
0.10223744064569473,
0.4011465609073639,
0.08458969742059708,
0.9661220908164978,
0.7241559624671936,
0.5027819275856018,
0.23761451244354248,
-0.02501295693218708,
0.6490037441253662,
-0.04457877576351166,
0.11701704561710358,
-0.5991194248199463,
0.26017868518829346,
-0.7456202507019043,
0.039981868118047714,
0.30769920349121094,
-0.6172582507133484,
0.1999039649963379,
-0.5860903859138489,
0.4477759897708893,
0.6200999021530151,
0.24881744384765625,
0.12452639639377594,
0.3813025653362274,
-1.1683391332626343,
-0.39589253067970276,
-0.6437796950340271,
0.15759702026844025,
-0.13615988194942474,
-0.4908907413482666,
-0.43785420060157776,
0.1714729219675064,
-0.3036365509033203,
-1.0972310304641724,
-0.18642820417881012,
0.7687191963195801,
-0.8237378597259521,
0.4163481295108795,
0.5274219512939453,
-0.25204208493232727,
-0.9824105501174927,
0.09595364332199097,
-0.8486483097076416,
-0.10459049046039581,
-0.6622792482376099,
0.3567970097064972,
1.174164056777954,
-0.818777322769165,
-0.0614967979490757,
-0.059519607573747635,
-0.17431271076202393,
0.454731285572052,
-0.17952196300029755,
0.38350796699523926,
0.13250447809696198,
0.6503170132637024,
-0.6840445399284363,
0.09811285138130188,
-0.4193266034126282,
-0.08295678347349167,
-0.01848442293703556,
-0.14142870903015137,
0.5901607275009155,
-0.23119142651557922,
0.24065496027469635,
0.506973147392273,
-0.856059730052948,
0.06587889045476913,
0.15358242392539978,
-0.4214887320995331,
0.4517318606376648,
-0.28954240679740906,
-0.08422000706195831,
-0.27037879824638367,
-0.8828132748603821,
0.36840716004371643,
0.27155083417892456,
-0.35506972670555115,
0.33939018845558167,
-0.020120693370699883,
-0.368921160697937,
0.1991126388311386,
-0.1506371945142746,
0.17311537265777588,
-0.14997625350952148,
0.37546178698539734,
0.040296874940395355,
0.030801983550190926,
-0.5393272638320923,
0.12391843646764755,
-0.6880343556404114,
-0.08670215308666229,
0.2823888063430786,
-0.30000752210617065,
-0.21895678341388702,
0.41973406076431274,
0.12518490850925446,
-0.5733689069747925,
0.44538286328315735,
-1.1008554697036743,
-1.017765760421753,
0.06617023050785065,
-0.7711111307144165,
0.3357366621494293,
0.3086329996585846,
-0.06846173852682114,
-0.3396133780479431,
0.1578322798013687,
-0.042722187936306,
0.14707136154174805,
0.5600970387458801,
-0.16905666887760162,
0.6312575340270996,
0.36425650119781494,
0.9537201523780823,
-0.675519585609436,
0.4156377613544464,
-0.053913503885269165,
-0.6855475306510925,
0.5162635445594788,
-0.204064279794693,
0.5343393683433533,
0.004450223874300718,
0.5296608209609985,
-0.2691825032234192,
0.10613375902175903,
-0.612589418888092,
-0.4428996741771698,
-0.7669516205787659,
-0.5005136728286743,
0.28722554445266724,
0.3154090642929077,
-0.6187641024589539,
-0.052323032170534134,
-0.4330580532550812,
-0.12844033539295197,
0.5484803915023804,
0.44031861424446106,
0.5078721046447754,
-0.32530468702316284,
0.2796975076198578,
0.2976962625980377,
-0.5215373039245605,
0.42537692189216614,
-0.0018055657856166363,
0.030712787061929703,
0.9245787262916565,
0.6875987648963928,
0.6029903292655945,
-0.5220702886581421,
-0.7139806747436523,
0.23846082389354706,
1.0035645961761475,
0.5238583087921143,
0.16167180240154266,
0.1967601776123047,
0.17637032270431519,
-0.02754824608564377,
-0.563587486743927,
0.0886615663766861,
-0.1597573608160019,
-0.3015226721763611,
0.2705799639225006,
-0.17455552518367767,
-0.38822534680366516,
-0.11793313920497894,
0.15044307708740234,
0.6012436151504517,
-0.03240298479795456,
-0.04769202321767807,
0.5311692357063293,
-0.07802113145589828,
0.19621966779232025,
0.5491622686386108,
-0.202651709318161,
-0.11159820109605789,
-0.6050588488578796,
0.2939540445804596,
0.20785248279571533,
-0.2418094128370285,
-0.3718203008174896,
-0.46032199263572693,
0.042765382677316666,
-0.9964422583580017,
0.609105110168457,
0.26273515820503235,
-0.2637479901313782,
0.21762923896312714,
0.07722000777721405,
0.24318726360797882,
-0.7851027846336365,
0.33767035603523254,
0.3479045033454895,
0.3221272826194763,
0.527579665184021,
-0.7988651990890503,
0.11091354489326477,
-0.42819610238075256,
0.13179489970207214,
0.7493571043014526,
0.3381026089191437,
-1.099440336227417,
-0.24459518492221832,
-0.41782307624816895,
-0.06258059293031693,
0.3567527234554291,
1.280474305152893,
0.6892213821411133,
-0.32442450523376465,
-0.3903697729110718,
-0.43325552344322205,
1.2341537475585938,
-0.4048266112804413,
-0.3959709405899048,
0.3612428307533264,
0.022450070828199387,
-0.352457731962204,
0.6064198017120361,
-0.2502380609512329,
-0.8346168398857117,
-0.41582080721855164,
-1.1054210662841797,
0.35179296135902405,
-0.2906399965286255,
-0.427006334066391,
-0.2999753952026367,
-0.16994141042232513,
-0.09084981679916382,
0.2734781801700592,
0.1696595698595047,
-0.4031558632850647,
-0.5366392135620117,
0.3106531500816345,
-0.1934058666229248,
-0.30233708024024963,
-0.06569725275039673,
0.5349354147911072,
1.2054475545883179,
0.9074075818061829,
0.5278929471969604,
0.018967706710100174,
0.1913396120071411,
0.04164091870188713,
-0.3181881606578827,
0.37216082215309143,
-0.08471155166625977,
-0.5634422898292542,
-0.7844550609588623,
0.006879993714392185,
-0.48257413506507874,
-0.38070735335350037,
-0.08000746369361877,
-0.047021057456731796,
0.6841844320297241,
0.4424983859062195,
-0.4691263735294342,
-0.847967803478241,
-0.19454146921634674,
-1.0240641832351685,
0.7742088437080383,
-0.14170637726783752,
-0.3747727572917938,
0.8371785879135132,
-0.18302085995674133,
0.15750840306282043,
-0.43336519598960876,
-0.3589283227920532,
-0.1339883655309677,
0.2849824130535126,
0.5900207161903381,
0.8621297478675842,
0.23307165503501892,
-0.11453007161617279,
1.161139965057373,
-0.5871270298957825,
0.19999489188194275,
-0.48185479640960693,
-0.24093760550022125,
-0.5170160531997681,
-0.23381805419921875,
0.44687679409980774,
-0.10401137918233871,
-0.11123234033584595,
-0.2454928755760193,
-0.2538926303386688,
0.2081834226846695,
-0.14639393985271454,
-0.6261899471282959,
-0.13278666138648987,
0.2062840312719345,
0.23460479080677032,
-0.4552523195743561,
-0.21554403007030487,
0.28136447072029114,
0.27129197120666504,
-0.30908817052841187,
-0.11688810586929321,
-0.0969352200627327,
0.09874428808689117,
-0.4301152229309082,
0.14698229730129242,
-0.6377871632575989,
0.0850510448217392,
0.1469375193119049,
-0.30696162581443787,
0.3261328339576721,
-0.009266156703233719,
-0.07693106681108475,
-0.13351412117481232,
-0.5864388942718506,
-0.4731966257095337,
0.051008593291044235,
-0.703258216381073,
-0.48262304067611694,
-0.5176913142204285,
-0.13536404073238373,
-0.10187719017267227,
0.6098289489746094,
-0.23779672384262085,
0.3078843057155609,
0.09229034930467606,
-0.3406512439250946,
0.05537569150328636,
0.3904894292354584,
0.5225840210914612,
0.008170687593519688,
0.034167103469371796,
0.49965086579322815,
-0.31106051802635193,
0.6046529412269592,
-0.6520053148269653,
0.8251831531524658,
-0.4167790114879608,
1.0050950050354004,
-0.683939516544342,
0.14431235194206238,
-0.4923149645328522,
0.2767351269721985,
0.7577386498451233,
-0.760827362537384,
0.5682175755500793,
0.8100979328155518,
-0.48340362310409546,
0.1206294447183609,
0.5044891834259033,
-0.714563250541687,
0.02548365294933319,
-0.08175945281982422,
-0.5618351697921753,
0.7144432663917542,
-0.050138816237449646,
0.39655715227127075,
-0.8466998338699341,
-1.0228835344314575,
0.09733522683382034,
-0.0601993128657341,
-0.1835193932056427,
0.27231886982917786,
0.3961331248283386,
0.23857489228248596,
-0.08758694678544998,
0.02592983841896057,
-0.07241234183311462,
-0.0664171576499939,
-0.8235341906547546,
-0.5101476907730103,
0.03153999522328377,
0.1563136875629425,
-0.2539713978767395,
-1.1152198314666748,
-0.12523341178894043,
0.5094054341316223,
-0.3032205402851105,
-0.10368134081363678,
0.7501732707023621,
-0.5421937108039856,
-0.5015320777893066,
-0.6272255182266235,
0.3187185525894165,
0.48233675956726074,
0.1907164603471756,
0.6721295118331909,
-0.14079198241233826,
0.005833693780004978,
0.5709406733512878,
-0.10434252768754959,
-0.03264603391289711,
-0.6063991785049438,
0.816453218460083,
-0.4132583737373352,
-0.371564656496048,
0.8808553218841553,
0.09703105688095093,
-0.6989274621009827,
-0.21043071150779724,
-0.9398048520088196,
0.1618724912405014,
-0.5420549511909485,
0.5375762581825256,
-0.14967398345470428,
-0.27673402428627014,
0.08758683502674103,
0.23832152783870697,
1.1057183742523193,
0.18242406845092773,
0.05231017246842384,
0.15174683928489685,
-0.14925405383110046,
-0.9620213508605957,
-0.03967896103858948,
0.70017409324646,
0.12462969124317169,
-1.0162619352340698,
0.6429111957550049,
0.6069486141204834,
-0.5554121732711792,
-0.23446083068847656,
0.66802978515625,
-1.347008466720581,
-0.05534759536385536,
-0.2854699194431305,
-0.5512683987617493,
0.606121838092804,
0.05587353929877281,
0.1842009276151657,
0.14236396551132202,
-0.17045965790748596,
-0.6583338975906372,
-0.13821959495544434,
-0.18490514159202576,
0.45219719409942627,
0.4681098461151123,
0.45459461212158203,
0.3789905607700348,
-0.12036626040935516,
-0.24953825771808624,
0.10770668089389801,
-0.6864385604858398,
0.07049228996038437,
-0.6651215553283691,
-0.15510214865207672,
-0.03762650489807129,
-0.3553040623664856,
0.6400413513183594,
0.7483961582183838,
-0.18014056980609894,
-0.18640218675136566,
-0.6317791938781738,
-0.03252534195780754,
0.3964148759841919,
0.22254678606987,
0.03271877393126488,
-1.1475282907485962,
0.1415536105632782,
-0.14305296540260315,
-0.23645325005054474,
-0.7138550281524658,
0.011319885030388832,
0.2928829491138458,
-0.0012418216792866588,
0.30666524171829224,
0.006605857517570257,
0.6858236789703369,
-0.9600929021835327,
-0.6123415231704712,
0.08858099579811096,
0.1761673241853714,
-0.3437172472476959,
0.7558537721633911,
0.2527340054512024,
1.0331010818481445,
0.5870839357376099,
-0.5309599041938782,
-0.13470229506492615,
-0.24377800524234772,
-0.417184442281723,
-0.24611814320087433,
0.18460343778133392,
0.09128811955451965,
-0.05381304770708084,
-0.7898348569869995,
-0.5296825170516968,
-0.013818607665598392,
-1.3551859855651855,
-0.13423694670200348,
-0.19787082076072693,
0.08180472999811172,
-0.4785158932209015,
0.7559816241264343,
0.43059778213500977,
-0.25525355339050293,
0.5100155472755432,
1.4205056428909302,
-0.5298060774803162,
0.08857973664999008,
0.7040623426437378,
0.530799388885498,
-0.37930870056152344,
0.466167151927948,
0.64146488904953,
-0.28998687863349915,
-0.1221078485250473,
0.6713145971298218,
0.01544803474098444,
-0.0218189787119627,
0.05336663872003555,
-0.2591082453727722,
-0.0982447937130928,
-0.3711184859275818,
-0.2964458763599396,
0.6873428225517273,
0.7409681677818298,
-0.7371120452880859,
-0.09370443969964981,
-0.26703307032585144,
-0.8736403584480286,
0.07910484075546265,
-0.591646134853363,
-0.3183380663394928,
0.22674569487571716,
-0.5678181648254395,
0.20138436555862427,
0.5518122911453247,
0.08919285237789154,
0.39594483375549316,
0.34277838468551636,
0.4532381296157837,
0.5274909734725952,
0.12099005281925201,
-0.2880809009075165,
0.3133082985877991,
-0.7656635642051697,
-0.5637238621711731,
-0.19586165249347687,
0.8909698724746704,
-0.9371232986450195,
-1.278455138206482,
-0.8097364902496338,
0.7284876108169556,
-0.5295163989067078,
0.1876005381345749,
-0.36138537526130676,
-0.22646082937717438,
0.07096391171216965,
-0.04358406364917755,
-0.9987497925758362,
-0.229880690574646,
-0.6739107966423035,
0.8112183213233948,
-0.18096290528774261,
-0.8859241008758545,
0.10205914825201035,
-0.1952923983335495,
0.7386519312858582,
-0.13081197440624237,
0.2833114564418793,
1.039060115814209,
0.5581585168838501,
-0.3032865822315216,
0.5661861896514893,
0.3151644766330719,
0.7164875268936157,
0.45887213945388794,
-0.22996480762958527,
0.16058306396007538,
0.42033299803733826,
-0.25574731826782227,
0.6729363799095154,
0.409397691488266,
0.6353784203529358,
0.6515113115310669,
0.3002704381942749,
0.1613776981830597,
0.11736981570720673,
0.20636288821697235,
0.12365314364433289,
0.4634348154067993,
-0.44405901432037354,
-0.43437322974205017,
0.2736440896987915,
0.14460055530071259,
0.089947909116745,
-0.38222137093544006,
-0.055346015840768814,
-0.0847044512629509,
0.19926336407661438,
0.048235129565000534,
-1.554362416267395,
-0.2672828137874603,
-0.20113560557365417,
0.3502904176712036,
-0.043230485171079636,
0.051532164216041565,
-0.2019474059343338,
0.4113048017024994,
0.20292076468467712,
0.30671426653862,
0.2818273603916168,
1.0304449796676636,
0.03558046743273735,
0.7343645095825195,
0.802603542804718,
-0.12977978587150574,
0.11991055309772491,
-0.22099123895168304,
0.6784517765045166,
-0.5428226590156555,
-0.14499691128730774,
0.42366889119148254,
-0.789383590221405,
-0.08471014350652695,
-0.21084733307361603,
0.03751639649271965,
-0.9953756928443909,
-0.4175454378128052,
0.19757413864135742,
-0.8049593567848206,
-0.3271658420562744,
0.9186254739761353,
0.18542328476905823,
0.7292327284812927,
0.4810723066329956,
0.14917691051959991,
0.0943291112780571,
0.17139482498168945,
0.037265073508024216,
-0.41685721278190613,
0.9002518653869629,
1.5281729698181152,
0.17137396335601807,
0.22890768945217133,
0.07188456505537033,
-0.4549950361251831,
0.4202497899532318,
0.6515798568725586,
0.07090428471565247,
0.9882664084434509,
-0.22176675498485565,
-0.13008727133274078,
0.2599336802959442,
0.020712347701191902,
-0.2191036492586136,
-0.6333910226821899,
-0.056183647364377975,
-0.2584422528743744,
-0.07837475091218948,
-0.3663942515850067,
1.4088938236236572,
0.3237307369709015,
-0.5248629450798035,
-0.3946644067764282,
0.4410935044288635,
-0.6688231825828552,
0.11190072447061539,
-0.7446898818016052,
0.6015296578407288,
-0.41677969694137573,
-0.4410237669944763,
0.03812527656555176,
-0.39909297227859497,
-0.2836602032184601,
-0.6962652802467346,
0.34636643528938293,
-0.3164074122905731,
0.5207830667495728,
0.504555881023407,
0.014450851827859879,
0.2789918780326843,
-0.4017052948474884,
0.15539999306201935,
0.45218923687934875,
0.6657465100288391,
-0.157212495803833,
-0.2578994035720825,
0.5725221633911133,
0.4311579763889313,
-0.5643396973609924,
0.572115957736969,
0.22888778150081635,
-0.1649942547082901,
0.34565651416778564,
-0.8185161352157593,
0.6391783356666565,
0.46790704131126404,
-0.38262248039245605,
0.06685122102499008,
-0.2540164589881897,
0.06917740404605865,
-0.23541267216205597,
-0.2391560822725296,
-0.1218232661485672,
-0.8720596432685852,
0.427905797958374,
-0.5017102360725403,
0.3145722448825836,
-0.11462405323982239,
0.6544268727302551,
-0.00737969484180212,
-1.0047787427902222,
4.344222545623779,
0.8327797055244446,
0.3328467309474945,
0.48630785942077637,
0.7747145295143127,
1.046209692955017,
-0.5137064456939697,
-0.41774702072143555,
-0.029315967112779617,
-0.0768594816327095,
-0.7204517722129822,
0.13788387179374695,
0.15258687734603882,
-0.02678324282169342,
-0.18575507402420044,
0.5616755485534668,
-0.33673107624053955,
0.15516123175621033,
-0.005280126351863146,
-0.781445324420929,
-0.6342931389808655,
0.17348136007785797,
0.15470509231090546,
0.16184979677200317,
0.018978336825966835,
0.46243464946746826,
0.19274725019931793,
-0.15388868749141693,
-0.35714495182037354,
-0.8930386304855347,
-0.5084481239318848,
-0.7132292985916138,
0.7157289981842041,
0.10224965959787369,
-1.0162708759307861,
0.0186057947576046,
0.1774064004421234,
-0.4734450876712799,
0.24756376445293427,
0.01737639680504799,
-0.30476030707359314,
-0.3101326823234558,
0.2574479579925537,
-0.6855173110961914,
-0.1517786830663681,
0.40404537320137024,
-0.2549956142902374,
0.3906093239784241,
0.23558536171913147,
-0.8539562225341797,
0.5448125004768372,
0.258344829082489,
0.1968616545200348,
-1.0305978059768677,
-0.7284535765647888,
0.15592661499977112,
-0.8491554856300354,
-0.2271333485841751,
0.17266897857189178,
-0.17543119192123413,
-0.3676169812679291,
-0.25754815340042114,
-0.5428177118301392,
0.3618772029876709,
-0.40258675813674927,
0.5806890726089478,
-0.4073382019996643,
-0.25582650303840637,
-0.7251321077346802,
0.1691451072692871,
0.14220458269119263,
-0.08256635814905167,
-0.33575788140296936,
0.0010064562084153295,
0.8057909607887268,
0.3166286051273346,
-0.4278876483440399,
0.42222079634666443,
-0.5705096125602722,
-0.056963011622428894,
0.09535355120897293,
-0.3642910122871399,
0.14240093529224396,
0.21526892483234406,
0.003970807418227196,
0.48312196135520935,
-0.6831607222557068,
0.7372617125511169,
-0.2981375455856323,
0.6891310811042786,
0.5712677240371704,
1.1058349609375,
0.16543546319007874,
0.577154815196991,
-1.3136045932769775
] |
Chiral Yukawa models in the planar limit
|
We consider the most general renormalizable chiral Yukawa model with $SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w )$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c \rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio $\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$ only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to $m_t \le 1~TeV$.
|
G. Bathas and H. Neuberger
|
hep-lat hep-ph
|
July
| 1,992 |
https://arxiv.org/abs/hep-lat/9207034
|
hep-lat/9207035
|
[
0.32651999592781067,
-0.5458890199661255,
0.1974482536315918,
0.5330839157104492,
0.05277271568775177,
-0.5314160585403442,
-0.22756890952587128,
-0.41422441601753235,
-0.9858635663986206,
1.8277716636657715,
0.7501654028892517,
-0.5144057273864746,
0.8235737085342407,
-0.8013775944709778,
-0.004369609523564577,
0.7521409392356873,
-0.47127071022987366,
-0.9166088700294495,
-1.4693280458450317,
0.5922818779945374,
0.6518808603286743,
-0.22608470916748047,
-1.4127168655395508,
-0.9079735279083252,
-0.2501576244831085,
1.033302664756775,
-0.18894915282726288,
0.34329450130462646,
0.7011753916740417,
0.6161603331565857,
0.12704862654209137,
-0.1221141591668129,
-0.35946446657180786,
-0.732440710067749,
-0.5331577658653259,
-0.23045922815799713,
-0.48828795552253723,
-0.932843804359436,
0.30542221665382385,
-0.07159120589494705,
0.7598523497581482,
-0.7154125571250916,
0.00812816433608532,
-0.18616710603237152,
-0.12850452959537506,
-0.12383360415697098,
-0.01382417418062687,
-0.5124314427375793,
-0.05862368643283844,
-0.93672114610672,
-0.10046757012605667,
0.4328656494617462,
0.9824700355529785,
-0.717186450958252,
-0.6325176954269409,
-0.1269986629486084,
0.5370758771896362,
0.16311919689178467,
-0.8294150829315186,
-0.30315595865249634,
0.5853008031845093,
0.07175120711326599,
0.9082757234573364,
-0.6634460091590881,
-0.3987276256084442,
1.1403197050094604,
-0.29057779908180237,
0.830546498298645,
0.34723910689353943,
-0.6643111109733582,
-0.6968432068824768,
-0.35862529277801514,
-0.9739155173301697,
0.06863252818584442,
-0.5800884366035461,
-0.00737612321972847,
-0.059493470937013626,
-0.9023727774620056,
-0.470930814743042,
-0.16881433129310608,
0.3272545039653778,
0.3496190011501312,
-0.35856127738952637,
0.7001070380210876,
-0.33365532755851746,
-0.3067046105861664,
-0.18195028603076935,
0.055636774748563766,
0.024654677137732506,
0.447872519493103,
0.1703064739704132,
0.8611682653427124,
-0.23340190947055817,
0.24794524908065796,
0.375040203332901,
0.6633873581886292,
0.19389252364635468,
0.8867824673652649,
0.6559837460517883,
0.16215942800045013,
-0.028373053297400475,
0.992277204990387,
-0.8050589561462402,
0.24869781732559204,
-0.41841191053390503,
0.2733302712440491,
-0.34366458654403687,
-0.18237833678722382,
-0.13123579323291779,
-0.7613247036933899,
0.29227083921432495,
-0.2304951697587967,
0.1845017373561859,
0.32275262475013733,
0.349076509475708,
0.640940248966217,
-0.018645387142896652,
0.05625176802277565,
-1.0331929922103882,
-0.6831251978874207,
0.25947847962379456,
0.9439573287963867,
-0.08309842646121979,
0.1460007280111313,
0.4347027838230133,
-0.18334653973579407,
1.2416352033615112,
0.6830014586448669,
-0.5470840930938721,
0.4227118492126465,
0.4493921101093292,
-0.27324211597442627,
-0.5551559329032898,
0.7309201955795288,
-0.46497854590415955,
0.11264491826295853,
-0.17468135058879852,
0.22610004246234894,
0.14506177604198456,
0.25766652822494507,
0.4061069190502167,
-0.580143392086029,
-0.14322610199451447,
1.039052128791809,
0.6437214612960815,
0.005541949067264795,
0.4826466739177704,
-0.10391322523355484,
-0.24242283403873444,
0.29611173272132874,
-1.0877565145492554,
-0.028861811384558678,
0.40554121136665344,
-0.05836862698197365,
-0.39111238718032837,
0.7979356050491333,
-0.835392951965332,
0.17496836185455322,
-0.7705501317977905,
-0.6863149404525757,
0.22915752232074738,
-0.4488018751144409,
-0.8564809560775757,
0.8684218525886536,
-0.7670021057128906,
0.06634938716888428,
-0.4379689693450928,
-0.27215299010276794,
0.11437371373176575,
-0.45823484659194946,
-0.31400853395462036,
0.7139904499053955,
-0.4571983814239502,
0.8180946707725525,
0.5494093298912048,
0.14464977383613586,
0.7653998136520386,
-0.6355124115943909,
-0.0013556756312027574,
0.4912014901638031,
-0.5367938876152039,
0.1106724962592125,
0.31637412309646606,
0.16975483298301697,
0.1095423772931099,
0.504600465297699,
-0.4927135109901428,
-0.35656747221946716,
0.28172263503074646,
0.10903367400169373,
-0.3201870024204254,
0.3947732746601105,
-0.21529912948608398,
0.7522544264793396,
-0.6868407130241394,
-0.034664638340473175,
-0.9181297421455383,
0.2204194813966751,
-0.8253377676010132,
-0.3239627480506897,
0.3823240399360657,
0.5922501683235168,
-0.7042068243026733,
0.27094128727912903,
-1.1973083019256592,
0.10874420404434204,
0.544517457485199,
-0.038490552455186844,
-0.7610357403755188,
-0.3298349976539612,
0.44765913486480713,
-0.27899792790412903,
0.048453643918037415,
-0.6793126463890076,
0.20283013582229614,
0.12504051625728607,
-0.513801634311676,
0.24014613032341003,
0.6096821427345276,
0.28180867433547974,
0.6546448469161987,
0.06940113753080368,
-0.7567306160926819,
1.2340712547302246,
-0.2570655345916748,
-0.4765675961971283,
0.15202733874320984,
0.7373509407043457,
0.08661127090454102,
-0.1717493087053299,
-0.3076399266719818,
0.5169822573661804,
-0.08660813421010971,
0.42217203974723816,
0.8758764863014221,
0.3691226541996002,
0.6934562921524048,
0.7300841212272644,
0.3187694251537323,
0.38291630148887634,
-0.23922446370124817,
0.07488571852445602,
0.5965451598167419,
-0.3291780352592468,
-0.06501246243715286,
0.4055921733379364,
-0.8059247732162476,
-0.18579258024692535,
-0.7222659587860107,
0.21993954479694366,
-0.013107981532812119,
0.9671647548675537,
0.1672348529100418,
0.40207961201667786,
-1.0645447969436646,
-0.11367335170507431,
-0.15612514317035675,
-0.10848162323236465,
-0.14755289256572723,
-0.232069194316864,
0.6003669500350952,
-0.17812269926071167,
-0.1257432997226715,
-0.5130839347839355,
-0.3950665593147278,
0.8503785729408264,
-0.5918843746185303,
-0.2445923238992691,
0.32250741124153137,
-0.28452301025390625,
-0.7876651287078857,
-0.18647390604019165,
-0.7914994359016418,
0.0674782246351242,
-0.509512186050415,
0.2711430788040161,
0.5012239813804626,
-0.6908442378044128,
0.44092923402786255,
0.18578608334064484,
-0.14830845594406128,
0.5804533362388611,
-0.9042903184890747,
0.5217299461364746,
0.04133899509906769,
0.5291147828102112,
-0.782709538936615,
0.583064615726471,
-0.6463790535926819,
-0.13511872291564941,
-0.14355289936065674,
-0.2579589784145355,
1.0177921056747437,
-0.17839892208576202,
0.7248679995536804,
-0.053707145154476166,
-0.18250077962875366,
-0.17387111485004425,
0.15074151754379272,
-0.575400173664093,
0.37428778409957886,
0.5019875764846802,
0.308397114276886,
-0.10399819910526276,
-0.2675492465496063,
0.32434728741645813,
-0.3448397219181061,
-0.19516022503376007,
0.5316886305809021,
0.5776305794715881,
-0.17212150990962982,
0.4466150104999542,
-0.5419403910636902,
0.8671966195106506,
-0.08402112871408463,
0.8783008456230164,
0.7035748958587646,
-0.24136163294315338,
-0.052775971591472626,
-0.4046165347099304,
-0.3746654987335205,
0.45980823040008545,
0.22816874086856842,
-0.4884687662124634,
-0.028346585109829903,
0.4116349518299103,
0.23950666189193726,
-0.4644874334335327,
0.10142184048891068,
-0.6614336967468262,
-0.6970897912979126,
0.07775769382715225,
-1.0137652158737183,
0.6954347491264343,
-0.11226597428321838,
0.09108919650316238,
-1.0937154293060303,
-0.07768598943948746,
0.06907465308904648,
0.7284985780715942,
0.36147814989089966,
0.1265142410993576,
0.6365898251533508,
-0.0507543571293354,
0.25870653986930847,
-0.157316192984581,
0.005009343381971121,
-0.3819699287414551,
-0.5120108723640442,
0.5321000218391418,
-0.8327692747116089,
0.39008527994155884,
0.2652929425239563,
0.5357017517089844,
-0.6913425922393799,
0.6734405755996704,
-0.4563913345336914,
-0.6593634486198425,
-0.366001695394516,
-0.8677810430526733,
-0.052544258534908295,
0.5884482860565186,
-0.7041985988616943,
-0.15227539837360382,
-0.513133704662323,
-0.4220508933067322,
0.23580388724803925,
0.15296202898025513,
0.6956663131713867,
-0.18938502669334412,
0.570410430431366,
0.1165328100323677,
-0.311901330947876,
-0.18913237750530243,
-0.3005983531475067,
0.1134415790438652,
0.5123531222343445,
-0.16193895041942596,
0.7171072363853455,
-0.13280600309371948,
-0.6966269612312317,
-0.17119517922401428,
0.619292676448822,
0.5913097262382507,
0.957683801651001,
0.28969553112983704,
-0.5311521887779236,
0.7259278893470764,
-0.3155776858329773,
-0.6635575294494629,
-0.1379035860300064,
-0.35900887846946716,
0.15076465904712677,
-0.23095326125621796,
0.30936509370803833,
-0.20251411199569702,
0.5133137106895447,
0.9279845356941223,
0.0424690842628479,
0.19154612720012665,
0.00770403491333127,
0.14617758989334106,
0.358599990606308,
0.2755453884601593,
-0.26022249460220337,
0.3089713156223297,
-1.0445154905319214,
0.6341527104377747,
0.07119956612586975,
0.16722552478313446,
-0.0061867088079452515,
-0.548255205154419,
-0.19571903347969055,
-0.4938194751739502,
0.4901004433631897,
0.2558753490447998,
-0.9692283272743225,
0.5481941103935242,
-0.1114528700709343,
0.6160603761672974,
-0.6663893461227417,
-0.3851604461669922,
1.0605194568634033,
0.5568923950195312,
0.3169596493244171,
-0.9594645500183105,
0.016831614077091217,
-0.5891169905662537,
0.2753571569919586,
-0.0627058744430542,
-0.6390063166618347,
-0.5782973766326904,
-0.9324076771736145,
0.1144815981388092,
-0.4260258674621582,
0.15784183144569397,
1.0889830589294434,
-0.164145365357399,
0.21967308223247528,
-0.9302219748497009,
-0.6167876720428467,
0.9730001091957092,
-0.38259580731391907,
-0.7193570733070374,
0.41345351934432983,
-0.23094427585601807,
-0.11218541860580444,
0.734061598777771,
-0.4979393184185028,
-0.7032610177993774,
-0.11815732717514038,
-0.25925251841545105,
0.09937306493520737,
-0.03853485360741615,
-0.2500002086162567,
-0.03831829875707626,
-0.8745864033699036,
-0.14319190382957458,
0.29953497648239136,
0.2622096836566925,
-0.13460980355739594,
0.24523727595806122,
0.3295591175556183,
-0.7281437516212463,
0.484103262424469,
-0.10316191613674164,
-0.26074084639549255,
0.9321010112762451,
0.8699878454208374,
0.3128907382488251,
0.041588567197322845,
0.48997971415519714,
-0.11606897413730621,
-0.1039295494556427,
0.48219308257102966,
0.130298912525177,
-0.20186369121074677,
-0.3846117854118347,
0.06484569609165192,
-0.7819061279296875,
-0.452545702457428,
-0.0636964961886406,
-0.16203437745571136,
1.2089152336120605,
0.1091536283493042,
-0.8159567713737488,
-0.28878965973854065,
-0.14317037165164948,
-0.24844181537628174,
0.45723679661750793,
0.04197412729263306,
-0.3106021285057068,
0.37353360652923584,
-0.4521450698375702,
0.21832548081874847,
-0.3350946605205536,
0.02144356071949005,
-0.5437264442443848,
0.053527042269706726,
0.9364397525787354,
-0.13518033921718597,
0.9931364059448242,
-0.7866948843002319,
0.09632022678852081,
-0.7358781695365906,
0.12889136373996735,
-0.446859747171402,
-0.22462426126003265,
-0.22936750948429108,
-0.639039158821106,
0.25011417269706726,
-0.3415994942188263,
0.301592081785202,
-0.1481335610151291,
-0.19137825071811676,
-0.1624874770641327,
0.012865876778960228,
0.010851544328033924,
-0.17661358416080475,
0.5825902819633484,
-0.14011257886886597,
-0.9719240665435791,
0.399850457906723,
0.7478795051574707,
0.3890759348869324,
0.2731252610683441,
-0.15861459076404572,
-0.45363953709602356,
-0.11720879375934601,
-0.19558292627334595,
0.3277285099029541,
-0.5620701909065247,
-0.41578882932662964,
0.15535542368888855,
-0.02785360813140869,
0.6745538115501404,
0.42777231335639954,
0.29553818702697754,
-0.15744909644126892,
-0.4044419229030609,
-0.5765543580055237,
0.3078470230102539,
-0.5131439566612244,
-0.4908738136291504,
-0.6219221949577332,
-0.4309001564979553,
-0.470076322555542,
0.952297568321228,
-0.21441145241260529,
0.37009328603744507,
0.33696866035461426,
0.12786921858787537,
-0.2584782540798187,
0.5564577579498291,
0.3354009985923767,
0.02062404528260231,
0.0061165387742221355,
0.7075098156929016,
-0.3917088806629181,
0.599026083946228,
-0.3912712037563324,
0.19317498803138733,
-0.79671710729599,
1.000240445137024,
-0.8885236382484436,
-0.09329535067081451,
-0.424928218126297,
-0.2670179605484009,
0.8536937236785889,
-1.0426446199417114,
0.526841402053833,
0.37615102529525757,
-0.02564184181392193,
0.6986819505691528,
0.49772170186042786,
-0.5767338275909424,
0.019555987790226936,
-0.282343327999115,
-0.9494731426239014,
0.4820843040943146,
0.363643616437912,
-0.2151021957397461,
-1.1127054691314697,
-0.7226328253746033,
0.13144150376319885,
0.01636226661503315,
0.12116513401269913,
0.8082913160324097,
-0.5924066305160522,
0.11523723602294922,
-0.03189603239297867,
0.17564237117767334,
-0.09829016774892807,
0.11001084744930267,
0.11768364161252975,
0.0648031085729599,
-0.14975734055042267,
-0.20714199542999268,
-0.5440707206726074,
-0.3476768136024475,
-0.3426981270313263,
0.592583417892456,
0.3862043023109436,
-0.47278016805648804,
0.7581425309181213,
-0.3657573163509369,
-1.0228744745254517,
-0.4186382293701172,
0.20493923127651215,
0.5408843755722046,
0.13522949814796448,
0.3803223669528961,
0.4982375502586365,
-0.04015355557203293,
-0.019222110509872437,
0.4590221345424652,
-0.3268260657787323,
-0.13739953935146332,
0.5355730056762695,
-0.766975462436676,
-0.47260889410972595,
0.6849728226661682,
0.28287893533706665,
-0.5320408940315247,
-0.6349124312400818,
-1.133256435394287,
0.2672996520996094,
-0.31417369842529297,
-0.36329883337020874,
0.0005989304045215249,
-0.42973068356513977,
-0.32858341932296753,
0.8005203604698181,
1.0249654054641724,
0.26241570711135864,
-0.478044331073761,
0.05958715081214905,
-0.6398680210113525,
-0.6559938788414001,
0.3101232051849365,
1.115692138671875,
-0.26161301136016846,
-0.6498938202857971,
0.005372954532504082,
0.058222558349370956,
-0.31220361590385437,
0.2476436048746109,
0.3679695725440979,
0.32702192664146423,
0.8369998335838318,
0.020732413977384567,
0.12209101021289825,
0.3613501191139221,
0.6483579277992249,
-0.06941471248865128,
-0.007842869497835636,
-0.3264369070529938,
-0.8153082728385925,
-0.15019072592258453,
-0.5762110948562622,
0.41996821761131287,
0.9431943893432617,
-0.23645871877670288,
0.2309640794992447,
-0.349633127450943,
-0.8231754302978516,
-0.5375242233276367,
-0.45819807052612305,
-0.24247229099273682,
-1.0129107236862183,
-0.09107337146997452,
-0.5306103229522705,
-0.15659278631210327,
-0.09470017999410629,
0.4572162628173828,
0.11470185220241547,
0.2506110370159149,
-0.6296221017837524,
0.0023407854605466127,
0.024489300325512886,
0.1990261822938919,
0.21540911495685577,
-0.9484031200408936,
-0.31230980157852173,
-0.09028760343790054,
-0.4338279664516449,
-0.42301151156425476,
0.23961962759494781,
0.553452730178833,
-0.47766903042793274,
0.4519123136997223,
-0.32325422763824463,
0.8398220539093018,
-1.16652250289917,
-1.123282790184021,
0.4225948750972748,
-0.00782953854650259,
0.07993973791599274,
0.43351057171821594,
0.09997863322496414,
0.6653580069541931,
-0.1196165457367897,
-0.5532252192497253,
-0.4637039601802826,
0.4744093120098114,
-1.5700701475143433,
-0.2394750565290451,
0.7832223176956177,
0.5632871985435486,
-0.12301898002624512,
-0.8267238140106201,
-0.20203475654125214,
0.47042205929756165,
-1.1723673343658447,
0.8050200939178467,
-0.3590032458305359,
0.6802324652671814,
-0.7656545042991638,
0.24441289901733398,
0.3590121567249298,
0.03453271836042404,
-0.16978567838668823,
0.7983615398406982,
-0.4776235520839691,
0.045184023678302765,
0.3589819073677063,
0.12782132625579834,
-0.2188994288444519,
0.5468977093696594,
0.24371123313903809,
-0.6336356997489929,
-0.01757849007844925,
0.29080256819725037,
0.13951680064201355,
0.4328317642211914,
-0.027117908000946045,
-0.5403172373771667,
0.04662556201219559,
-0.17616166174411774,
-0.5651828050613403,
0.6775688529014587,
0.6082062125205994,
-0.686754047870636,
0.35730212926864624,
-0.7706625461578369,
-0.49593767523765564,
0.04870878532528877,
-0.532382071018219,
-0.4689333736896515,
-0.2911500930786133,
0.3958570957183838,
-0.3442201316356659,
0.45803117752075195,
-0.49493661522865295,
-0.059028156101703644,
-0.32032331824302673,
0.044401735067367554,
-0.16802148520946503,
-0.46563148498535156,
-0.39434128999710083,
0.104338638484478,
-0.990134060382843,
-0.2817654013633728,
0.03957593813538551,
0.777779757976532,
-0.6049661040306091,
-0.09109535813331604,
-0.38508209586143494,
0.16511137783527374,
0.455466628074646,
0.20197473466396332,
-0.2852674126625061,
-0.6308196783065796,
-0.5189783573150635,
-0.3509158790111542,
-0.046347927302122116,
-0.1567365527153015,
-0.9778433442115784,
0.3367438018321991,
-0.04853785037994385,
-0.9826293587684631,
0.002050188137218356,
-0.29294639825820923,
0.00302753783762455,
0.11057794839143753,
-0.18771877884864807,
1.0618183612823486,
0.5889990925788879,
-0.9326654672622681,
0.3951151967048645,
-0.1965581178665161,
-0.4400821328163147,
0.23080110549926758,
-0.6559819579124451,
-0.02221611514687538,
0.5253055095672607,
0.3347560167312622,
0.8269253373146057,
1.0541324615478516,
0.1946435272693634,
0.6202874183654785,
0.1979852318763733,
0.2437945455312729,
-0.15880440175533295,
0.5454833507537842,
0.42827361822128296,
0.7022873163223267,
-0.1397416740655899,
0.15972717106342316,
-0.5509743690490723,
-0.1687191277742386,
-0.06184959411621094,
0.36479607224464417,
0.008404377847909927,
-0.3453551232814789,
0.46067824959754944,
0.43766552209854126,
-0.6650055646896362,
-0.18294501304626465,
-0.24268154799938202,
0.11821863800287247,
0.2992478311061859,
0.12156588584184647,
0.2599327564239502,
0.904656171798706,
0.4688809812068939,
0.07135040313005447,
0.020294083282351494,
0.5251056551933289,
-0.06014455109834671,
0.9265679717063904,
0.631879985332489,
0.7330276370048523,
0.6785385012626648,
0.1413423717021942,
0.17200148105621338,
-1.0724132061004639,
-0.2501567602157593,
0.46416738629341125,
-1.1092932224273682,
0.060269858688116074,
-0.15880106389522552,
0.14872334897518158,
-0.3766948878765106,
-0.5947004556655884,
0.04782051965594292,
-0.5560476779937744,
0.25409388542175293,
0.23083294928073883,
-0.2860536575317383,
0.43208956718444824,
0.6824047565460205,
0.346182256937027,
0.4721996486186981,
0.5465077757835388,
-0.02733399160206318,
-0.09616024047136307,
0.9390051364898682,
1.9116239547729492,
0.24473857879638672,
0.6440699100494385,
0.4143282175064087,
-0.8493119478225708,
0.4156010150909424,
0.5727950930595398,
-0.6594310998916626,
0.3449524939060211,
-0.6421023011207581,
-0.4618123769760132,
0.28486934304237366,
0.3449382483959198,
-0.04618823900818825,
-0.29334092140197754,
0.00571359321475029,
0.11233886331319809,
0.1399645060300827,
-0.7161498069763184,
1.273123860359192,
0.8512311577796936,
-0.4756016135215759,
-0.5722846388816833,
-0.21285951137542725,
-0.6452553272247314,
0.2742592692375183,
-0.5530104041099548,
0.616984486579895,
-0.07641085982322693,
-0.14043106138706207,
0.1886662095785141,
-0.7039006948471069,
-0.44744154810905457,
-0.9100790619850159,
0.2841242849826813,
-0.4454520046710968,
-0.09032711386680603,
0.3419326841831207,
0.4921216368675232,
0.22171948850154877,
-0.2382000982761383,
0.10167408734560013,
0.2581804692745209,
0.7341082096099854,
0.41550353169441223,
-0.055395860224962234,
0.6771859526634216,
0.5829489231109619,
-1.1102262735366821,
0.48657941818237305,
0.9941409230232239,
-0.09147769957780838,
0.6937696933746338,
-0.3107947111129761,
-0.03490818664431572,
0.30463385581970215,
0.017848385497927666,
0.1838323473930359,
0.3766013979911804,
0.3772500455379486,
0.16715370118618011,
-0.12001717835664749,
-0.7349280714988708,
-1.1680128574371338,
-0.3934440016746521,
-0.41546788811683655,
0.5352181196212769,
0.08406118303537369,
0.1410844624042511,
0.5039591789245605,
-0.4791449308395386,
4.163144111633301,
1.1085065603256226,
0.25193965435028076,
0.03268514201045036,
0.5838209986686707,
1.0855673551559448,
-0.1434682011604309,
-0.42417842149734497,
1.1158241033554077,
-0.8624409437179565,
-0.9284189343452454,
0.14702770113945007,
-0.3552611172199249,
-0.06778807193040848,
-0.46499714255332947,
0.5523306131362915,
-0.4375763535499573,
-0.30335837602615356,
-0.4193570911884308,
-0.8328596353530884,
-0.5228958129882812,
0.5317153930664062,
0.40909385681152344,
0.6027069687843323,
0.2761594355106354,
0.025219261646270752,
0.9110085964202881,
-0.8026929497718811,
-0.607009768486023,
-0.06217954307794571,
-0.8939006924629211,
-0.8115308284759521,
-0.06880633533000946,
0.06892120093107224,
-1.1095635890960693,
0.29900336265563965,
0.042646877467632294,
-0.371910035610199,
0.16236591339111328,
0.24711178243160248,
0.030255813151597977,
-0.22058121860027313,
0.23388397693634033,
-0.14475752413272858,
-0.40465250611305237,
0.7138258218765259,
-0.05651358887553215,
0.5997982025146484,
0.059492383152246475,
-0.3126409351825714,
0.34583568572998047,
-0.03246598318219185,
0.7253941297531128,
-0.4648388624191284,
-1.2836331129074097,
-0.2640637457370758,
-0.010058462619781494,
-0.39715465903282166,
0.15176348388195038,
-0.44563353061676025,
0.10243897885084152,
-0.15376362204551697,
0.0311873909085989,
-0.03504006192088127,
-0.2036661058664322,
0.796532392501831,
0.21652887761592865,
-0.1394779086112976,
-0.46425309777259827,
0.03721223771572113,
-0.21728023886680603,
-0.11341249197721481,
-0.48200082778930664,
0.21895703673362732,
-0.16702327132225037,
-0.03497988358139992,
0.2773644030094147,
0.2843206226825714,
-0.06764727830886841,
0.4420882761478424,
-0.1307511031627655,
-0.33498236536979675,
-0.3104136884212494,
0.42256951332092285,
0.2048635184764862,
0.7179703712463379,
-0.7498879432678223,
-0.2843809127807617,
0.09619920700788498,
0.25007346272468567,
0.483892560005188,
0.9126643538475037,
0.28955748677253723,
0.5368009805679321,
-0.5508142709732056
] |
The Phase Diagram of the $N=2$ Kazakov-Migdal Model
|
We have determined the phase diagram of the simplest version of a lattice model introduced in the recent work of Kazakov and Migdal. If $m_0$ and $\lambda$ are the bare mass and self coupling of the scalar field in the model respectively, we find a line of first order phase transitions in the ($m_0, \lambda$) plane ending in a critical point where $\lambda$ is nonzero. Kazakov and Migdal speculate that their model of scalar field theory could induce QCD. Our work indicates that for $N=2$ there is no continuum limit for the Kazakov-Migdal model except at the critical end point. Whether or not a nontrivial continuum limit exists in the vicinity of the critical point requires careful study of the renormalization group properties of the model.
|
Andreas Gocksch and Yue Shen
|
hep-lat hep-th
|
July
| 1,992 |
https://arxiv.org/abs/hep-lat/9207035
|
hep-lat/9208001
|
[
-0.1973714530467987,
0.48568859696388245,
0.49935004115104675,
0.6903221607208252,
-0.11935234814882278,
-0.08899915218353271,
-1.2621358633041382,
-0.452666699886322,
-0.014238274656236172,
1.3117444515228271,
0.870375394821167,
0.15791969001293182,
-0.003689432516694069,
-0.6178836822509766,
-0.5496355891227722,
0.9265857934951782,
-0.14913375675678253,
-0.6125898361206055,
-0.9650831818580627,
-0.12032802402973175,
-0.0632726401090622,
-0.5690116882324219,
-1.3103270530700684,
-1.2519327402114868,
-0.1920860856771469,
0.5293391942977905,
-0.01854974590241909,
-0.47042420506477356,
1.5255954265594482,
0.8868206143379211,
0.6674535870552063,
-0.14279206097126007,
-0.24934668838977814,
-0.9209002256393433,
0.19718961417675018,
-0.6383987069129944,
0.3911494314670563,
0.3868248760700226,
0.2679862380027771,
-0.7919400334358215,
0.7502825260162354,
0.2707756459712982,
0.4827263653278351,
-0.37732911109924316,
-0.9952372312545776,
-0.13976964354515076,
0.16602148115634918,
0.17775167524814606,
-0.1030987799167633,
-1.0591504573822021,
0.2702072560787201,
0.004904620815068483,
-0.010362365283071995,
-0.3759407699108124,
-0.5695148706436157,
0.5732038021087646,
-0.27693867683410645,
0.08726935088634491,
-0.23494011163711548,
0.6048824191093445,
1.2258350849151611,
0.19755928218364716,
0.35470741987228394,
-0.800137996673584,
0.18224428594112396,
1.1336203813552856,
-0.6571767330169678,
0.8136518597602844,
0.3200591802597046,
-0.5736719369888306,
-0.6619623303413391,
-0.8008735179901123,
0.21109195053577423,
0.1788417547941208,
-0.4342402219772339,
1.00137460231781,
-0.601198136806488,
0.306369423866272,
-0.6487824320793152,
-0.6852126121520996,
-0.5378215909004211,
-0.06394407898187637,
-0.1754545420408249,
0.29044029116630554,
-0.2345864325761795,
-0.33223021030426025,
-0.31302207708358765,
0.5216054320335388,
0.3817462921142578,
0.8428075909614563,
-0.14149625599384308,
1.331109881401062,
0.4295738637447357,
-0.6493878960609436,
-0.5791831016540527,
0.41041460633277893,
-0.08997049182653427,
0.5100844502449036,
0.3997695744037628,
0.10131988674402237,
-0.06529740989208221,
0.5642901062965393,
-0.3547270596027374,
0.5458833575248718,
-0.25572073459625244,
-0.3748798072338104,
0.4744988679885864,
0.03661659359931946,
-0.7341867685317993,
-0.5454435348510742,
-0.2305654138326645,
-0.033162929117679596,
-0.09557180106639862,
1.4582048654556274,
0.1250256597995758,
0.7722612619400024,
-0.01129632443189621,
0.39925670623779297,
-0.16538746654987335,
-0.10728595405817032,
-0.21296757459640503,
0.41774997115135193,
0.2488328218460083,
0.3443700969219208,
0.3444455564022064,
-0.06806051731109619,
0.30567577481269836,
0.6578950881958008,
-0.5134577751159668,
-0.06625606119632721,
-0.21384164690971375,
-0.04674128070473671,
-0.42107969522476196,
0.5158026814460754,
-0.021793583407998085,
0.47400903701782227,
-0.22001142799854279,
0.8465450406074524,
0.007835007272660732,
-0.019870098680257797,
-0.029832901433110237,
-0.0318753719329834,
0.04184412583708763,
1.0050456523895264,
-0.2527792751789093,
0.3151671886444092,
0.8087275624275208,
-0.7063883543014526,
0.03250350058078766,
0.47781819105148315,
-0.7168241739273071,
0.07900635898113251,
-0.5152456164360046,
0.3108927011489868,
-0.39768683910369873,
-0.01417839340865612,
-1.192257285118103,
0.7647981643676758,
-0.3356667757034302,
-1.0327656269073486,
-0.5647966265678406,
-0.37440192699432373,
-0.4329221248626709,
0.3862805664539337,
-0.3059299886226654,
-0.11827294528484344,
-0.03566878288984299,
0.12038583308458328,
-0.43138352036476135,
-0.16703914105892181,
0.20912200212478638,
0.6459746360778809,
-0.1481950581073761,
0.4273253083229065,
0.16758736968040466,
-0.36007365584373474,
1.0254700183868408,
0.12904679775238037,
0.46386995911598206,
-0.06014521047472954,
-0.5273948907852173,
-0.2725614309310913,
1.0702470541000366,
0.39055711030960083,
-0.11955564469099045,
-0.05387202650308609,
-0.8997575044631958,
0.29065215587615967,
0.5727519989013672,
0.5327273607254028,
-0.284901887178421,
0.71356600522995,
-1.0171700716018677,
-0.006428743712604046,
-0.46678462624549866,
-0.6436263918876648,
-0.104141004383564,
0.5464074611663818,
-0.8143519759178162,
-0.5156710743904114,
-0.6525015234947205,
-0.3847278952598572,
-1.4821735620498657,
0.046588700264692307,
-1.5927287340164185,
0.20197786390781403,
0.46925732493400574,
-0.05609823763370514,
-0.5571596026420593,
0.017429912462830544,
0.08825220912694931,
-0.2233099788427353,
-0.34723466634750366,
-0.3326110541820526,
-0.14966121315956116,
-0.7804226279258728,
-0.5560190081596375,
0.17842192947864532,
0.6276111006736755,
-0.3955928683280945,
1.0136268138885498,
-0.33799248933792114,
0.3358904719352722,
0.5881431698799133,
0.37342023849487305,
-0.05215435102581978,
0.3967434763908386,
0.5281294584274292,
0.2927936911582947,
0.4159739017486572,
0.279463529586792,
0.9922245740890503,
0.015623165294528008,
0.3294489085674286,
1.0800477266311646,
0.7060487270355225,
0.7832339406013489,
0.934717059135437,
0.605701744556427,
0.010091613978147507,
0.5393354892730713,
0.7267991304397583,
0.36645200848579407,
0.6232380270957947,
-0.30643728375434875,
-0.14426225423812866,
-0.5587559342384338,
-0.40914788842201233,
-1.0040889978408813,
-0.17980921268463135,
-0.8714321255683899,
0.6207027435302734,
0.9122103452682495,
0.18521834909915924,
-0.09525437653064728,
0.06790589541196823,
0.14258305728435516,
0.2685084342956543,
-0.9052814245223999,
-0.06483767181634903,
0.00798934604972601,
0.060083772987127304,
-0.43002110719680786,
-0.254413366317749,
0.21993118524551392,
1.1136513948440552,
0.04454343393445015,
0.6256278157234192,
-0.39138954877853394,
-0.6221205592155457,
-0.7014085650444031,
-0.44156768918037415,
-0.40915897488594055,
-0.10761760175228119,
-0.6482023000717163,
-0.18863551318645477,
0.3810734152793884,
-0.4394337832927704,
0.8095744848251343,
0.6551651954650879,
-0.2872132658958435,
-0.1310700923204422,
-0.045383475720882416,
0.8567792177200317,
0.01643989235162735,
-0.10435464233160019,
-0.45344769954681396,
0.26275283098220825,
-0.7190225720405579,
0.12009297311306,
-0.33206355571746826,
0.0052040088921785355,
-0.35660648345947266,
-0.14020147919654846,
-0.45586973428726196,
0.03289178013801575,
-0.6593238711357117,
-0.534802258014679,
-0.7658735513687134,
-0.10607556998729706,
-0.43985065817832947,
0.36894580721855164,
-0.5409159660339355,
-0.21195372939109802,
-0.8557908535003662,
1.4792535305023193,
0.5312370657920837,
-0.09985512495040894,
0.3368228077888489,
0.714614987373352,
-0.1518925428390503,
0.7666091322898865,
-0.455622136592865,
0.08373868465423584,
-0.11793850362300873,
1.1262515783309937,
0.9430322051048279,
0.7749613523483276,
0.15384885668754578,
-0.6747389435768127,
-1.1425690650939941,
0.27875369787216187,
0.5312978625297546,
-1.1667988300323486,
-0.29779961705207825,
1.26621413230896,
0.31795886158943176,
-0.5398749709129333,
0.5936958193778992,
-0.4210396111011505,
-0.7384495139122009,
-0.20104368031024933,
-0.42406129837036133,
0.19767864048480988,
0.48903799057006836,
0.09795325249433517,
-0.04180262237787247,
0.30606329441070557,
-0.14710696041584015,
-0.05979407951235771,
0.022605441510677338,
-0.18745507299900055,
0.2881838083267212,
0.29686006903648376,
-0.0718323290348053,
0.5369616150856018,
0.2719570994377136,
-0.422902375459671,
0.10308054834604263,
0.4912160038948059,
-1.0111172199249268,
-0.1104493960738182,
0.465524822473526,
0.45146748423576355,
0.16438168287277222,
-0.06034901365637779,
-0.37894701957702637,
-0.523293673992157,
-0.9243334531784058,
-0.06528252363204956,
0.6256873607635498,
0.605260968208313,
-0.16768422722816467,
-0.0738450363278389,
-0.4816366732120514,
-0.446089506149292,
0.521675169467926,
-0.31044676899909973,
0.5649256706237793,
-0.41981783509254456,
0.2837527394294739,
0.5186770558357239,
-0.5967872142791748,
-0.2881828248500824,
-0.15856227278709412,
-0.12723974883556366,
0.2547563314437866,
0.7630009651184082,
0.503261148929596,
-0.9162430167198181,
-1.1989306211471558,
-0.33984214067459106,
0.8250752091407776,
0.9462645649909973,
0.4983893036842346,
0.18921807408332825,
-0.6860774755477905,
-0.6201825141906738,
-0.8213468194007874,
-0.45856279134750366,
-0.20951926708221436,
-0.40913233160972595,
-0.18218085169792175,
-0.7948398590087891,
-0.2663241922855377,
-0.30372586846351624,
1.1438040733337402,
0.5454685688018799,
-0.6020994782447815,
0.38760676980018616,
0.4327598810195923,
0.40420717000961304,
0.18087579309940338,
0.8131791949272156,
0.5411460995674133,
-0.2680817246437073,
-0.367888867855072,
0.15898452699184418,
-0.0369807630777359,
0.01614627055823803,
-0.20528237521648407,
-0.14437653124332428,
-0.5184682011604309,
-0.4027451276779175,
0.655151903629303,
0.46101945638656616,
-0.14064790308475494,
0.42447996139526367,
-0.05778895318508148,
-0.14753872156143188,
-0.35049787163734436,
-0.5613616704940796,
-0.25603535771369934,
0.7428138852119446,
0.42753058671951294,
-0.37523868680000305,
0.36287617683410645,
-0.6733950972557068,
1.0202679634094238,
0.3318996727466583,
-0.04175839573144913,
-0.6621578931808472,
-0.1178678423166275,
0.07245360314846039,
-1.2645307779312134,
0.40148594975471497,
0.7519673705101013,
-0.5248157382011414,
-0.02660784125328064,
-0.05498907342553139,
-0.5107724070549011,
-0.3364611268043518,
-0.5213338732719421,
-0.7475176453590393,
0.03140443190932274,
0.29394930601119995,
-0.37121936678886414,
0.8666481375694275,
0.4752998352050781,
0.23654814064502716,
-0.2982160747051239,
-0.8594003915786743,
0.5754372477531433,
-1.040315866470337,
-0.45731258392333984,
0.3399851322174072,
-0.10684706270694733,
-0.6032284498214722,
0.5026500821113586,
0.08039102703332901,
0.5862232446670532,
-0.3402223587036133,
-0.04856358841061592,
-0.7618172764778137,
0.3420790433883667,
0.4251823425292969,
-0.05893651023507118,
0.1081807091832161,
0.7653703689575195,
0.27988067269325256,
0.5270108580589294,
-0.5081004500389099,
0.7857824563980103,
-0.03842047601938248,
0.19620855152606964,
-0.18620096147060394,
0.1165640726685524,
-0.4164196848869324,
-0.26255151629447937,
-0.6132999062538147,
-0.944616973400116,
-0.01973220519721508,
-0.19799305498600006,
0.6644935011863708,
0.08354457467794418,
-0.35822463035583496,
-0.955228328704834,
0.16405485570430756,
-0.6376919150352478,
0.4847075939178467,
0.03205370157957077,
-0.10110796242952347,
0.28092119097709656,
-0.6498064398765564,
-0.7169814705848694,
0.12052726000547409,
-0.28290456533432007,
0.0229861568659544,
-0.01161019504070282,
0.569305956363678,
-0.29341956973075867,
0.08980610966682434,
-1.1946055889129639,
0.8963332176208496,
0.043626874685287476,
-0.2871128022670746,
-0.4741325080394745,
-0.6221913695335388,
-0.011445937678217888,
0.006256990600377321,
-0.13323931396007538,
-0.6096121668815613,
-0.3060036599636078,
0.3740845322608948,
0.44708627462387085,
-0.5704290866851807,
0.20663030445575714,
-0.06865103542804718,
-0.30348992347717285,
1.0629292726516724,
-0.1432587206363678,
-1.1674102544784546,
-1.0824196338653564,
0.4478702247142792,
-0.19498927891254425,
0.11779280006885529,
0.377860426902771,
-0.5222730040550232,
0.2345283031463623,
-0.45327791571617126,
-0.31193506717681885,
-0.5481578707695007,
-0.09107538312673569,
-0.4195977747440338,
0.36941319704055786,
0.23684130609035492,
0.3828981816768646,
0.11897830665111542,
0.015976091846823692,
-0.3935244381427765,
-0.5627431869506836,
0.39226898550987244,
-0.37048739194869995,
0.31450074911117554,
-0.037827592343091965,
-0.19249862432479858,
-1.0601168870925903,
0.6343457698822021,
-0.47669488191604614,
-0.47523969411849976,
0.4835447371006012,
0.09969248622655869,
0.36441728472709656,
1.004015326499939,
0.015381467528641224,
-0.342866986989975,
-0.13342279195785522,
0.18304795026779175,
-0.15996064245700836,
0.014672411605715752,
-0.30904608964920044,
0.22575320303440094,
-0.8060340881347656,
1.1348358392715454,
0.5546947717666626,
0.07474864274263382,
0.4886549711227417,
-1.163975715637207,
0.8898182511329651,
-0.6659398674964905,
-0.4030213952064514,
0.3891138434410095,
0.16011108458042145,
0.7857049107551575,
-0.11039280891418457,
-0.7089619040489197,
-0.05539580062031746,
-0.9170392155647278,
-1.0660247802734375,
0.6420066952705383,
-0.11088959872722626,
-0.694352388381958,
-0.5649032592773438,
-0.197854146361351,
0.21712784469127655,
-0.22939635813236237,
-0.04151877015829086,
0.6868775486946106,
-0.45700231194496155,
-0.6817095279693604,
0.1454886645078659,
0.5556058287620544,
-0.34023532271385193,
-0.2283271849155426,
0.5572108626365662,
0.5066342353820801,
-0.576945424079895,
0.11500765383243561,
-0.32443341612815857,
-0.9530175924301147,
-0.40633243322372437,
0.8502781987190247,
0.1777854859828949,
0.47016969323158264,
0.6563677787780762,
-0.790536105632782,
-0.14269261062145233,
-0.2840220630168915,
0.3596716523170471,
0.24454937875270844,
0.11775868386030197,
0.38882845640182495,
-0.31959134340286255,
0.4205520749092102,
-0.8563631772994995,
-0.40226536989212036,
-1.0102620124816895,
0.40015676617622375,
1.069542407989502,
-0.007153239566832781,
-0.0854286253452301,
-0.011451467871665955,
-0.03994813933968544,
-0.5296320915222168,
-0.9464437961578369,
-0.6078248620033264,
0.0706232562661171,
0.17351457476615906,
-0.6992988586425781,
0.3962251543998718,
0.002823757939040661,
-0.3531562387943268,
0.6666934490203857,
0.680579662322998,
-0.49054452776908875,
0.5990338325500488,
0.18831686675548553,
-0.5982657670974731,
-0.8167195320129395,
-0.3828313648700714,
0.942568302154541,
-0.2491348832845688,
0.05206422135233879,
-0.738106369972229,
-0.7439519166946411,
-0.0804724246263504,
0.13508209586143494,
0.7336921691894531,
0.12378004193305969,
0.08199556171894073,
0.44594210386276245,
0.5649343132972717,
0.33898451924324036,
0.8705419301986694,
0.6643090844154358,
-0.142693430185318,
0.0157115887850523,
-0.5904411673545837,
-0.06677551567554474,
0.28177136182785034,
0.43305620551109314,
0.5900055170059204,
-0.46775078773498535,
0.10913649946451187,
-0.06540067493915558,
0.24337409436702728,
-0.35647374391555786,
-0.7820640802383423,
-0.5129470229148865,
-1.2918415069580078,
-0.37795212864875793,
-0.8455992341041565,
-0.6404411792755127,
-0.026538701727986336,
0.2572203576564789,
0.010775375179946423,
0.25750747323036194,
-1.0347014665603638,
-0.28899216651916504,
-0.01659836433827877,
0.17148029804229736,
-0.3017396926879883,
-0.624447762966156,
-0.6526244878768921,
-0.26194265484809875,
-0.17200487852096558,
-0.28903427720069885,
-0.04692823439836502,
0.3810447156429291,
0.2087177038192749,
-0.05818089097738266,
-1.1254383325576782,
0.8922568559646606,
-0.923712968826294,
0.4996701776981354,
0.8277037143707275,
-0.3650834560394287,
-0.05593260005116463,
0.47021347284317017,
-0.11690119653940201,
0.3865795433521271,
0.8686314225196838,
-0.02522961236536503,
-0.1376037448644638,
0.19246649742126465,
-0.7323986291885376,
-0.3739492893218994,
-0.39641273021698,
0.41946980357170105,
-0.2956143021583557,
-0.637811541557312,
0.2516496181488037,
0.1778140515089035,
-0.9023814797401428,
-0.41249001026153564,
-0.055523958057165146,
0.5967020392417908,
-0.5889703035354614,
0.30691322684288025,
-0.4820577800273895,
0.9683314561843872,
-0.4394347369670868,
0.24611219763755798,
-0.4755164086818695,
-0.3241272568702698,
-0.09522310644388199,
-0.3792351484298706,
-0.18613596260547638,
0.1175617054104805,
0.8708556294441223,
-1.0715571641921997,
-0.258741557598114,
0.7465502619743347,
-1.2508903741836548,
0.03430371731519699,
-0.2738218307495117,
0.189620703458786,
0.1855471134185791,
-0.6603713035583496,
-0.5624973773956299,
0.5697870850563049,
-0.08380816131830215,
-1.0312864780426025,
-0.04415969178080559,
-0.08397015929222107,
0.03251601755619049,
-0.3680095076560974,
-0.8669823408126831,
-0.11193549633026123,
-0.366569459438324,
0.13187235593795776,
-0.4294164180755615,
-0.50435471534729,
-0.27270403504371643,
0.06624045222997665,
0.05517090857028961,
0.18218569457530975,
-0.5886399745941162,
0.02026418037712574,
-0.05035233125090599,
0.7353612780570984,
-0.7279707193374634,
-0.14062219858169556,
0.1965273916721344,
0.4290233850479126,
-0.22762998938560486,
-0.6273273229598999,
-0.1773247867822647,
-0.20977361500263214,
0.10930216312408447,
-0.29888486862182617,
0.13130125403404236,
1.2053635120391846,
-0.049459878355264664,
0.3874068856239319,
-0.822220504283905,
0.1582493931055069,
0.20081932842731476,
0.9184255003929138,
-0.1744932234287262,
-0.5803161859512329,
0.011048375628888607,
0.8322935104370117,
0.40358471870422363,
-0.2594429850578308,
-0.7344439029693604,
0.2700917720794678,
0.5430908203125,
-0.6836826801300049,
0.8011372685432434,
-0.23795107007026672,
1.070204496383667,
-0.07229790836572647,
0.1782766431570053,
-0.26301735639572144,
0.10298731923103333,
0.22726285457611084,
0.05987054854631424,
0.6732375621795654,
0.8987913131713867,
0.4075770974159241,
0.4054063856601715,
-0.4778849184513092,
0.6095181107521057,
0.4487093985080719,
-0.25924813747406006,
0.018596425652503967,
0.33118388056755066,
0.8033217191696167,
-0.1992630660533905,
0.45151451230049133,
-0.04381861165165901,
-0.10618467628955841,
0.20637352764606476,
0.39133742451667786,
0.20155730843544006,
0.1832074373960495,
-0.5023215413093567,
-0.29322099685668945,
-0.4572642743587494,
0.3129200041294098,
0.4023430645465851,
0.30676308274269104,
-1.1332510709762573,
0.8011589050292969,
0.7955102324485779,
0.7183818817138672,
0.04253443330526352,
0.3109181225299835,
0.4408215582370758,
-0.04634590446949005,
-0.40038958191871643,
0.7918264269828796,
0.7115759253501892,
0.3793565630912781,
0.5516203045845032,
-0.5063815712928772,
-0.2525739073753357,
0.8049086332321167,
-2.053854465484619,
-0.24370819330215454,
-0.27563050389289856,
-0.17860494554042816,
0.10330156981945038,
-0.891954243183136,
0.17105688154697418,
-0.4416968524456024,
0.3645458519458771,
0.5160220265388489,
0.07929452508687973,
0.02019520476460457,
0.5435650944709778,
0.4487335681915283,
0.925320029258728,
0.7131601572036743,
0.1136929839849472,
-0.7506961822509766,
1.288981318473816,
0.6640788316726685,
-0.006711984984576702,
-0.048677247017621994,
0.7720623016357422,
-0.326076865196228,
-0.8045876622200012,
0.26317697763442993,
-0.29427218437194824,
0.7882382869720459,
-0.7133625745773315,
-0.2502650022506714,
0.12300068885087967,
0.18384462594985962,
-1.2144767045974731,
0.03679538145661354,
0.45766228437423706,
0.7409011721611023,
-0.15172989666461945,
-0.24014191329479218,
0.9506908059120178,
0.030106859281659126,
0.10647530853748322,
0.22039732336997986,
0.23696830868721008,
0.30262959003448486,
-0.3567940890789032,
-0.8765014410018921,
0.031543660908937454,
-0.008664866909384727,
0.512058436870575,
-0.046814560890197754,
-0.5907179713249207,
-0.768445611000061,
-0.16587677597999573,
-0.4892694652080536,
-0.4643065631389618,
0.6258896589279175,
0.1638859212398529,
1.2092204093933105,
-0.03758297488093376,
-0.5506617426872253,
0.8929868936538696,
0.12941507995128632,
1.046433925628662,
0.14560404419898987,
0.5105962157249451,
0.48788735270500183,
0.08705641329288483,
-0.21683740615844727,
0.6573383808135986,
0.7901789546012878,
-0.7335045337677002,
1.051939845085144,
-0.28363004326820374,
0.7312344908714294,
-0.4996434152126312,
-0.25586429238319397,
0.6834972500801086,
0.8033338785171509,
-0.0005772330332547426,
-0.9872769713401794,
-0.4946768283843994,
-0.2558515965938568,
-0.9118706583976746,
-0.16632026433944702,
-1.0905958414077759,
0.391921728849411,
0.776250422000885,
-0.025469256564974785,
-0.021008601412177086,
-0.008656702935695648,
3.972184658050537,
1.3858343362808228,
0.6810108423233032,
0.23127365112304688,
1.1593815088272095,
0.11649694293737411,
-0.05621586740016937,
-0.8492546081542969,
0.37564072012901306,
0.10070967674255371,
0.4175635576248169,
0.17230024933815002,
0.16004343330860138,
-0.0288039930164814,
0.5172486901283264,
0.6493057608604431,
-0.5561455488204956,
0.48108306527137756,
0.26996541023254395,
-1.0323307514190674,
-0.6584978103637695,
0.22370730340480804,
-0.21410991251468658,
-0.12845957279205322,
0.09098208695650101,
0.23401640355587006,
-0.2145291268825531,
-0.6682157516479492,
-0.3187898099422455,
-0.384507954120636,
-0.005621838383376598,
-0.3512008786201477,
0.15499839186668396,
0.27399662137031555,
-0.5236595869064331,
0.1972455382347107,
0.6211386322975159,
-0.26602083444595337,
0.06152338534593582,
0.7125177979469299,
-0.03395621106028557,
-0.2326604425907135,
-0.12292631715536118,
-0.02002093382179737,
-1.0772520303726196,
0.33696967363357544,
-0.3710501194000244,
0.7720763087272644,
0.029967783018946648,
-0.1371246576309204,
0.5659365057945251,
-0.4295952618122101,
-0.0313442163169384,
-0.6284757256507874,
-1.2741985321044922,
-0.13808414340019226,
0.16712158918380737,
-0.4426979422569275,
0.6112452149391174,
0.18367764353752136,
0.7371269464492798,
0.5059730410575867,
-0.20796197652816772,
0.09536400437355042,
-0.37147489190101624,
-0.2505992650985718,
0.49148571491241455,
0.4666465222835541,
-0.23369663953781128,
0.1864905208349228,
-0.4539848566055298,
-0.6087571978569031,
-0.4656601846218109,
-0.1527036875486374,
0.3923299312591553,
0.017838643863797188,
-0.8040960431098938,
0.35322439670562744,
0.09987539798021317,
0.23211613297462463,
0.16008339822292328,
-0.6375579237937927,
-0.22925473749637604,
-0.06391391903162003,
0.4043474495410919,
0.9129051566123962,
-0.18249443173408508,
0.4566360414028168,
0.17145900428295135,
0.8987213373184204,
0.5008856058120728,
0.6309078335762024,
-0.40792927145957947,
-0.32576605677604675,
-0.6280580163002014
] |
Non-Exponential Relaxation Time Scales in Disordered Systems: an Application to Protein Dynamics
|
We study the dynamics of an heteropolymeric chain relaxing toward a new equilibrium configuration after the action of an external perturbation. We compare the results from Monte Carlo simulations with the results of a Langevin normal mode decomposition. We discuss, for sake of comparison, the case of an ordered homopolymeric chain.
|
G. Iori, E. Marinari and G. Parisi
|
hep-lat cond-mat q-bio.QM
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208001
|
hep-lat/9208002
|
[
-0.44251957535743713,
-0.3683549761772156,
-0.09406159818172455,
0.012986579909920692,
0.27704310417175293,
0.24492359161376953,
0.41482099890708923,
0.05236164107918739,
-0.36584123969078064,
1.589872121810913,
0.6877985000610352,
-0.020260339602828026,
0.42039188742637634,
-1.1369916200637817,
-0.2933123707771301,
0.12461282312870026,
-0.08890338987112045,
-0.26659661531448364,
-1.0020127296447754,
0.8182974457740784,
0.4748683571815491,
0.1565726399421692,
-0.6340605616569519,
-1.188297152519226,
-0.45195823907852173,
1.0371627807617188,
0.3428805470466614,
0.39735147356987,
1.3239555358886719,
0.9656369090080261,
0.5526430010795593,
-0.44776198267936707,
-0.723227322101593,
-0.3976907432079315,
-0.6294300556182861,
-0.6518838405609131,
-0.40951740741729736,
-0.366085410118103,
0.8290360569953918,
-0.4202820658683777,
0.4961806833744049,
-0.5459085702896118,
-0.2629286050796509,
-0.1673538088798523,
0.08088301867246628,
-0.001997306477278471,
-0.06933645159006119,
-0.39128488302230835,
0.06502560526132584,
-1.1958165168762207,
0.5560641288757324,
0.15226392447948456,
0.9482765793800354,
-0.7964066863059998,
0.10987195372581482,
-0.45091870427131653,
-0.014202346093952656,
0.6078782677650452,
-0.6415735483169556,
-0.475506067276001,
0.04334218427538872,
0.49661195278167725,
0.27481546998023987,
-1.0100361108779907,
0.3233329951763153,
0.7291501760482788,
0.22948449850082397,
0.854899525642395,
-0.1736559122800827,
-0.3049933612346649,
-0.7393203973770142,
0.03347781300544739,
-0.8368074893951416,
-0.6930193305015564,
-0.7735692262649536,
0.2620409429073334,
-0.2503872811794281,
-0.5227742195129395,
-1.0511322021484375,
-0.7887688875198364,
-0.5529307126998901,
-0.28084510564804077,
-0.1750817447900772,
0.4210069179534912,
-0.5153367519378662,
-0.03487369418144226,
-0.22790972888469696,
-0.5763764381408691,
0.00974486768245697,
0.4385187029838562,
0.6472373604774475,
0.9218547940254211,
0.009955426678061485,
-0.01743183843791485,
0.35822972655296326,
0.8368132710456848,
0.02732137218117714,
0.8978743553161621,
0.2575454115867615,
0.5017649531364441,
0.11153985559940338,
1.216220498085022,
-0.5984541177749634,
0.5584434270858765,
-0.47452977299690247,
0.26732754707336426,
-0.39811596274375916,
0.5772245526313782,
-0.48926958441734314,
-0.7061249017715454,
0.5057419538497925,
-0.23640212416648865,
0.5273991823196411,
0.34034082293510437,
0.2788909375667572,
0.738217830657959,
-0.5440616011619568,
0.2834284007549286,
-0.8961939811706543,
-0.35816022753715515,
0.08621352910995483,
-0.021044008433818817,
0.7533729076385498,
0.6458960771560669,
-0.5243027806282043,
-0.34911438822746277,
0.38386985659599304,
0.3291216194629669,
-0.4110914468765259,
0.2293238788843155,
0.4329022467136383,
0.23517872393131256,
-0.36429113149642944,
0.3343864381313324,
-0.5432562828063965,
0.12973247468471527,
-0.9534480571746826,
0.276857852935791,
0.6365868449211121,
-0.49543309211730957,
0.27477413415908813,
-0.3359464704990387,
0.18949992954730988,
1.079529881477356,
-0.24204689264297485,
0.28757205605506897,
-0.024195265024900436,
-0.21505647897720337,
-0.23376916348934174,
0.14880788326263428,
-0.35121628642082214,
-0.04834112524986267,
-0.24583855271339417,
-0.508712112903595,
0.27636781334877014,
0.38853126764297485,
-0.7459896802902222,
0.5886986255645752,
-0.24218390882015228,
-0.2767994999885559,
0.3164641857147217,
0.1042548269033432,
-0.04573407396674156,
0.5423008799552917,
-0.4429827630519867,
0.14749878644943237,
-0.8119127154350281,
-0.6219394207000732,
-0.11408931761980057,
-0.6928321719169617,
0.21285736560821533,
0.24473939836025238,
-0.14153173565864563,
0.5949043035507202,
1.118855595588684,
0.6099065542221069,
0.5793592929840088,
-0.8808015584945679,
0.10997114330530167,
0.43756288290023804,
0.19815561175346375,
-0.7453787326812744,
0.6174898743629456,
0.6339401006698608,
-0.710264265537262,
-0.009932859800755978,
-0.37201204895973206,
-0.512108564376831,
0.20714211463928223,
-0.27670884132385254,
-0.45887619256973267,
0.4723309576511383,
0.0003351938503328711,
0.28055334091186523,
-0.8805984854698181,
0.7188934683799744,
-1.3169065713882446,
0.3819369077682495,
-0.4489802122116089,
-0.6678829193115234,
-0.28859245777130127,
0.1217016950249672,
-0.7374114394187927,
0.11094491183757782,
-1.257211685180664,
-0.27156534790992737,
0.8354671001434326,
0.1483527570962906,
-0.31109607219696045,
-0.24834014475345612,
0.22740010917186737,
-0.09506414830684662,
0.4199444651603699,
-0.5680720210075378,
0.4036348760128021,
0.5420087575912476,
-0.5887321829795837,
-0.06969651579856873,
-0.060831427574157715,
0.09843647480010986,
0.4308837652206421,
0.33101794123649597,
-0.17781367897987366,
0.91034334897995,
-0.3823619484901428,
-0.6918577551841736,
-0.08121302723884583,
0.37205854058265686,
0.29883304238319397,
0.02501211129128933,
-0.19890528917312622,
0.2516367435455322,
-0.1390622854232788,
0.43974435329437256,
0.6140153408050537,
-0.09498743712902069,
0.07047052681446075,
0.7376911640167236,
0.6915027499198914,
0.4309445023536682,
0.07898405194282532,
-0.06528563052415848,
0.8816433548927307,
-0.2897942066192627,
-0.442839652299881,
0.2246738076210022,
-0.7945586442947388,
0.16384178400039673,
-0.935673713684082,
0.706957221031189,
-0.26402175426483154,
0.3191606104373932,
-0.00555599108338356,
0.23509377241134644,
-1.0279755592346191,
-0.35088440775871277,
-0.2174946516752243,
-0.10635082423686981,
0.20968179404735565,
-0.4564913213253021,
-0.08073530346155167,
0.4476330280303955,
-0.30040550231933594,
-0.8026108145713806,
0.017607836052775383,
1.2083606719970703,
-0.20258381962776184,
0.10962364077568054,
0.24465295672416687,
-0.38005703687667847,
-1.0333306789398193,
-0.1334618479013443,
-0.9414188861846924,
0.5683592557907104,
-0.8646696209907532,
0.11199148744344711,
0.28929343819618225,
-0.43805742263793945,
0.649962842464447,
-0.05122112110257149,
-0.5415973663330078,
0.06815281510353088,
-0.5599403977394104,
0.05197498947381973,
0.841084361076355,
-0.21384604275226593,
-0.8977835178375244,
-0.11852318048477173,
-0.8117448687553406,
-0.5108604431152344,
-0.5723070502281189,
-0.4813752770423889,
0.9603996276855469,
-0.1914025843143463,
-0.23457950353622437,
-0.11114083975553513,
0.06120501831173897,
-0.32762762904167175,
-0.060437463223934174,
-0.6989014744758606,
0.45329365134239197,
0.012443841435015202,
-0.2848769426345825,
0.5730838775634766,
-1.2367053031921387,
1.0051348209381104,
-0.11325262486934662,
0.030214229598641396,
0.7620843648910522,
0.45851412415504456,
-0.5993610620498657,
0.7295085787773132,
0.44473081827163696,
0.1711067408323288,
-0.31939461827278137,
0.76973557472229,
0.49022549390792847,
0.23895296454429626,
-0.05736350640654564,
-0.038506850600242615,
-0.16703523695468903,
-0.2823587954044342,
0.08306023478507996,
-0.5858942270278931,
-0.012514338828623295,
0.8035864233970642,
0.3508251905441284,
-0.7955199480056763,
0.010244367644190788,
-0.7687130570411682,
-0.07951591908931732,
0.19465309381484985,
0.1208455041050911,
0.5132652521133423,
-0.14808261394500732,
-0.14500679075717926,
-0.590133786201477,
0.17814069986343384,
0.6319013833999634,
0.01688726246356964,
0.5583143830299377,
-0.35705140233039856,
0.364920437335968,
0.6671913266181946,
0.5195971727371216,
-0.2939276695251465,
-0.2688978314399719,
-0.3544326424598694,
-0.8622908592224121,
0.15058542788028717,
-0.7925927042961121,
0.15506839752197266,
0.09760686755180359,
0.1359615921974182,
0.3969343304634094,
0.7364754676818848,
0.1213705837726593,
-0.3998085856437683,
-0.2661682963371277,
-0.2704545557498932,
0.6102380752563477,
0.6063846349716187,
0.49694547057151794,
-0.06364655494689941,
-0.9030025005340576,
-0.748714029788971,
-0.19194261729717255,
-0.04047178104519844,
0.6814082860946655,
-1.2647961378097534,
0.23768354952335358,
-0.052397966384887695,
-0.06877108663320541,
0.4006272852420807,
-0.3179513216018677,
0.23114013671875,
0.0959322601556778,
0.08378414064645767,
0.6893025040626526,
-0.3572482466697693,
-0.5079543590545654,
0.361426442861557,
0.44545114040374756,
0.5557156801223755,
0.6869964599609375,
0.5064348578453064,
-0.31150302290916443,
0.6302562355995178,
-0.32874736189842224,
-0.4456859230995178,
-0.46602097153663635,
-0.4678650200366974,
-0.006177281495183706,
-0.22119134664535522,
-0.039145275950431824,
-0.21422742307186127,
0.6969259977340698,
0.12981010973453522,
0.5121334791183472,
0.19611716270446777,
0.7818393707275391,
0.6503297686576843,
0.5699307322502136,
0.7832372188568115,
-0.2620970606803894,
0.31434324383735657,
-0.9363144040107727,
0.472398966550827,
0.2987286150455475,
0.06636331975460052,
-0.3750694990158081,
-0.7624289393424988,
-0.1442832052707672,
-0.3429625332355499,
0.7450646758079529,
0.10793411731719971,
-0.8244618773460388,
0.4425780177116394,
0.42264628410339355,
0.7072654962539673,
-0.1807953417301178,
-0.24366572499275208,
1.039430022239685,
0.5943617820739746,
0.21509356796741486,
-0.448334276676178,
-0.4692474901676178,
-0.514812171459198,
0.8236938714981079,
0.2085643857717514,
-0.5803493857383728,
-1.3281456232070923,
-0.8391094207763672,
0.2850158214569092,
-0.5296564102172852,
-0.3490280508995056,
0.508427619934082,
0.15450939536094666,
0.3705108165740967,
-0.6900367736816406,
-0.04667574167251587,
0.4436744153499603,
-0.1796719878911972,
-0.1303917020559311,
0.22704914212226868,
0.29777494072914124,
-0.07286052405834198,
0.6558698415756226,
-0.4253006875514984,
-0.386260449886322,
-0.2577895224094391,
-0.03830915689468384,
0.6777715086936951,
0.1816859096288681,
-0.3892441987991333,
-0.3220391273498535,
-0.5836454629898071,
-0.05194069445133209,
0.6241427659988403,
-0.27230849862098694,
-0.3524063229560852,
0.2840421795845032,
0.24251128733158112,
0.2711678147315979,
0.08723630011081696,
0.3960758149623871,
0.15275703370571136,
1.3396357297897339,
0.5982292294502258,
0.2865506112575531,
0.16779321432113647,
-0.321773886680603,
0.11462929844856262,
0.003504432737827301,
0.4650520980358124,
-0.4332282841205597,
-0.18172962963581085,
-0.27380287647247314,
0.040690597146749496,
-0.6252108812332153,
-0.8265605568885803,
0.6292001605033875,
-0.224783793091774,
0.453002393245697,
-0.07813790440559387,
-0.7154058814048767,
-0.023128561675548553,
-0.8885848522186279,
-1.164157748222351,
0.7661311030387878,
-0.22424602508544922,
-0.45349186658859253,
0.7781707048416138,
-0.15006352961063385,
0.2213556468486786,
-0.7498639225959778,
-0.20653758943080902,
-0.6323240995407104,
-0.08031631261110306,
0.5418055653572083,
0.3628908097743988,
0.47993576526641846,
-0.3256666362285614,
-0.14795425534248352,
-0.49109765887260437,
0.5652351379394531,
-0.5171347856521606,
0.49818482995033264,
-0.11576388031244278,
-0.2537969648838043,
0.3040542006492615,
-0.08380312472581863,
-0.13094443082809448,
-0.2779792547225952,
0.30933400988578796,
0.1328527182340622,
0.05042540282011032,
0.09271125495433807,
-0.1498842090368271,
0.6833202242851257,
-0.16741764545440674,
-0.6253803968429565,
-0.022559452801942825,
1.200070858001709,
-0.043385930359363556,
-0.03485306352376938,
0.6779254078865051,
-0.48216813802719116,
-0.0007069398416206241,
-0.08530455827713013,
1.1302781105041504,
-0.8447302579879761,
-0.13624326884746552,
-0.155043363571167,
-0.08829047530889511,
0.4299924075603485,
0.9488094449043274,
-0.270760178565979,
-0.027436014264822006,
-0.5477991104125977,
-0.14854587614536285,
0.741379976272583,
0.1447700411081314,
0.2987090051174164,
-0.4203438460826874,
-0.35549280047416687,
-0.9627524018287659,
0.8698802590370178,
-0.49551331996917725,
0.4338902235031128,
0.4155324697494507,
0.0658351257443428,
0.04287681356072426,
0.6708021759986877,
0.27334779500961304,
-0.0808454230427742,
-0.1995753049850464,
0.4191153049468994,
0.18065540492534637,
0.40314310789108276,
-0.6483336687088013,
0.4704638421535492,
-0.7978727221488953,
1.0022616386413574,
-0.30913156270980835,
-0.04534337297081947,
0.47538599371910095,
0.2788178026676178,
0.8844324946403503,
-0.7655591368675232,
0.3918116092681885,
0.43877530097961426,
-0.098674476146698,
0.5398950576782227,
-0.26286426186561584,
-0.9489659667015076,
-0.5390253067016602,
-0.586667001247406,
-1.0382832288742065,
0.5241705179214478,
0.19901692867279053,
-0.32748961448669434,
-0.5157251954078674,
-1.342786431312561,
0.2382017970085144,
0.011975186876952648,
0.36043012142181396,
0.7656581401824951,
0.14868856966495514,
0.21076039969921112,
0.39496690034866333,
-0.22334875166416168,
-0.6844309568405151,
0.03400262072682381,
-0.17489182949066162,
-0.3995403051376343,
-0.2906525433063507,
-0.05735502019524574,
-0.5287461876869202,
-1.3787122964859009,
0.09936083853244781,
-0.1458069384098053,
-0.43802353739738464,
-0.9464918375015259,
0.3436855971813202,
-0.08371114730834961,
-0.40605345368385315,
-0.36027103662490845,
-0.07723371684551239,
0.32074183225631714,
0.4065508544445038,
0.7170511484146118,
0.5980663895606995,
-0.4585208594799042,
0.399292528629303,
1.1389820575714111,
-0.9501937031745911,
-0.45310506224632263,
0.8892170786857605,
-0.7611023187637329,
-0.3531101942062378,
0.4549214541912079,
0.01864093914628029,
-0.29790937900543213,
-0.18364226818084717,
-0.6953943371772766,
-0.23319649696350098,
0.16609011590480804,
0.06342490017414093,
-0.14085903763771057,
-0.17061176896095276,
-0.23414450883865356,
0.25759556889533997,
0.9799765348434448,
0.38950034976005554,
0.34019744396209717,
0.5065109133720398,
-0.652665913105011,
-0.0688057541847229,
-0.2143850326538086,
1.010321855545044,
0.12541744112968445,
-0.7119737267494202,
-0.4038706421852112,
-0.19982708990573883,
-0.2556447982788086,
-0.35460221767425537,
0.9203327894210815,
-0.6430740356445312,
0.20990553498268127,
-0.13434500992298126,
0.5867646932601929,
0.7357800006866455,
0.6509884595870972,
-0.18836785852909088,
-0.06874606013298035,
0.20062413811683655,
-1.1055030822753906,
-0.23187416791915894,
-0.34899160265922546,
-0.08517365902662277,
0.2977229058742523,
-0.11182153970003128,
0.3546953797340393,
0.2762277126312256,
-0.6649275422096252,
-0.49778151512145996,
-0.8295390009880066,
-0.2885333299636841,
-1.161979079246521,
-0.512579619884491,
-0.9060018062591553,
0.23370182514190674,
-0.18630893528461456,
0.33542346954345703,
-0.06329865008592606,
-0.11140535771846771,
-0.11984020471572876,
0.2160494476556778,
0.2517903447151184,
0.8210458159446716,
-0.13694870471954346,
-0.8444541692733765,
-0.6252981424331665,
-0.36376094818115234,
-0.6587573289871216,
-0.009490378201007843,
0.15120013058185577,
-0.4145883321762085,
0.1394387036561966,
-0.10562469065189362,
0.012865760363638401,
0.4497969150543213,
-0.4282510280609131,
-0.46892011165618896,
0.6365883946418762,
0.22122253477573395,
-1.1697992086410522,
0.09698579460382462,
-0.04255710169672966,
0.2308134287595749,
0.6159213185310364,
0.6975141763687134,
-0.5735467076301575,
0.6023613810539246,
-1.058319330215454,
0.34239906072616577,
-0.10188226401805878,
0.29699981212615967,
-0.09472984075546265,
-0.34510013461112976,
0.056320976465940475,
0.04825681075453758,
-0.8875535726547241,
0.3809140622615814,
-0.6726046800613403,
-0.6490166783332825,
-0.3279212713241577,
0.06778524816036224,
0.5745534896850586,
0.26946884393692017,
-0.27852874994277954,
0.6917485594749451,
-0.3567104637622833,
0.12334426492452621,
0.22998541593551636,
0.1446855366230011,
-0.09519626200199127,
-0.23454102873802185,
0.2301509976387024,
-0.4447629749774933,
-0.5607122778892517,
0.11881686002016068,
-0.45745986700057983,
0.6169224381446838,
-0.1919906884431839,
-0.31973227858543396,
-0.30174022912979126,
0.10166139155626297,
-0.9137685298919678,
0.2305416613817215,
0.13147465884685516,
-0.1862601786851883,
0.5282716155052185,
-0.5864983797073364,
-0.9614410400390625,
-0.22956246137619019,
-0.6648199558258057,
-0.5561726689338684,
-0.25305241346359253,
-0.06487620621919632,
-0.4384377896785736,
0.22390708327293396,
-0.5351988077163696,
0.12493456900119781,
0.022217905148863792,
0.37815114855766296,
-0.06698799133300781,
-0.7106740474700928,
0.16380105912685394,
0.13017423450946808,
-0.8786035776138306,
-0.14151377975940704,
-0.546958327293396,
1.119312047958374,
-0.038619689643383026,
-0.24292300641536713,
0.26611676812171936,
0.46041738986968994,
-0.03255884721875191,
0.13294649124145508,
-0.35393187403678894,
-0.20357413589954376,
0.07553421705961227,
-0.012466119602322578,
-0.3017866909503937,
-0.5988819599151611,
-1.2495734691619873,
0.1839364767074585,
-0.30517396330833435,
-0.6146590113639832,
0.5530229806900024,
0.6309625506401062,
-0.29229649901390076,
0.00038552313344553113,
-0.26067817211151123,
1.0326430797576904,
-0.014660592190921307,
-0.20950062572956085,
0.6931420564651489,
0.6215285062789917,
0.10690552741289139,
-0.011597645469009876,
-0.15515777468681335,
0.09010922163724899,
-0.21124893426895142,
0.6359540820121765,
0.8395059704780579,
0.47461700439453125,
0.02925763465464115,
0.4468627870082855,
0.27679383754730225,
0.49266865849494934,
0.45076191425323486,
-0.390580952167511,
0.38884255290031433,
0.6488828659057617,
0.07787108421325684,
-0.11673782765865326,
0.03190605714917183,
0.020044350996613503,
-0.033740103244781494,
-0.5114648342132568,
-0.45522481203079224,
-0.1767347753047943,
0.2355552613735199,
0.11382783949375153,
-1.1465511322021484,
-0.12288004904985428,
-0.3941943347454071,
-0.03779430314898491,
0.5766321420669556,
-0.2280869036912918,
-0.3464434742927551,
0.36906301975250244,
0.7649050951004028,
0.03903241455554962,
0.06348491460084915,
0.29838263988494873,
-0.2822595536708832,
0.9251770973205566,
0.5848755240440369,
0.35599446296691895,
0.5682488679885864,
0.6894866824150085,
0.1638338416814804,
-1.0769779682159424,
0.6711390614509583,
0.6471070051193237,
-0.6717384457588196,
0.5129632353782654,
0.43331846594810486,
0.04782683402299881,
-0.0737241879105568,
-0.28155577182769775,
0.26562583446502686,
-0.6677794456481934,
-0.3401045799255371,
0.6611146926879883,
-0.0258968323469162,
-0.32733702659606934,
0.9075978994369507,
-0.3853185474872589,
0.39137139916419983,
0.5758936405181885,
0.28544482588768005,
0.140875443816185,
0.5220099091529846,
1.3069250583648682,
0.02831372804939747,
0.46885231137275696,
-0.0779050961136818,
-0.6200456023216248,
0.23627443611621857,
0.6950170397758484,
-0.5192195177078247,
0.21242952346801758,
-0.34335124492645264,
0.039071083068847656,
0.18732602894306183,
0.16850225627422333,
-0.3502790331840515,
0.019902128726243973,
0.3326561748981476,
0.3285042941570282,
-0.2801571190357208,
-0.4039706587791443,
1.3167035579681396,
0.3376288115978241,
-1.0875247716903687,
-0.7727625966072083,
0.03636739403009415,
-0.467366486787796,
-0.27073830366134644,
-0.9182143807411194,
0.29964542388916016,
-0.27770718932151794,
-0.5117767453193665,
-0.4193649888038635,
-0.48053139448165894,
-0.4959035813808441,
-0.4383447468280792,
0.7559917569160461,
-0.7328503727912903,
0.5622426271438599,
0.5502164959907532,
0.1361408531665802,
0.33115488290786743,
-0.7968157529830933,
-0.36191821098327637,
-0.31526824831962585,
1.0464348793029785,
0.31138360500335693,
0.22032612562179565,
0.88677579164505,
0.5965402126312256,
-0.7883877158164978,
0.30182766914367676,
0.6034616231918335,
-0.42611804604530334,
0.9257542490959167,
-0.31075212359428406,
-0.12436380237340927,
0.659626305103302,
0.044627558439970016,
0.39487138390541077,
-0.14832015335559845,
0.17335645854473114,
-0.39790526032447815,
-0.1941729336977005,
-0.6739616990089417,
-0.2174014300107956,
0.6560431718826294,
-0.5894419550895691,
0.1433536857366562,
0.02847900055348873,
0.13205133378505707,
0.14994999766349792,
-0.8206126689910889,
4.179812431335449,
0.5131942629814148,
0.9036753177642822,
0.22851185500621796,
0.30745983123779297,
1.1136438846588135,
-0.23158718645572662,
-0.11673981696367264,
0.2751528024673462,
-0.7448283433914185,
-0.32171866297721863,
0.13035741448402405,
-0.23379288613796234,
-0.1319187730550766,
-0.23248246312141418,
0.981931746006012,
-0.47870171070098877,
0.3634805977344513,
-0.25614258646965027,
-1.1151663064956665,
-0.6191607713699341,
-0.27597758173942566,
0.16842180490493774,
-0.22637733817100525,
0.5431503653526306,
0.3514769971370697,
-0.00542087247595191,
-1.147160530090332,
-0.6950991749763489,
-0.7834581732749939,
-0.5169982314109802,
-0.5198703408241272,
-0.020383037626743317,
0.2106092870235443,
-0.9113254547119141,
0.035627108067274094,
0.14412599802017212,
-0.6185338497161865,
0.17263367772102356,
-0.029789509251713753,
-0.12359902262687683,
-0.25410938262939453,
0.7426166534423828,
-0.5928158164024353,
-0.22094157338142395,
0.7386279106140137,
-0.062130335718393326,
0.9996994733810425,
0.6693465709686279,
-0.3889676332473755,
0.30526116490364075,
0.4264574944972992,
0.48838257789611816,
-0.45575815439224243,
-0.6484363079071045,
0.20630361139774323,
-0.41768544912338257,
-0.22767671942710876,
0.6176959276199341,
0.5250115394592285,
-0.05858222767710686,
0.18719768524169922,
-0.18681012094020844,
-0.10800308734178543,
0.2375231832265854,
0.777391791343689,
0.19124339520931244,
0.2653915286064148,
-0.2861578166484833,
-0.08084665983915329,
0.25643518567085266,
-0.7613473534584045,
-0.545968770980835,
0.2713782787322998,
0.011462568305432796,
0.592056930065155,
-0.15711484849452972,
0.6137100458145142,
0.33891594409942627,
0.24286450445652008,
-0.41385185718536377,
0.23230800032615662,
-0.013319849036633968,
0.12305095791816711,
0.28639301657676697,
0.992429256439209,
-0.5876746773719788,
-0.7105921506881714,
-0.5655340552330017,
0.2839180529117584,
0.10297638922929764,
1.1889525651931763,
0.17771010100841522,
0.27890288829803467,
-1.0616213083267212
] |
Chern-Simons term in the 4-dimensional SU(2) Higgs model
|
Using a variation of Lueschers geometric charge definition for SU(2) lattice gauge theory, we have managed to give a geometric expression for it's Chern-Simons ter. From this definition we have checked the periodic structure. we determined the Chern-Simons density for symmetric and asymmetric lattices near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature.
|
F.Karsch, M.L.Laursen, T.Neuhaus, B.Plache and U.-J.Wiese
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208002
|
hep-lat/9208003
|
[
-0.19901123642921448,
0.6097962260246277,
-0.011046215891838074,
0.4091300070285797,
0.37549087405204773,
-0.5045972466468811,
-0.15710137784481049,
-0.7166154384613037,
-0.22444035112857819,
1.2541208267211914,
0.5708147883415222,
-0.3228062093257904,
0.5681408047676086,
-1.0647114515304565,
0.05212736874818802,
-0.13932162523269653,
-0.6997390389442444,
-1.2922853231430054,
-0.8186163306236267,
-0.28999677300453186,
0.1381959319114685,
-0.8377375602722168,
-1.6582328081130981,
-0.92508465051651,
-0.19226616621017456,
0.5635340809822083,
-0.06381653249263763,
0.37291890382766724,
1.2549115419387817,
0.2600327730178833,
0.0044243899174034595,
-0.5210482478141785,
-0.008751865476369858,
-0.19797810912132263,
-0.4723995625972748,
-0.600125789642334,
0.37911078333854675,
0.06540795415639877,
0.01700785383582115,
-0.5580806136131287,
0.6882380843162537,
0.08324730396270752,
0.9023119807243347,
-1.121358036994934,
-0.8282856941223145,
0.102043017745018,
0.3223932981491089,
-0.055606335401535034,
0.07621192932128906,
-1.2982443571090698,
0.43990612030029297,
0.09179937839508057,
-0.4163666069507599,
-0.261298269033432,
-0.46620848774909973,
-0.08929407596588135,
-0.4889787435531616,
0.2878064215183258,
-0.46695268154144287,
0.4651646912097931,
0.7357010841369629,
0.13274206221103668,
0.8943303823471069,
-0.6721852421760559,
0.41470569372177124,
0.941959798336029,
-0.3151014447212219,
-0.04587394744157791,
-0.11327973008155823,
-0.23712891340255737,
-1.4587351083755493,
-0.8386883735656738,
-0.09995104372501373,
-0.19109708070755005,
-0.0665363296866417,
1.030874490737915,
0.5090895295143127,
0.27914154529571533,
-1.1037466526031494,
-1.0526607036590576,
0.05603700503706932,
-0.16786426305770874,
-0.492678165435791,
0.35041671991348267,
-0.5860114097595215,
-1.1164605617523193,
0.6784568428993225,
-0.0534086674451828,
0.013418959453701973,
-0.20314253866672516,
0.4340835511684418,
0.7663129568099976,
1.004427433013916,
-0.2375991940498352,
0.04744892567396164,
0.7090966701507568,
-0.4122515320777893,
0.8226576447486877,
0.025598440319299698,
0.5660300254821777,
-0.3524627387523651,
0.9262344241142273,
-0.4078235924243927,
0.38933613896369934,
-0.982715368270874,
-0.07223323732614517,
0.718049168586731,
-0.005588662810623646,
-0.010196015238761902,
-0.8427079916000366,
-0.05706967040896416,
0.037812598049640656,
-0.5878531336784363,
1.0033785104751587,
0.42605340480804443,
0.43555814027786255,
-0.07882039994001389,
0.22461706399917603,
-0.5250775814056396,
0.5477517247200012,
0.2504349946975708,
-0.19221900403499603,
0.3495660424232483,
0.6649457812309265,
-0.6288576722145081,
-0.9522686004638672,
0.12262377887964249,
1.097887635231018,
-0.8112511038780212,
-0.49369147419929504,
-0.2651688754558563,
-0.24874241650104523,
-1.1118037700653076,
0.6359408497810364,
0.632253110408783,
0.529403805732727,
0.4203091263771057,
0.4381004273891449,
0.5240535736083984,
-0.23819848895072937,
0.7845694422721863,
-0.6149203181266785,
0.7731236815452576,
1.3589874505996704,
-0.1643715798854828,
0.46569952368736267,
0.17678354680538177,
-0.18654683232307434,
-0.1646425724029541,
0.7143607139587402,
-1.1426466703414917,
-0.2213556468486786,
-0.2902953326702118,
0.8643184900283813,
0.31338435411453247,
-0.2172084003686905,
-0.5537535548210144,
0.568909227848053,
-0.6046558618545532,
-0.16021417081356049,
0.09665026515722275,
-0.6227335333824158,
-0.2343299239873886,
0.36863774061203003,
-0.21385392546653748,
-0.11349308490753174,
-0.058319881558418274,
0.3064582645893097,
-0.026390505954623222,
-0.8404811024665833,
0.09912145137786865,
-0.009704042226076126,
-0.3618353307247162,
0.4386378824710846,
0.2076728790998459,
1.0416738986968994,
0.49890077114105225,
-0.09903723001480103,
0.23123320937156677,
0.4492035210132599,
-0.28684455156326294,
-0.09572438895702362,
0.8462814092636108,
-0.20146404206752777,
0.6800947189331055,
0.8376355767250061,
-0.4559646546840668,
-0.2629927098751068,
0.041052352637052536,
0.546943187713623,
0.108589306473732,
0.6750995516777039,
-0.3003566265106201,
0.7133188843727112,
-0.3322558104991913,
-0.021782472729682922,
-0.43333548307418823,
-0.5631194710731506,
-0.5056913495063782,
-0.7395546436309814,
0.3130551278591156,
0.03450467064976692,
-0.7556398510932922,
-0.0353606678545475,
-1.1375977993011475,
0.15960194170475006,
-0.2918868362903595,
0.21099843084812164,
-0.579127848148346,
-0.23100468516349792,
0.5584839582443237,
-0.24712100625038147,
0.18493254482746124,
0.10335087031126022,
0.2396775186061859,
0.21951717138290405,
-0.6792461276054382,
-0.05221390724182129,
1.1001899242401123,
-0.6179428100585938,
0.8771572709083557,
0.3678206205368042,
-0.2809008061885834,
0.3602319359779358,
-0.16372673213481903,
-0.35998663306236267,
0.48247000575065613,
0.09829246997833252,
0.5951616168022156,
0.36730659008026123,
0.5015004873275757,
1.2258834838867188,
-0.6822711825370789,
0.6823758482933044,
0.9867063760757446,
0.23116227984428406,
0.5140926241874695,
0.3890145719051361,
-0.249585822224617,
0.24681603908538818,
-0.14766362309455872,
-0.2357105314731598,
0.9066141247749329,
0.3570517897605896,
-0.30002307891845703,
0.299030065536499,
0.25144389271736145,
0.16286437213420868,
-0.6786903142929077,
0.3433554470539093,
-0.7236377000808716,
1.068687915802002,
-0.508702278137207,
-0.20619308948516846,
-0.11673911660909653,
0.4175555408000946,
0.08081208914518356,
0.7385402321815491,
-0.7604430913925171,
-0.9401264786720276,
-0.014858279377222061,
-0.045682258903980255,
-0.29117369651794434,
-0.3144185245037079,
-0.4694240093231201,
1.5349414348602295,
0.22607378661632538,
0.3627053499221802,
-0.6849390864372253,
-0.3206951916217804,
-0.7313033938407898,
-0.5827772617340088,
-0.5047571063041687,
-0.7725550532341003,
-0.5059381723403931,
-0.4842575192451477,
1.2812104225158691,
-0.5423766374588013,
0.5506190061569214,
0.004565953742712736,
-0.3155086636543274,
0.42046287655830383,
0.37430045008659363,
0.6252838969230652,
0.22433263063430786,
-0.7117513418197632,
-0.4498549699783325,
0.3524986505508423,
-0.6049543619155884,
0.5507349371910095,
-0.1475115716457367,
0.29118311405181885,
0.3207818865776062,
-0.2383682280778885,
0.5755366086959839,
-0.4691591262817383,
-0.345215767621994,
-0.30849334597587585,
0.07281964272260666,
-0.793959379196167,
0.0021761967800557613,
0.20239649713039398,
-0.020152609795331955,
-0.9828364253044128,
-1.10653817653656,
1.18065345287323,
0.23945963382720947,
-0.48721247911453247,
1.0628713369369507,
0.5920725464820862,
-0.16061170399188995,
-0.011432824656367302,
-0.8894822597503662,
-0.6261719465255737,
-0.33468911051750183,
1.504385232925415,
0.8241973519325256,
0.28087183833122253,
-0.04649244248867035,
-0.40670597553253174,
-0.3500448763370514,
-0.2375209480524063,
-0.023555278778076172,
-0.7976076602935791,
-0.4240981936454773,
1.4235281944274902,
0.33663100004196167,
-0.9460576772689819,
1.0345377922058105,
-0.3183913230895996,
-0.3727780282497406,
0.1032869815826416,
-0.5194272398948669,
1.2657941579818726,
0.06727278977632523,
0.3161679804325104,
-0.3771362900733948,
0.5510827302932739,
-0.3389502465724945,
0.22437156736850739,
0.41116946935653687,
-0.7161232829093933,
0.5561162829399109,
0.5775400996208191,
-0.22763313353061676,
-0.6642693877220154,
0.7032415270805359,
-0.3020893633365631,
0.12237704545259476,
0.4439893662929535,
-1.0229872465133667,
-0.19126377999782562,
-0.010337790474295616,
0.20020219683647156,
0.8012760281562805,
0.6980453133583069,
-1.0065622329711914,
-0.1183132752776146,
-0.8557003736495972,
0.25273388624191284,
0.23467732965946198,
0.14208205044269562,
-0.14745637774467468,
0.6374212503433228,
-0.5011090636253357,
-0.37320536375045776,
0.7133235931396484,
-0.010622639209032059,
0.5072375535964966,
-0.35853925347328186,
0.5817345380783081,
0.44304952025413513,
-0.16526088118553162,
-0.033206529915332794,
-0.07186286896467209,
-0.6236306428909302,
-0.3383725583553314,
0.40229079127311707,
1.0683656930923462,
-0.12854425609111786,
-0.8154252767562866,
-0.13023774325847626,
0.9143086075782776,
0.7685456871986389,
0.39657047390937805,
0.6792361736297607,
-0.34753119945526123,
0.19767114520072937,
-0.6734408736228943,
-0.01854754239320755,
-0.10204913467168808,
-0.06788774579763412,
-0.7408861517906189,
-0.20726749300956726,
-0.38522911071777344,
-0.2714707553386688,
0.9498185515403748,
0.3987181484699249,
0.20439155399799347,
-0.2855839729309082,
0.9637628793716431,
-0.0020941738039255142,
0.342807799577713,
0.7299779057502747,
0.8135166168212891,
-0.7153435349464417,
-1.4933807849884033,
0.32168304920196533,
0.9269898533821106,
0.11248528957366943,
-0.39264845848083496,
-0.41362571716308594,
-0.34793469309806824,
-0.19048543274402618,
0.35302597284317017,
-0.16849984228610992,
-0.5240808725357056,
-0.027551740407943726,
-0.902608335018158,
0.44638511538505554,
-0.48345306515693665,
-0.09386800974607468,
-0.2962382137775421,
0.813528299331665,
-0.13599896430969238,
-0.7652583122253418,
0.24160508811473846,
-0.7595120072364807,
0.9393220543861389,
0.6036838889122009,
-0.4253580868244171,
-1.0631698369979858,
0.050512224435806274,
0.2909211218357086,
-0.8246093392372131,
0.22592882812023163,
0.5017209649085999,
-0.6811197400093079,
-0.3750559091567993,
-1.1736215353012085,
-0.5564908981323242,
-0.007938086986541748,
0.30080726742744446,
-0.8129145503044128,
0.4423912465572357,
-0.14709129929542542,
-0.5724703073501587,
0.46804723143577576,
-0.10530631989240646,
-0.5463871359825134,
0.08768265694379807,
-0.24285303056240082,
0.05508411303162575,
-0.6689673066139221,
-0.10959547758102417,
-0.02984417788684368,
-0.3011825978755951,
0.11865375190973282,
1.3274445533752441,
-0.10745123773813248,
0.2212878316640854,
0.07112839818000793,
0.2726152539253235,
-0.7838454246520996,
-0.6453025341033936,
0.5073695182800293,
0.16420020163059235,
0.3201407194137573,
0.26624828577041626,
1.2688260078430176,
-0.17619165778160095,
0.5182724595069885,
0.6086552143096924,
0.5522385835647583,
0.8984993100166321,
-0.2826167941093445,
0.3596345782279968,
-0.2576250731945038,
0.30700281262397766,
-0.7048919796943665,
-0.4425606429576874,
0.4168066382408142,
0.02227816917002201,
0.30487221479415894,
0.09129103273153305,
-0.21369674801826477,
-0.453799843788147,
-0.32384374737739563,
-0.326569139957428,
0.19964444637298584,
-0.3312484920024872,
-0.3119427561759949,
0.29356658458709717,
-0.4842289686203003,
0.11289685219526291,
0.3432946801185608,
0.37092325091362,
0.0998709574341774,
0.37879759073257446,
0.5676875710487366,
0.004618593025952578,
0.49843063950538635,
-1.168631672859192,
-0.014129727147519588,
-0.40451034903526306,
-0.10079063475131989,
-1.0014567375183105,
-0.7035532593727112,
-0.6912557482719421,
-0.01157769188284874,
-0.3919159173965454,
-1.306556224822998,
0.022044923156499863,
0.21626342833042145,
0.6235465407371521,
0.3126843273639679,
-0.4093353748321533,
-0.3051306903362274,
-0.5298306941986084,
1.0256670713424683,
0.3217550218105316,
-0.9188030362129211,
-0.2665061950683594,
0.19500741362571716,
-0.6282238960266113,
0.14738509058952332,
0.5140507817268372,
-0.7264218330383301,
0.08304945379495621,
0.003972222097218037,
0.41844525933265686,
-0.5950108766555786,
-0.0844094380736351,
0.006926589645445347,
-1.3447421789169312,
-0.3281858265399933,
0.22307486832141876,
0.4701862931251526,
-0.5262850522994995,
-0.4425944983959198,
-0.8485741019248962,
0.12975089251995087,
0.1676013320684433,
0.1998978555202484,
-0.4125421941280365,
0.12385858595371246,
-0.20802909135818481,
0.5218571424484253,
-0.01123782154172659,
-0.2557426989078522,
0.23613914847373962,
0.3162960410118103,
-0.1097942590713501,
0.9297486543655396,
-0.3048609495162964,
-0.5540132522583008,
0.5293749570846558,
1.089717984199524,
-0.1489742249250412,
0.39603155851364136,
-0.9438878893852234,
0.3133140802383423,
-0.43285974860191345,
0.717642605304718,
-0.2512647211551666,
0.3007849156856537,
0.24476321041584015,
-0.11754954606294632,
0.8799124956130981,
-0.6458283066749573,
0.2479020357131958,
0.06799213588237762,
0.4317239820957184,
0.586637020111084,
0.4904193580150604,
-0.2466685026884079,
-0.20410136878490448,
-0.9277418255805969,
-1.4524614810943604,
1.075337290763855,
-0.7432090640068054,
-0.24069441854953766,
-1.1045271158218384,
0.017981944605708122,
0.2806616723537445,
-0.19140061736106873,
0.7723446488380432,
0.46912238001823425,
0.4739546477794647,
0.1401648223400116,
0.7129653096199036,
-0.4171741008758545,
-0.4109535813331604,
-0.5971298217773438,
0.3617277443408966,
-0.3726077079772949,
-1.0338373184204102,
-0.07886386662721634,
0.09422513097524643,
-1.8019676208496094,
0.09471633285284042,
0.22309263050556183,
0.3373410105705261,
-0.059131622314453125,
0.4150088131427765,
-0.49543580412864685,
-0.1397401988506317,
-0.7974045276641846,
-0.5505776405334473,
-0.9510130882263184,
0.2966275215148926,
0.651308000087738,
0.198068767786026,
0.617825448513031,
-0.7223933339118958,
0.7130014300346375,
-0.8028605580329895,
0.09289757907390594,
0.25769418478012085,
-0.3516274094581604,
-0.205174520611763,
0.10829699039459229,
0.4929841160774231,
-0.8922450542449951,
-1.1367464065551758,
-0.31980815529823303,
0.283503919839859,
-0.12722863256931305,
-0.954390287399292,
0.15344814956188202,
-0.45383888483047485,
-0.6981473565101624,
0.10551977902650833,
0.7946916818618774,
-0.011158766224980354,
0.06426340341567993,
0.40704742074012756,
-0.38670217990875244,
-0.6440237760543823,
0.828383207321167,
0.6717901229858398,
0.4081251919269562,
-0.0997837632894516,
-0.8181123733520508,
-0.6799208521842957,
0.2070038616657257,
-0.33988454937934875,
0.3834810256958008,
-0.16636934876441956,
0.16741037368774414,
0.6491885781288147,
0.8814796209335327,
0.6044514179229736,
-0.02383265271782875,
0.4085046648979187,
-0.3906644582748413,
-0.015506036579608917,
-0.8823785185813904,
-0.9194453954696655,
-0.26698821783065796,
0.1112101674079895,
1.2097123861312866,
-0.3079405128955841,
0.6912615299224854,
0.20567724108695984,
-0.8561055660247803,
-0.345213383436203,
-1.3368033170700073,
0.5300144553184509,
-1.357683539390564,
-0.4073907136917114,
-0.34670886397361755,
-0.9306467175483704,
-0.1374524086713791,
-0.036101944744586945,
0.8511360883712769,
-0.5167736411094666,
-1.3750720024108887,
-0.11994101107120514,
0.4505856931209564,
-0.031220179051160812,
0.0025514881126582623,
-0.19244125485420227,
-1.0737088918685913,
-0.19464434683322906,
-0.191318541765213,
0.04789778217673302,
-0.3753724694252014,
0.6707866191864014,
-0.4492690861225128,
-0.05339507386088371,
-0.5198825001716614,
0.5000879764556885,
-0.6357308030128479,
-0.427247554063797,
-0.19859808683395386,
-0.20246361196041107,
-0.9166763424873352,
-0.15803609788417816,
-0.5740174651145935,
0.29684117436408997,
0.1595434546470642,
-0.06726378947496414,
-0.2025415152311325,
-0.15922683477401733,
-0.38435956835746765,
-0.5450751185417175,
-0.041258618235588074,
0.5653488039970398,
-0.5137890577316284,
-0.9267028570175171,
0.2798398435115814,
0.1856524646282196,
-0.9148080348968506,
0.3171234726905823,
0.2768636643886566,
0.43012624979019165,
-0.6547737717628479,
-0.10656584054231644,
0.5056746602058411,
0.656356692314148,
-0.19515377283096313,
0.8319417238235474,
-0.29224345088005066,
0.2293514460325241,
-0.659351646900177,
-0.25610145926475525,
-0.31821414828300476,
0.9401496648788452,
0.4632524847984314,
-0.736393928527832,
0.3240518271923065,
0.38875073194503784,
-0.6627705693244934,
0.08899268507957458,
-0.37892216444015503,
-0.033924661576747894,
-0.1773955076932907,
0.3351496160030365,
-0.11549394577741623,
1.3340373039245605,
0.3249991834163666,
-0.9969935417175293,
-0.5689772963523865,
-0.5276915431022644,
-0.7891052961349487,
-0.16303230822086334,
-1.0628340244293213,
-0.30580902099609375,
-0.38647276163101196,
-0.7966169714927673,
0.049928680062294006,
-0.016928352415561676,
0.14209653437137604,
0.06327348947525024,
0.10808546841144562,
0.14573724567890167,
-0.4414226710796356,
-0.052632369101047516,
0.10924147069454193,
0.3354448676109314,
-0.8705257773399353,
-0.6367518901824951,
-0.22893986105918884,
0.07213424891233444,
-0.5866628885269165,
-0.8113954067230225,
0.13315582275390625,
0.8052093386650085,
0.06798067688941956,
-0.13235945999622345,
-0.9802994132041931,
0.1876344233751297,
0.3328733444213867,
0.13963285088539124,
-1.0615291595458984,
0.30683737993240356,
-0.10598418116569519,
0.17659150063991547,
-0.031232956796884537,
-0.5704749822616577,
-0.16547764837741852,
0.8124727010726929,
0.35417017340660095,
0.42550644278526306,
-0.8578742146492004,
0.5025342702865601,
0.37279024720191956,
-0.8978419899940491,
1.4195181131362915,
-0.18965446949005127,
1.31414794921875,
0.32250645756721497,
0.08640949428081512,
0.27367550134658813,
0.2434411495923996,
0.7115305662155151,
0.9676496386528015,
0.8423284888267517,
0.7978349924087524,
0.03978059068322182,
0.13745994865894318,
-0.17439307272434235,
0.028518356382846832,
-0.05818405747413635,
0.1523553431034088,
0.13977280259132385,
-0.0937127098441124,
0.07071760296821594,
-0.202071413397789,
0.5588403344154358,
0.22310218214988708,
-0.025060882791876793,
-0.40658584237098694,
-0.5828793048858643,
-0.4458765387535095,
0.026033880189061165,
0.45171019434928894,
-0.4009293019771576,
-0.2571617066860199,
0.01863379403948784,
-0.04752899706363678,
0.14732210338115692,
0.13260102272033691,
0.07931054383516312,
0.713701069355011,
0.596955418586731,
0.40015873312950134,
0.36328765749931335,
0.20646944642066956,
0.2944580614566803,
0.22134040296077728,
1.0099226236343384,
0.7515553832054138,
0.4065597653388977,
0.2028646171092987,
-0.7968408465385437,
-0.286359965801239,
1.326753854751587,
-1.3082116842269897,
-0.3163031339645386,
-0.6425856947898865,
-0.5138267874717712,
-0.10612884908914566,
-1.2554469108581543,
0.5437586307525635,
-0.3471320569515228,
0.66956627368927,
1.593961477279663,
0.6970668435096741,
-0.5143676996231079,
0.6282586455345154,
-0.4540634751319885,
0.5601711273193359,
1.4713078737258911,
-0.18680383265018463,
-0.20430605113506317,
1.232412576675415,
1.3084543943405151,
0.12450234591960907,
0.32674476504325867,
-0.5870987772941589,
-0.50420081615448,
-0.008413872681558132,
-0.07796212285757065,
0.08556561172008514,
1.223140001296997,
-0.803192675113678,
-0.9021006226539612,
0.26893264055252075,
0.7419975996017456,
-0.8042780756950378,
0.08715024590492249,
0.06431544572114944,
0.4228658676147461,
-0.5737923979759216,
-0.12880831956863403,
0.915473461151123,
0.18070198595523834,
-0.13451813161373138,
-0.08121325820684433,
0.1925860494375229,
-0.05726230889558792,
0.3667397201061249,
-0.3496931195259094,
0.7616708874702454,
0.8805520534515381,
0.06509494036436081,
-0.3909299075603485,
-1.2215335369110107,
-0.9336655735969543,
-0.9180148243904114,
-0.3362072706222534,
-0.16324585676193237,
0.5096302628517151,
0.6471365690231323,
1.0090301036834717,
0.485509991645813,
-0.7918334603309631,
-0.2365303486585617,
1.0258700847625732,
1.1311616897583008,
-0.0282845888286829,
0.790691077709198,
0.5817862153053284,
0.7612894773483276,
-0.8284400105476379,
0.7659534215927124,
0.5527853965759277,
-0.6745058298110962,
0.29613053798675537,
0.12486836314201355,
-0.175312802195549,
-0.5109090209007263,
-0.282747358083725,
0.24719244241714478,
0.27953121066093445,
0.6564960479736328,
-0.9744376540184021,
0.38551053404808044,
-0.5195866227149963,
-1.2724977731704712,
-0.5703767538070679,
-1.2936028242111206,
0.16897033154964447,
0.5901539921760559,
-0.027718890458345413,
-0.5832600593566895,
0.4590519964694977,
3.5732827186584473,
0.602323591709137,
0.7388427257537842,
-0.4203821122646332,
0.8914805054664612,
1.0666673183441162,
0.2716153562068939,
-0.5879262089729309,
0.6673370003700256,
-0.6414570808410645,
0.31492921710014343,
0.2954576015472412,
0.8853875994682312,
-0.09225411713123322,
-0.29959189891815186,
0.647524356842041,
-0.3324578106403351,
0.8779174089431763,
0.6306778788566589,
-1.1221826076507568,
-0.23279260098934174,
-0.03893003985285759,
-0.30810368061065674,
-0.2558472156524658,
0.33306679129600525,
-0.3930453658103943,
-0.10637905448675156,
-0.6772259473800659,
-0.4359864294528961,
0.5247182250022888,
-0.14021867513656616,
-0.492014080286026,
0.24150805175304413,
-0.22321365773677826,
-0.06714645028114319,
1.0494211912155151,
0.31003257632255554,
-0.10079435259103775,
0.06843965500593185,
0.7556848526000977,
-0.1753312200307846,
0.020587889477610588,
0.16020260751247406,
-0.20743684470653534,
-0.6965057253837585,
1.7207362651824951,
0.38081902265548706,
1.0133306980133057,
0.8812859058380127,
-0.2537687122821808,
0.18910542130470276,
-0.23830848932266235,
0.5223531126976013,
-0.27738890051841736,
-1.077111005783081,
-0.1911938488483429,
-0.5496360659599304,
-1.2506331205368042,
-0.07027045637369156,
0.3645673096179962,
1.079357624053955,
0.007475269492715597,
0.12710456550121307,
0.6000010967254639,
-0.23024991154670715,
0.3317550718784332,
0.34721148014068604,
0.04334535822272301,
-1.2241336107254028,
0.07372447103261948,
0.5136147141456604,
-0.16355472803115845,
-0.1835409551858902,
0.19053395092487335,
0.1289774477481842,
-0.217585027217865,
-0.7299824953079224,
0.8078680634498596,
-0.11063998192548752,
0.4154508709907532,
-0.10042013972997665,
-0.8049167990684509,
-0.1946682333946228,
-0.10280438512563705,
-0.06641273945569992,
0.9508478045463562,
-0.1495858132839203,
0.10886087268590927,
-0.5471339821815491,
0.42850789427757263,
0.3721114695072174,
1.2885332107543945,
0.06080501899123192,
0.024914899840950966,
-0.5985422134399414
] |
A Parallel Cluster Labeling Method for Monte Carlo Dynamics
|
We present an algorithm for cluster dynamics to efficiently simulate large systems on MIMD parallel computers with large numbers of processors. The method divides physical space into rectangular cells which are assigned to processors and combines a serial local procedure with a nearest neighbor relaxation process. By controlling overhead and reducing inter-processor communication this method attains good performance and speed-up. The complexity and scaling properties of the algorithm are analyzed. The algorithm has been used to simulate large 2d Ising systems (up to 27808 X 27808 sites) with Swendsen-Wang dynamics. Typical updating times on the order of 82 nanosecs/site and efficiencies larger than 90% have been obtained using 256 processors on the CM-5 supercomputer.
|
Mike Flanigan and Pablo Tamayo
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208003
|
hep-lat/9208004
|
[
0.8984137177467346,
-0.32866397500038147,
-0.4395078122615814,
-0.33566153049468994,
-0.41210705041885376,
-0.4162553548812866,
-0.3998701274394989,
-0.5831734538078308,
-1.0941210985183716,
1.2718092203140259,
0.6782289147377014,
-0.14112479984760284,
0.13270018994808197,
-0.6814888119697571,
-0.5585645437240601,
0.5154637694358826,
-0.3198317289352417,
-0.3636985123157501,
-1.62297785282135,
0.9192097783088684,
0.5102325677871704,
0.02290995977818966,
-1.379173994064331,
-0.1424035280942917,
-0.14067965745925903,
0.9004912376403809,
0.30230337381362915,
-0.03277767449617386,
1.2658717632293701,
0.6893315315246582,
0.4108232855796814,
-0.7676025629043579,
-0.17346572875976562,
-0.5818774700164795,
0.05025678128004074,
-0.40993762016296387,
-0.11345192044973373,
-0.0038255928084254265,
0.9083120226860046,
-0.35604044795036316,
0.8952881097793579,
0.12347328662872314,
-0.18338745832443237,
-0.12474199384450912,
-0.9080086350440979,
-0.10149245709180832,
-0.5772157311439514,
-0.454062819480896,
0.3611198663711548,
-1.0068382024765015,
-0.1367153376340866,
0.7196980714797974,
0.7783768773078918,
-0.6211771965026855,
-0.35959210991859436,
-0.5545545816421509,
0.3746611773967743,
-0.03543580695986748,
-0.6767117977142334,
-0.6414756178855896,
0.8342686891555786,
-0.4901716709136963,
0.0731327161192894,
-1.0522314310073853,
0.6349630951881409,
0.6689492464065552,
-0.5427039265632629,
0.6523200273513794,
0.23663130402565002,
-0.49090927839279175,
0.3346390128135681,
-0.6073341369628906,
-0.7903433442115784,
0.0821608453989029,
-0.9811379909515381,
0.007742659654468298,
0.2722947895526886,
-0.6383187770843506,
-1.2655383348464966,
-0.1022922620177269,
-0.34427332878112793,
-0.3718695640563965,
-0.3292996883392334,
-0.023001305758953094,
-0.23208580911159515,
-0.4024939239025116,
0.16489827632904053,
-0.3947505056858063,
-0.17538735270500183,
0.6762555241584778,
-0.12400948256254196,
0.8612426519393921,
0.27998510003089905,
-0.13710825145244598,
0.4386548697948456,
0.5830865502357483,
-0.12411316484212875,
0.5096414685249329,
0.10756073892116547,
-0.44079408049583435,
-0.197806254029274,
0.8892564177513123,
-0.8782970309257507,
0.5405725836753845,
-0.3585609793663025,
0.1031118780374527,
0.564971923828125,
-0.5350908637046814,
-0.18565934896469116,
-0.49310725927352905,
0.5881463289260864,
0.07514355331659317,
0.12344129383563995,
0.8073301315307617,
-0.06801853328943253,
0.7701721787452698,
0.2955710291862488,
0.2750963866710663,
-0.4249458909034729,
-0.8577863574028015,
0.2460055649280548,
0.03482871502637863,
0.43492329120635986,
0.10763293504714966,
0.40232181549072266,
0.17445693910121918,
-0.010501599870622158,
0.8722217679023743,
-1.1874244213104248,
-0.07533226907253265,
-0.23031389713287354,
-0.1483009308576584,
-0.6135181188583374,
0.6731097102165222,
-0.5809592008590698,
0.20228683948516846,
-0.3477819263935089,
-0.07612788677215576,
-0.18614354729652405,
-0.25528988242149353,
1.1323260068893433,
-0.5551629662513733,
0.2634296119213104,
1.0551501512527466,
-0.18401451408863068,
0.10255823284387589,
0.13461853563785553,
0.24197140336036682,
0.02291589416563511,
0.588761568069458,
-0.34348592162132263,
-0.08314615488052368,
-0.6317646503448486,
0.2580035328865051,
0.224885955452919,
0.6377090215682983,
-0.3054976463317871,
-0.1932789832353592,
-0.8941119313240051,
-0.902974009513855,
0.5261467099189758,
-0.06468911468982697,
-0.3647247552871704,
0.06813932210206985,
-0.7208238840103149,
0.3310627341270447,
-0.6796372532844543,
-0.3137891888618469,
-0.39901262521743774,
-0.8173913955688477,
0.5099408030509949,
0.028907066211104393,
0.31616851687431335,
0.42653578519821167,
0.0907706767320633,
0.5990501046180725,
0.35489821434020996,
-0.43085718154907227,
0.3355887830257416,
0.05422281473875046,
-0.8434178829193115,
-0.5051243305206299,
0.35232028365135193,
-0.22738800942897797,
-0.2022768259048462,
-0.49501943588256836,
-0.23769690096378326,
-0.16965748369693756,
0.0805526003241539,
0.5686028003692627,
0.07087064534425735,
-0.1387695074081421,
-0.021482540294528008,
0.993708610534668,
-0.2505981922149658,
-0.29470187425613403,
-0.6536024212837219,
0.0424630343914032,
-1.2222567796707153,
-0.4265004098415375,
-0.2799072563648224,
0.09082361310720444,
-0.3952098488807678,
0.47652745246887207,
-1.4703999757766724,
0.008345858193933964,
1.1238067150115967,
-0.20934900641441345,
-0.7713921070098877,
0.005492630880326033,
0.026038814336061478,
0.039533670991659164,
0.2869035303592682,
-0.20478470623493195,
0.29383882880210876,
0.117389976978302,
0.6349115371704102,
0.6568771004676819,
0.7979495525360107,
0.7927970290184021,
-0.07549533247947693,
0.4490961730480194,
-0.018704082816839218,
0.19733981788158417,
-0.05897687375545502,
-0.6802886128425598,
-0.03213200345635414,
1.0494613647460938,
0.3860975205898285,
0.009565634652972221,
-0.2800493836402893,
0.30015453696250916,
-0.27332350611686707,
0.49784496426582336,
0.08235884457826614,
-0.03421110287308693,
0.7059066295623779,
-0.043324582278728485,
0.7716516256332397,
0.7121453881263733,
-0.20423877239227295,
-0.20178385078907013,
0.5835855603218079,
-0.4400796592235565,
0.2653757929801941,
0.47268810868263245,
-0.4489833414554596,
0.09888367354869843,
-0.33298033475875854,
0.44509726762771606,
0.3721858561038971,
0.849581241607666,
0.6852585077285767,
0.6094256639480591,
-1.0060986280441284,
-0.2839464545249939,
-0.16641895473003387,
0.4981982111930847,
-0.2343408763408661,
-0.0991160050034523,
0.32302016019821167,
0.2149590700864792,
-0.21937531232833862,
-0.6329665184020996,
-0.06520657241344452,
0.8393210768699646,
0.09292061626911163,
0.22131690382957458,
0.8785980343818665,
-0.5471320748329163,
-0.6038594841957092,
-0.03894917666912079,
-1.2074331045150757,
-0.12027381360530853,
-0.01604396663606167,
0.08070675283670425,
0.5528252124786377,
-0.5788125395774841,
0.2679021656513214,
-0.3309151828289032,
-0.3830544948577881,
0.5365819334983826,
-0.17871594429016113,
0.9329310059547424,
0.22128021717071533,
0.21142373979091644,
-0.3803878426551819,
0.4449498951435089,
-0.12685371935367584,
-0.8285093307495117,
-0.06472065299749374,
0.24828335642814636,
0.6373768448829651,
-0.5814986228942871,
0.37260037660598755,
-0.1988617479801178,
-0.3664841055870056,
0.35790202021598816,
0.20375601947307587,
-0.49843069911003113,
0.2131929248571396,
0.6181119680404663,
-0.16115893423557281,
-0.3158720135688782,
-1.0270719528198242,
0.5208791494369507,
0.023927459493279457,
-0.15455633401870728,
0.12166343629360199,
0.18790140748023987,
-0.8162164092063904,
0.7225351929664612,
-0.3213384449481964,
0.03285142779350281,
0.22085663676261902,
1.1451770067214966,
0.6811121106147766,
-0.09211039543151855,
-0.03437631204724312,
-0.854037880897522,
-0.22733458876609802,
0.10348872095346451,
-0.07456813752651215,
-0.33815211057662964,
-0.3453538715839386,
0.48303958773612976,
0.19969455897808075,
-0.2412869930267334,
0.28037747740745544,
-0.4494013488292694,
-0.5789550542831421,
-0.10306252539157867,
-0.36182132363319397,
0.49572277069091797,
-0.10883251577615738,
0.3342893719673157,
-0.9981915950775146,
0.6430200338363647,
0.2975271940231323,
0.17240998148918152,
0.29286837577819824,
-0.26374995708465576,
0.6520854830741882,
0.48240432143211365,
0.6578555107116699,
0.20631928741931915,
-0.3549157679080963,
-0.017997026443481445,
-0.938975989818573,
0.9042738080024719,
-0.8269252777099609,
0.2363101989030838,
-0.07199215888977051,
0.9719278812408447,
-0.416290819644928,
0.19548219442367554,
-0.30265718698501587,
-0.21739019453525543,
-0.5140151381492615,
-0.18693430721759796,
0.48330533504486084,
0.8174890279769897,
-0.3770066499710083,
-0.2939491271972656,
-0.9122496843338013,
-0.5545980930328369,
0.09265198558568954,
0.10587691515684128,
0.22290688753128052,
-0.43573206663131714,
0.14136508107185364,
-0.38696473836898804,
-0.46975359320640564,
-0.1855958104133606,
0.08406294882297516,
0.6420056819915771,
0.17628252506256104,
-0.0015206965617835522,
0.8676539063453674,
-0.24720200896263123,
-0.5458765625953674,
0.64368736743927,
0.758926510810852,
0.3629895746707916,
0.9613285660743713,
0.09032700210809708,
-0.051008179783821106,
-0.14832113683223724,
0.08943719416856766,
-0.5554213523864746,
-0.3845162093639374,
-0.04534542188048363,
0.011074492707848549,
-0.20315667986869812,
0.34992215037345886,
-0.4062456786632538,
0.6620496511459351,
0.3145407438278198,
0.27537408471107483,
0.1543463170528412,
0.34782925248146057,
0.11178073287010193,
0.3716863989830017,
0.7294585704803467,
0.6733077168464661,
0.7013146877288818,
-0.83389812707901,
0.1640424281358719,
-0.38956418633461,
0.5762770175933838,
-0.31254589557647705,
0.12858733534812927,
0.1372089684009552,
-0.979551374912262,
-0.13112540543079376,
0.31085312366485596,
-0.7921147346496582,
0.28791502118110657,
-0.18916428089141846,
0.4336961507797241,
0.20243799686431885,
-0.06629259139299393,
0.8142635226249695,
-0.0430041067302227,
0.030857214704155922,
-1.3540104627609253,
0.6942125558853149,
-0.6623318195343018,
0.5186929106712341,
0.39741528034210205,
-0.6442102789878845,
-0.3209409713745117,
-1.2750906944274902,
-0.2620171308517456,
-0.4122030735015869,
0.058727264404296875,
0.7614765167236328,
-0.05045287311077118,
0.49797675013542175,
-0.17167147994041443,
-0.23838889598846436,
0.12970057129859924,
-0.6657065153121948,
-0.7726865410804749,
0.7873708605766296,
-0.09198203682899475,
-0.0013952687149867415,
0.6758579611778259,
0.4965955317020416,
-0.5745748281478882,
0.2372765839099884,
-0.6542530059814453,
-0.16630585491657257,
-0.3920435607433319,
-0.722971498966217,
0.34068772196769714,
-0.3932143449783325,
-0.007245707791298628,
0.04826439917087555,
0.5725065469741821,
0.10991989821195602,
-0.23329868912696838,
-0.2917214632034302,
-0.3455442786216736,
0.052291981875896454,
-0.13624410331249237,
0.34092977643013,
1.0618640184402466,
0.5115300416946411,
0.24278093874454498,
0.7363719344139099,
0.28023087978363037,
0.16639700531959534,
-0.08338212221860886,
0.05180675908923149,
0.5924904346466064,
-0.22814831137657166,
-0.005618036724627018,
-0.15025222301483154,
-0.07199446111917496,
-0.6233673691749573,
-0.08434021472930908,
-0.002962616039440036,
0.5725516676902771,
0.06997683644294739,
-1.0710809230804443,
0.15055522322654724,
-0.15726102888584137,
-1.032649278640747,
0.6200029850006104,
-0.18498142063617706,
-0.04860023036599159,
0.6855366230010986,
-0.3237427771091461,
-0.09464649111032486,
-0.498077929019928,
-1.0787067413330078,
-0.49402958154678345,
0.5643525123596191,
0.24866683781147003,
1.0085192918777466,
0.2645093500614166,
-0.6802423596382141,
0.08016233891248703,
-0.32868310809135437,
-0.36989277601242065,
-0.46755877137184143,
-0.37666603922843933,
-0.39951181411743164,
0.10130868852138519,
-0.07552611082792282,
0.2146448940038681,
-0.07130321860313416,
0.1479896605014801,
-0.15829719603061676,
-0.6852285861968994,
0.1381809115409851,
-0.3354921340942383,
-0.18081480264663696,
0.5874651670455933,
0.6285656690597534,
-1.0461177825927734,
-0.7068271636962891,
0.25575292110443115,
-0.5702077746391296,
0.4922085106372833,
-0.2581367790699005,
-0.38428381085395813,
0.1731814295053482,
-0.25079628825187683,
0.16167181730270386,
-0.8316103219985962,
-1.0443828105926514,
-0.39176470041275024,
-1.3207889795303345,
-0.1618737429380417,
0.16968977451324463,
0.1197766438126564,
0.23201888799667358,
-0.8865225911140442,
-0.013748873956501484,
0.3353387713432312,
0.10220673680305481,
-0.15757623314857483,
-0.0553743839263916,
-0.31564489006996155,
-0.3802463710308075,
0.7111055254936218,
-0.5320315957069397,
0.07101544737815857,
0.20584125816822052,
-0.07942572981119156,
0.5360645651817322,
1.0640544891357422,
0.4139902591705322,
-0.3702230751514435,
0.35446956753730774,
0.1703624725341797,
-0.0899135172367096,
0.22994032502174377,
-0.3793286681175232,
0.7038577198982239,
-1.1650139093399048,
1.6529195308685303,
-0.3051609694957733,
-0.23294246196746826,
-0.4972066581249237,
0.4444756507873535,
0.3161092698574066,
-0.9796062707901001,
0.1382199227809906,
0.6457156538963318,
-0.0023861255031079054,
-0.3209698796272278,
0.3418337106704712,
-0.7014846205711365,
0.18795643746852875,
-0.6916272640228271,
-0.6587313413619995,
0.5211389660835266,
-0.142875075340271,
0.5060364007949829,
-0.6321238875389099,
-0.6412672996520996,
0.07776579260826111,
0.15234525501728058,
0.21602146327495575,
0.2804180085659027,
-0.06467597186565399,
0.44100603461265564,
-0.21357914805412292,
-0.048060931265354156,
-0.8380129933357239,
0.2855970859527588,
0.5540280938148499,
-0.23473188281059265,
0.1898520290851593,
-0.037766169756650925,
-0.281298965215683,
-0.9350828528404236,
0.031472254544496536,
0.7690944075584412,
0.0627293586730957,
-0.11471646279096603,
0.22639858722686768,
-0.8957135677337646,
-0.6789649128913879,
-0.25262489914894104,
0.07737923413515091,
0.6078722476959229,
0.38889989256858826,
0.17802731692790985,
-0.28925222158432007,
0.6478173136711121,
-0.0680350661277771,
0.361331582069397,
0.19012224674224854,
-0.3520027995109558,
0.34355875849723816,
-0.1640213578939438,
-0.48205336928367615,
0.9114329218864441,
-0.17130473256111145,
-0.6810795068740845,
-0.1679610013961792,
-0.3798202574253082,
-0.27089375257492065,
-0.8283745050430298,
-0.5043243169784546,
-0.44246765971183777,
-0.17174729704856873,
-0.05588628351688385,
0.6066216230392456,
0.3706911504268646,
-0.289679616689682,
-0.5543317794799805,
-0.2832559645175934,
-0.43438979983329773,
-0.39079388976097107,
-0.5880975723266602,
1.476176381111145,
-0.05017052963376045,
-0.9300071001052856,
0.5294583439826965,
0.3746378719806671,
-0.567547082901001,
-0.09717723727226257,
0.6615576148033142,
-0.27568188309669495,
0.39997896552085876,
0.4740031361579895,
-0.06320113688707352,
0.7465276718139648,
0.6052815914154053,
0.4252757728099823,
0.35718855261802673,
-0.09431961923837662,
-1.307619333267212,
-0.7343944907188416,
-0.5851410627365112,
0.19945868849754333,
0.7525360584259033,
0.06762060523033142,
-0.24267902970314026,
0.5120886564254761,
-0.36495545506477356,
-0.1724984496831894,
-0.7959303855895996,
-0.05468849465250969,
-0.9959912896156311,
-0.3315052092075348,
0.14227139949798584,
-0.6205688118934631,
0.5873185992240906,
0.8264947533607483,
-0.21134908497333527,
-0.6875283122062683,
-0.39495766162872314,
0.06100666522979736,
0.35458552837371826,
0.30833062529563904,
-0.17875176668167114,
-0.7119784951210022,
-0.04246961325407028,
-0.8731875419616699,
0.14516261219978333,
-0.2941443920135498,
0.16105854511260986,
-0.07409807294607162,
-0.11368610709905624,
0.346860408782959,
-0.43374553322792053,
0.5479056239128113,
-0.8230980634689331,
-0.9495030045509338,
0.1943974792957306,
-0.32474687695503235,
-0.16795076429843903,
0.5494768023490906,
0.005223253276199102,
1.3836854696273804,
-0.017597565427422523,
0.36114951968193054,
-0.16458407044410706,
-0.6433783769607544,
-0.7964156270027161,
0.38776499032974243,
0.33529239892959595,
0.300886869430542,
-0.25618547201156616,
-0.8093799948692322,
-0.06564927101135254,
0.18890686333179474,
-1.3931432962417603,
0.15528619289398193,
-0.7331179976463318,
-0.10618934035301208,
-0.2141191065311432,
0.7497633695602417,
0.4324115812778473,
0.8417495489120483,
0.1638007014989853,
0.6384561657905579,
-0.05535326153039932,
-0.23351766169071198,
0.1438247561454773,
0.21324849128723145,
-0.1654244065284729,
0.4966858923435211,
-0.47703203558921814,
-1.0813508033752441,
-0.2698718011379242,
0.653609037399292,
-0.38608500361442566,
0.03924793004989624,
-0.3151525557041168,
-0.3169279992580414,
-0.2482023388147354,
-0.759642481803894,
-0.4058924615383148,
0.5249438285827637,
0.8417925238609314,
-0.6964790225028992,
-0.7398802638053894,
-0.36461126804351807,
-0.6332277655601501,
0.4627629220485687,
-0.9021622538566589,
-0.5713321566581726,
0.5575031042098999,
-0.1389642059803009,
0.29369017481803894,
0.023015480488538742,
0.04712160304188728,
0.47085803747177124,
0.42572304606437683,
0.07919567823410034,
-0.02316553331911564,
-0.3498263359069824,
-0.2507278621196747,
-0.017444102093577385,
-0.574099600315094,
-0.76810222864151,
-0.5815150737762451,
0.5515323877334595,
-1.1556799411773682,
-0.8403003811836243,
-0.5790874361991882,
0.8868025541305542,
0.6347902417182922,
-0.48492592573165894,
-0.2509131133556366,
-0.20071440935134888,
0.1441052109003067,
-0.3329833149909973,
-0.6652443408966064,
-0.021008333191275597,
-0.3079351782798767,
0.8783875107765198,
-0.5880656242370605,
-0.5211688876152039,
0.061947714537382126,
-0.07172521203756332,
-0.17100492119789124,
0.06276386976242065,
-0.09696687757968903,
0.5820743441581726,
0.18496155738830566,
-0.529258668422699,
0.9517354965209961,
-0.002228665864095092,
0.4177473187446594,
0.1607530117034912,
-0.2640128433704376,
0.5452178716659546,
0.4948541224002838,
0.37021246552467346,
0.5488919019699097,
0.010395464487373829,
0.2206609845161438,
0.11682315170764923,
0.4653317332267761,
0.05975818634033203,
0.5302942395210266,
1.044025182723999,
0.451888769865036,
0.4153631925582886,
0.019367771223187447,
0.2888883948326111,
-0.043542083352804184,
0.42080429196357727,
0.12554976344108582,
-0.005943865980952978,
0.14359471201896667,
0.09807433933019638,
-0.1081005111336708,
-0.022393707185983658,
-0.49452152848243713,
-0.3712778687477112,
-0.02458982542157173,
-0.02565130405128002,
1.0180495977401733,
0.030184000730514526,
0.2976192831993103,
0.08213745057582855,
0.5909009575843811,
0.14472384750843048,
-0.21310026943683624,
0.6210083961486816,
0.019322389736771584,
1.1012382507324219,
1.0115082263946533,
0.7174842953681946,
0.4466213881969452,
0.4564506411552429,
0.2875419557094574,
-1.1274826526641846,
0.3270045816898346,
0.22240190207958221,
-0.8555768132209778,
-0.06642397493124008,
-0.6426181793212891,
0.17190130054950714,
-0.1136367991566658,
-0.6992372870445251,
0.5520851612091064,
-0.7952090501785278,
-0.19788241386413574,
0.7884312272071838,
-0.4962906241416931,
0.38609352707862854,
0.6744191646575928,
0.8770110011100769,
0.6165021061897278,
0.8501299619674683,
0.6374420523643494,
-0.0551130585372448,
0.9285290241241455,
0.7683041095733643,
0.3783546984195709,
-0.26493436098098755,
0.4516855776309967,
-0.27842649817466736,
-0.2269294112920761,
0.15931400656700134,
-0.20425185561180115,
0.6922054886817932,
-0.3100798428058624,
-0.28143560886383057,
-0.01640675775706768,
0.1085982546210289,
0.031008796766400337,
-0.2449394315481186,
0.4941898584365845,
0.23325380682945251,
-0.4846816062927246,
-0.38852575421333313,
1.231019139289856,
0.5496548414230347,
-0.5826258063316345,
-0.6257360577583313,
0.4407742917537689,
-0.3502492606639862,
-0.1478600949048996,
-0.8012927174568176,
0.2929626703262329,
-0.2935429811477661,
-0.39715638756752014,
-0.23237162828445435,
-0.3417600691318512,
-0.474724680185318,
0.010877199470996857,
-0.0010852369014173746,
-0.46551740169525146,
0.26871973276138306,
0.17588283121585846,
0.051816973835229874,
0.2665947377681732,
-0.34788456559181213,
0.1819612681865692,
-0.38913702964782715,
0.47582441568374634,
-0.4964859187602997,
0.06999627500772476,
0.26956087350845337,
1.3024077415466309,
-0.4575311541557312,
0.25524067878723145,
1.1009763479232788,
-0.4990804195404053,
0.941471517086029,
-0.030216867104172707,
0.40802401304244995,
0.7015544176101685,
0.19173166155815125,
-0.18986529111862183,
0.0029795505106449127,
0.3596598505973816,
0.09564302861690521,
-0.4549303352832794,
-0.13611392676830292,
-0.5179641246795654,
0.30405595898628235,
-0.6025593280792236,
0.4630088806152344,
-0.44120028614997864,
0.16617047786712646,
0.6802798509597778,
-0.684951901435852,
4.170149803161621,
0.8991448283195496,
0.36067095398902893,
0.2154085338115692,
0.5644147992134094,
0.9682246446609497,
-0.4739665985107422,
-0.5908368229866028,
0.08010566979646683,
-0.7021300196647644,
-0.5385220646858215,
0.34620770812034607,
-0.20227140188217163,
-0.20354977250099182,
0.19447898864746094,
1.288362979888916,
0.26311519742012024,
-0.5937232971191406,
0.6873788237571716,
-0.7198038101196289,
-0.4017028510570526,
0.23575206100940704,
0.03609463572502136,
0.19980297982692719,
0.47383713722229004,
-0.23057428002357483,
0.18837988376617432,
-0.6161320805549622,
0.21793359518051147,
-0.4505138695240021,
-0.5420500636100769,
-0.7694196105003357,
-0.010733142495155334,
-0.09886825084686279,
-1.009714126586914,
0.8463061451911926,
-0.04841001331806183,
-0.5461774468421936,
-0.35764527320861816,
-0.11799207329750061,
-0.03502429276704788,
-0.624443769454956,
-0.3008693754673004,
-0.1782565712928772,
-0.6155399084091187,
0.7479234933853149,
-0.8729577660560608,
0.7075692415237427,
0.20800548791885376,
-0.9193586707115173,
1.0953457355499268,
0.10382617264986038,
0.5403108596801758,
-0.181856170296669,
-0.7886300683021545,
0.2239617556333542,
-0.19596312940120697,
-0.17206180095672607,
0.16128966212272644,
1.0169212818145752,
0.1874372810125351,
-0.21323968470096588,
-0.31964972615242004,
0.06540141999721527,
0.0019260732224211097,
0.25771790742874146,
-0.5172756314277649,
0.5007803440093994,
-0.3961665630340576,
-0.059491295367479324,
-0.14066357910633087,
-0.3913384974002838,
-0.5315951704978943,
0.24980729818344116,
0.568969190120697,
-0.029541298747062683,
-0.3004695773124695,
0.6238229870796204,
-0.5869225859642029,
-0.043279606848955154,
0.6476694941520691,
-0.6383886337280273,
0.09372695535421371,
-0.12938004732131958,
0.19860613346099854,
0.8599525690078735,
0.04503969848155975,
-0.02105986885726452,
0.048427432775497437,
0.3119206130504608,
0.4997228682041168,
0.6589547991752625,
0.3013560175895691,
-0.8534344434738159,
-0.54840087890625
] |
A Rigourous Treatment of the Lattice Renormalization Problem of F_B
|
The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.
|
Ph.Boucaud, J-P Leroy, J. Micheli, O. P\`ene and G.C Rossi
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208004
|
hep-lat/9208005
|
[
0.5086580514907837,
-0.7080012559890747,
0.4308069348335266,
-0.09014267474412918,
-0.6594846844673157,
-0.21475693583488464,
-0.0890393853187561,
-0.2400314211845398,
-0.7417500615119934,
1.0923900604248047,
0.5997444987297058,
-0.6434473395347595,
0.5870574712753296,
-0.23136581480503082,
-0.0430787168443203,
0.4842081069946289,
0.1324245184659958,
-0.43833568692207336,
-1.0850956439971924,
0.19527332484722137,
0.03688478842377663,
-0.41408565640449524,
-1.2745803594589233,
-0.3318040668964386,
-0.565357506275177,
0.3437623083591461,
0.1966630220413208,
0.1492566168308258,
1.012135624885559,
0.2000180184841156,
0.17468585073947906,
-0.4872745871543884,
-0.35815897583961487,
-0.6789714694023132,
-0.24544896185398102,
0.27662983536720276,
0.20961841940879822,
-0.1317565143108368,
0.5817433595657349,
-0.20934683084487915,
1.0043933391571045,
-0.662339448928833,
-0.3904849588871002,
-0.15109345316886902,
-0.4164851903915405,
-0.17964091897010803,
-0.5782389640808105,
-0.18643856048583984,
0.17124414443969727,
-1.2038495540618896,
0.7514355778694153,
0.31034448742866516,
0.4287633001804352,
-0.8262029886245728,
-0.7805395126342773,
-0.42838969826698303,
0.13320006430149078,
0.11947830766439438,
-0.5279772281646729,
-0.22713270783424377,
0.3618752062320709,
0.10106292366981506,
0.6430179476737976,
-0.6010810136795044,
-0.24892619252204895,
0.6040024161338806,
-0.44934317469596863,
0.6121339201927185,
0.05200045183300972,
-0.5865768194198608,
0.3379937708377838,
0.24259981513023376,
-0.9130671620368958,
0.4270939826965332,
-0.7075275778770447,
0.3386651873588562,
0.599905252456665,
-0.5401695370674133,
-0.7000101804733276,
-0.4026012718677521,
-0.12385202199220657,
-0.6608456969261169,
-0.17640255391597748,
0.07455465197563171,
-0.28024178743362427,
0.07271673530340195,
0.08928878605365753,
-0.30098211765289307,
0.32153603434562683,
0.29865744709968567,
0.7330446243286133,
0.8709423542022705,
-0.7604483366012573,
-0.6539411544799805,
0.3775540292263031,
0.38278305530548096,
-0.15952496230602264,
0.5251736044883728,
0.17325341701507568,
0.20571103692054749,
-0.12945066392421722,
0.284716933965683,
-0.5233140587806702,
0.6381719708442688,
-0.4074959456920624,
1.0350254774093628,
-0.016192331910133362,
-0.01637737639248371,
0.1327327936887741,
-0.658561646938324,
0.11356853693723679,
-0.5928949117660522,
0.35633623600006104,
0.2757573425769806,
-0.02519221045076847,
0.5067228674888611,
-0.011751257814466953,
0.26702213287353516,
0.06714412569999695,
-0.7506996393203735,
0.29052916169166565,
-0.019149720668792725,
0.15379072725772858,
0.06530552357435226,
-0.3635413944721222,
0.031073560938239098,
-0.07370341569185257,
0.0709298700094223,
-0.869393527507782,
-0.06750839948654175,
0.10146455466747284,
-0.14163702726364136,
-0.10690917074680328,
0.08814259618520737,
-0.33203864097595215,
0.5060910582542419,
-0.11613206565380096,
0.12366169691085815,
-0.1087343692779541,
-0.4207908809185028,
0.5644465684890747,
-0.68821781873703,
0.3409835994243622,
1.1568008661270142,
-0.1580456793308258,
0.3810649812221527,
0.04553038626909256,
0.597525954246521,
-0.49350857734680176,
0.37966495752334595,
-0.730412483215332,
-0.06370706111192703,
-0.42745694518089294,
0.4761258065700531,
-0.03359903767704964,
0.41456925868988037,
0.09314362704753876,
0.28281739354133606,
-0.49050626158714294,
-0.3761516809463501,
-0.1039532870054245,
0.08385498821735382,
-0.14747779071331024,
0.13635002076625824,
-0.5351428985595703,
-0.027038445696234703,
-0.554000735282898,
-0.4910026490688324,
0.2823798358440399,
-0.8017403483390808,
-0.062176428735256195,
0.20488153398036957,
-0.42037537693977356,
0.6040303111076355,
0.6153013706207275,
0.5312327146530151,
0.6450018286705017,
-0.28260499238967896,
-0.29443126916885376,
0.45355334877967834,
-0.3240472674369812,
-0.3993464708328247,
0.5888211131095886,
0.09224800020456314,
0.02920357882976532,
-0.10553546249866486,
-0.4022654891014099,
-0.3762907087802887,
0.19979557394981384,
0.5444532036781311,
-0.5378033518791199,
0.16336791217327118,
-0.10744895040988922,
0.46131157875061035,
-0.4658493399620056,
-0.3122541308403015,
-0.7989768981933594,
0.6008643507957458,
-0.662598192691803,
-0.9937313199043274,
-0.15964558720588684,
-0.27906516194343567,
-0.8732180595397949,
-0.0899885967373848,
-1.2253267765045166,
0.04620840772986412,
0.7004992961883545,
0.4458218514919281,
-0.7483880519866943,
-0.057758063077926636,
-0.1891375631093979,
-0.043101172894239426,
0.3722447454929352,
0.03509388118982315,
0.2942376732826233,
0.10345401614904404,
0.2674572169780731,
0.3310532569885254,
0.21612121164798737,
0.2272399663925171,
0.31941109895706177,
0.042960748076438904,
0.1186257004737854,
0.6839679479598999,
-0.634975016117096,
-0.5647960901260376,
0.181895449757576,
0.19569125771522522,
0.3192105293273926,
-0.573828399181366,
0.08358364552259445,
0.6834461688995361,
-0.2029840648174286,
0.4641117453575134,
-0.18886128067970276,
0.22561490535736084,
0.7899383306503296,
-0.22036810219287872,
0.3219776451587677,
0.18576863408088684,
-0.4307970106601715,
-0.41203904151916504,
0.03542017936706543,
0.25228577852249146,
0.029896331951022148,
0.16627560555934906,
-0.6358458399772644,
0.04275752231478691,
-0.3270288407802582,
0.36221399903297424,
-0.5003477334976196,
0.4744369089603424,
-0.07252905517816544,
0.331882119178772,
-1.1695747375488281,
-0.31245157122612,
0.3552330434322357,
0.22678311169147491,
0.00013462229981087148,
-0.38167133927345276,
-0.2877926826477051,
0.5236942768096924,
-0.2939656972885132,
-0.2938825786113739,
-0.07057289034128189,
1.4904824495315552,
-0.0157431922852993,
0.7884997129440308,
0.6746082901954651,
-0.007774708792567253,
-0.8520485162734985,
0.07126231491565704,
-0.577277660369873,
-0.03009939007461071,
-0.34641963243484497,
0.1211126521229744,
0.7518681883811951,
-0.7888038158416748,
0.9740278720855713,
-0.13050396740436554,
-0.3824509382247925,
0.40896931290626526,
0.009299073368310928,
0.2429351508617401,
0.23377002775669098,
-0.07608940452337265,
-0.7345144748687744,
0.7864745855331421,
-1.0804239511489868,
-0.15988396108150482,
-0.18578583002090454,
0.28145214915275574,
0.783108651638031,
-0.2553972899913788,
0.1015540212392807,
-0.7880088090896606,
-0.29341739416122437,
0.36101946234703064,
0.157938152551651,
-0.575214684009552,
0.27449536323547363,
0.9195122122764587,
-0.09256713092327118,
-0.6136252284049988,
-0.9813389778137207,
0.7208340764045715,
0.16540858149528503,
-0.6512708067893982,
0.22563956677913666,
-0.33189326524734497,
-0.4188767671585083,
0.6834543347358704,
-0.12059716135263443,
-0.3917270600795746,
0.09599566459655762,
0.8147820830345154,
0.5408466458320618,
0.09362542629241943,
-0.09600638598203659,
-0.3204691708087921,
-0.4388660192489624,
-0.10462423413991928,
-0.1025690883398056,
-0.2842941880226135,
-0.2579788267612457,
1.0130877494812012,
-0.19965685904026031,
-0.3620925545692444,
0.4765971004962921,
-0.7329410910606384,
-0.8299468159675598,
0.49261412024497986,
-0.20261409878730774,
0.4255366027355194,
-0.5959397554397583,
-0.192278653383255,
-0.6671859622001648,
0.16740763187408447,
0.5509135127067566,
0.10287869721651077,
0.5789098143577576,
-0.660930335521698,
0.39074230194091797,
0.6918715834617615,
0.20013749599456787,
0.160775288939476,
0.001351253013126552,
-0.33842015266418457,
-0.639234721660614,
-0.2865036129951477,
-1.0140354633331299,
0.1728900521993637,
-0.41372108459472656,
0.5062990784645081,
0.6020885705947876,
0.7441833019256592,
-0.5338945388793945,
-0.7005806565284729,
-0.6214442253112793,
-0.5726500153541565,
0.16580015420913696,
1.0723059177398682,
0.07700794190168381,
-0.08318042755126953,
-0.48411938548088074,
0.09402019530534744,
0.6607251167297363,
-0.449134886264801,
-0.12466403841972351,
-0.7082073092460632,
0.4118436276912689,
-0.6316019296646118,
0.048943061381578445,
-0.16156868636608124,
0.00919481460005045,
0.3305012583732605,
0.4096856415271759,
0.6575243473052979,
1.1328675746917725,
-0.18585731089115143,
-0.6222086548805237,
-0.20167909562587738,
0.2683955729007721,
0.4161284863948822,
0.5224435925483704,
0.3490775227546692,
0.4065898358821869,
0.16819368302822113,
-0.587157130241394,
-0.49616268277168274,
-0.5227410197257996,
-0.26036667823791504,
-0.2038242369890213,
0.02183547429740429,
0.05068983882665634,
0.37709641456604004,
0.19180290400981903,
0.09798416495323181,
0.6699649691581726,
-0.007287183310836554,
0.2486983984708786,
0.1003408432006836,
0.5906140208244324,
0.5075687766075134,
0.26456087827682495,
0.3334607183933258,
-0.8886889815330505,
-0.269184410572052,
0.12399417161941528,
0.2042759507894516,
-0.5227964520454407,
-0.49313148856163025,
-0.10090374201536179,
-0.3823193609714508,
0.42559242248535156,
-0.024981973692774773,
-0.4877389669418335,
0.29547563195228577,
-0.31829631328582764,
0.8179248571395874,
-0.027525901794433594,
0.10746807605028152,
0.546617329120636,
0.4363240897655487,
0.14831988513469696,
-0.7836021184921265,
0.3129196763038635,
-0.1482439488172531,
0.3134270906448364,
0.9623372554779053,
-1.049805760383606,
-0.5518245100975037,
-1.2279812097549438,
-0.276531457901001,
-0.3211119771003723,
0.44019684195518494,
0.5461109280586243,
0.18090352416038513,
0.24225984513759613,
-0.8377310037612915,
-0.22564074397087097,
0.855512797832489,
-0.492813378572464,
-0.09123308956623077,
0.5691840648651123,
-0.1690572053194046,
-0.3288744390010834,
0.2142476737499237,
-0.08046179264783859,
-0.41780170798301697,
0.5354793071746826,
-0.6262478828430176,
0.3784840703010559,
-0.9765721559524536,
-0.19488275051116943,
-0.07551825046539307,
-0.24725569784641266,
-0.8120611310005188,
0.42793670296669006,
0.5428230166435242,
-0.03949418291449547,
-0.3266960680484772,
0.20694194734096527,
-0.1557472199201584,
0.28655877709388733,
0.6023304462432861,
-0.12385573238134384,
0.7527288198471069,
0.5610162615776062,
0.16295059025287628,
0.5464385747909546,
0.66256183385849,
-0.4255449175834656,
0.11630557477474213,
0.356363445520401,
0.3352084457874298,
-0.4376281499862671,
-0.4682725965976715,
0.06343794614076614,
-1.0079988241195679,
-0.6036095023155212,
-0.16024249792099,
-0.2726060450077057,
0.4362046718597412,
0.4861161708831787,
-0.7242956757545471,
-0.8357709646224976,
-0.13679523766040802,
-0.6471564173698425,
0.2848280370235443,
-0.28398382663726807,
-0.5423306226730347,
0.8747725486755371,
-0.12230417877435684,
0.12582138180732727,
-0.2262326180934906,
-0.1723915934562683,
-0.3811039924621582,
0.41739389300346375,
0.38297635316848755,
-0.08819450438022614,
0.2686644494533539,
-1.0930384397506714,
0.5378755927085876,
-0.26788249611854553,
-0.1286686807870865,
-0.455983430147171,
-0.45982426404953003,
-0.4293665587902069,
0.03544183447957039,
0.09424358606338501,
0.3686462342739105,
-0.20021826028823853,
0.04132629930973053,
0.0032895777840167284,
0.07783513516187668,
0.6164802312850952,
-0.5890312790870667,
-0.45240190625190735,
0.45309945940971375,
0.38459348678588867,
-0.10678675025701523,
-0.08251184225082397,
0.7391839623451233,
0.06663548946380615,
0.5910380482673645,
-0.04052645340561867,
-0.7639725208282471,
0.6557061672210693,
-0.12968096137046814,
0.5422605276107788,
-0.534500777721405,
-0.20380638539791107,
-0.1314157098531723,
-1.076814889907837,
0.18313317000865936,
0.3039955794811249,
0.5741718411445618,
-0.5929475426673889,
-0.9097504019737244,
-0.16370104253292084,
0.3461979925632477,
0.064327672123909,
0.03636401891708374,
-0.5829634070396423,
-0.052235059440135956,
-0.8164963126182556,
0.40378206968307495,
-0.4719570577144623,
0.28170424699783325,
0.284268319606781,
-0.14636211097240448,
0.24923887848854065,
0.5057250261306763,
0.14479459822177887,
-0.40692993998527527,
0.23966637253761292,
0.5110538005828857,
-0.07494606822729111,
0.6682431697845459,
-0.09623226523399353,
0.3828313946723938,
-0.8933819532394409,
0.48848196864128113,
-0.01100089866667986,
-0.30274826288223267,
0.5141931176185608,
0.3800652027130127,
0.6242207288742065,
-0.7321166396141052,
-0.0006290971650741994,
0.6091459393501282,
0.23881569504737854,
0.4146805703639984,
0.1673152595758438,
0.23291124403476715,
-0.353079229593277,
-0.5080059170722961,
-0.39641818404197693,
0.4172706604003906,
0.08415196090936661,
-0.43319129943847656,
-0.21900254487991333,
-0.4567151963710785,
-0.024422334507107735,
-0.4486907720565796,
0.6767427921295166,
0.7554026246070862,
-0.28825268149375916,
0.23623159527778625,
0.2546859085559845,
-0.24999506771564484,
-0.695637583732605,
0.5579862594604492,
0.25927233695983887,
0.20843066275119781,
0.5554260015487671,
0.21111108362674713,
-0.7588406205177307,
-0.6734306812286377,
0.10967927426099777,
0.25719931721687317,
-0.0420619398355484,
0.04208529740571976,
1.1886727809906006,
0.5548579096794128,
-0.2012108713388443,
-0.06905046850442886,
0.04487686976790428,
0.06665083765983582,
0.21657304465770721,
0.22891353070735931,
0.2830667495727539,
0.47096961736679077,
-0.03000703826546669,
0.39406850934028625,
-0.5938864946365356,
-0.20837153494358063,
1.1221492290496826,
-1.1244529485702515,
-0.34291622042655945,
0.48182618618011475,
0.10237555205821991,
-0.5979552865028381,
-0.43490031361579895,
-0.7563217878341675,
0.2063901722431183,
-0.42865118384361267,
-0.23984003067016602,
-0.601733922958374,
-0.15597166121006012,
-0.6512324213981628,
0.051198478788137436,
0.22421252727508545,
-0.18038831651210785,
-0.04940797761082649,
-0.06652837246656418,
-0.1604936569929123,
0.0560784749686718,
-0.5292716026306152,
1.6769163608551025,
0.37663453817367554,
-0.5635737776756287,
-0.10454966127872467,
0.0359831266105175,
-0.4963577389717102,
0.009995975531637669,
0.6062618494033813,
-0.10783570259809494,
-0.025598233565688133,
0.1860990673303604,
0.6512170433998108,
0.03992617130279541,
1.1694122552871704,
0.15643922984600067,
-0.048116907477378845,
0.2199571281671524,
-0.5875235795974731,
0.045662131160497665,
-0.14230264723300934,
0.47958147525787354,
0.8044779896736145,
-0.013502593152225018,
-0.23458723723888397,
-0.19573569297790527,
-0.2657802999019623,
0.06449621915817261,
-0.7890664339065552,
0.3842550218105316,
-0.842574954032898,
-0.15440095961093903,
-0.25692158937454224,
-0.6107632517814636,
0.26956474781036377,
0.7706484794616699,
-0.36333534121513367,
-0.03862952068448067,
-0.845331609249115,
0.5343401432037354,
0.038740552961826324,
0.3263190984725952,
-0.4157369136810303,
-0.4434462785720825,
-0.4542548954486847,
-0.058220863342285156,
-0.3267551362514496,
0.018629122525453568,
-0.5085868239402771,
-0.09340175986289978,
-0.2169899046421051,
0.1792363077402115,
-0.14235317707061768,
1.204052448272705,
-1.1868553161621094,
-0.5538162589073181,
-0.03657019883394241,
-0.21846333146095276,
-1.4064979553222656,
0.09844294935464859,
-0.05393164977431297,
0.3232116997241974,
0.44357380270957947,
-0.08625289052724838,
-0.7072397470474243,
0.33865031599998474,
-0.7227991819381714,
-0.07942955195903778,
0.19264879822731018,
0.9547231793403625,
-0.24992364645004272,
-0.5907961130142212,
0.03785566985607147,
0.3423302471637726,
-1.2926462888717651,
0.3382103741168976,
-0.799445390701294,
0.6847647428512573,
-0.055700115859508514,
0.20623111724853516,
-0.36685189604759216,
0.4900907278060913,
0.24431855976581573,
0.9630664587020874,
-0.002901122672483325,
-0.37001630663871765,
0.19445301592350006,
0.1366475522518158,
-0.003334050066769123,
0.0467095710337162,
0.022335393354296684,
-0.4398859143257141,
-0.2343246042728424,
0.6885195374488831,
-0.10519558191299438,
0.22887486219406128,
-0.13055703043937683,
0.36445432901382446,
-0.16726846992969513,
-0.5605812668800354,
-1.0089974403381348,
0.31338614225387573,
0.09471863508224487,
-0.6949922442436218,
-0.22286975383758545,
-0.6963297128677368,
-0.8686547875404358,
1.0807572603225708,
-0.4404134154319763,
-0.6669586300849915,
-0.15873798727989197,
-0.7717978954315186,
0.29564231634140015,
0.044518765062093735,
-0.15721485018730164,
-0.051531776785850525,
0.022663557901978493,
-0.020122606307268143,
-0.32530832290649414,
-0.2599053680896759,
-0.8946452140808105,
0.16018331050872803,
-1.1249300241470337,
-0.622864305973053,
-1.0249520540237427,
0.20405542850494385,
-0.9667543172836304,
-1.1003814935684204,
0.4028591215610504,
0.808741569519043,
0.3089011013507843,
0.05541237071156502,
-0.44491639733314514,
-0.24137356877326965,
0.34757065773010254,
0.20774529874324799,
-1.1363121271133423,
-0.3859127461910248,
-0.4187527298927307,
0.23957492411136627,
-0.07273392379283905,
-0.22824357450008392,
0.5509427785873413,
0.47993287444114685,
0.4211130738258362,
-0.06370788812637329,
-0.17825748026371002,
0.8814991116523743,
0.5262729525566101,
-0.3223237097263336,
0.5658316016197205,
0.1585257649421692,
0.24867583811283112,
0.065413698554039,
-0.9025997519493103,
0.3556084632873535,
0.7906277775764465,
0.46507909893989563,
0.7511935830116272,
0.07976441085338593,
0.3889627158641815,
-0.16514894366264343,
0.029692845419049263,
-0.013539587147533894,
-0.25799304246902466,
0.5063959360122681,
0.3816724419593811,
0.5722056031227112,
0.41441968083381653,
-0.15457114577293396,
0.3084072768688202,
0.07148975878953934,
0.1374415010213852,
0.030110139399766922,
-0.4756719172000885,
-0.4613000750541687,
-0.18481005728244781,
0.5087648630142212,
-0.15859968960285187,
-0.5520693063735962,
-0.3504025936126709,
0.23251868784427643,
0.5391925573348999,
0.0034697838127613068,
-0.07365710288286209,
0.27330026030540466,
0.821811854839325,
0.035733915865421295,
-0.47612205147743225,
0.7298171520233154,
-0.1768551915884018,
0.8140960931777954,
0.2686309218406677,
0.9854260087013245,
0.24662721157073975,
0.6777262687683105,
0.4439198076725006,
-0.4124060571193695,
0.2897031903266907,
0.49287620186805725,
-0.6262680292129517,
0.21755380928516388,
-0.5855498313903809,
-0.19562947750091553,
-0.39602017402648926,
-0.3329818844795227,
0.6522771716117859,
-0.4987277388572693,
0.11280661821365356,
0.7979608178138733,
-0.22005027532577515,
-0.3698359429836273,
0.4153173565864563,
-0.18390913307666779,
0.25948357582092285,
0.8338024616241455,
-0.053308743983507156,
0.15988050401210785,
1.2142795324325562,
1.1835882663726807,
-0.125239759683609,
0.36116570234298706,
0.026034871116280556,
0.0035063112154603004,
0.25122594833374023,
0.37610670924186707,
-0.01583240181207657,
0.8102380037307739,
-0.6592069864273071,
-0.15608638525009155,
0.22935765981674194,
0.008700699545443058,
-0.2815360128879547,
-0.15373200178146362,
0.6168714761734009,
-0.018313998356461525,
-0.7619406580924988,
-0.6141273975372314,
1.2509195804595947,
0.6678940653800964,
-0.07037791609764099,
-0.6217504143714905,
-0.0501406230032444,
0.09404267370700836,
-0.4463159441947937,
-0.3815121054649353,
0.3786478638648987,
-0.2254188358783722,
-0.08660005033016205,
-0.07087398320436478,
-0.01986769586801529,
-0.7569205164909363,
-0.7968940734863281,
0.14949189126491547,
-0.22341258823871613,
0.2196500450372696,
0.4124854505062103,
0.238810732960701,
0.04718317836523056,
-0.6058380603790283,
-0.5496066212654114,
0.26400864124298096,
1.0927796363830566,
-0.022692475467920303,
0.13054056465625763,
0.7912291884422302,
0.047357287257909775,
-0.2455718219280243,
0.38869476318359375,
0.164776012301445,
-1.1853898763656616,
0.5674054026603699,
-0.8160593509674072,
0.9369192719459534,
0.20722870528697968,
0.03904390335083008,
-0.407041996717453,
0.22965922951698303,
-0.28358209133148193,
0.14832153916358948,
0.05461859330534935,
0.012434076517820358,
-0.47190964221954346,
-0.021990273147821426,
-0.31238865852355957,
0.20341485738754272,
-0.22294485569000244,
0.12935273349285126,
0.30057185888290405,
-0.8835417032241821,
4.358043670654297,
0.6885281801223755,
0.9309036731719971,
0.5658553242683411,
0.503461480140686,
0.6915222406387329,
0.019950581714510918,
-1.1506532430648804,
-0.20154978334903717,
-0.6223635673522949,
-0.30133122205734253,
-0.1960398107767105,
0.28059613704681396,
-0.46003293991088867,
-0.10733512043952942,
1.1569126844406128,
-0.3576761782169342,
-0.4124361276626587,
0.2610664963722229,
-0.879199206829071,
-0.42183297872543335,
0.11865410208702087,
0.021648075431585312,
0.3257937729358673,
0.1420813351869583,
0.09538338333368301,
0.22557654976844788,
-0.5077670216560364,
-0.2248735874891281,
-0.14316605031490326,
-0.7213833928108215,
-0.8556634783744812,
0.3557470738887787,
-0.08817189931869507,
-0.46404945850372314,
-0.05490774288773537,
0.14491510391235352,
-0.0917859748005867,
-0.0752066969871521,
-0.09993524104356766,
-0.3006155490875244,
0.11116913706064224,
0.6020768880844116,
-0.444625586271286,
-0.7558631300926208,
1.3793165683746338,
-0.36283445358276367,
1.0017107725143433,
0.6783388257026672,
-0.4436908960342407,
1.000887393951416,
-0.31993839144706726,
0.29295074939727783,
-0.6386598348617554,
-0.8460780382156372,
0.3901674747467041,
-0.557010293006897,
-0.01695406436920166,
0.1993652582168579,
-0.017044425010681152,
0.5846154093742371,
-0.5975209474563599,
0.06537027657032013,
0.2156880646944046,
-0.10529371351003647,
0.7632933855056763,
0.7184249758720398,
0.34293562173843384,
-0.20866641402244568,
-0.07362941652536392,
-0.2633654773235321,
-0.39501646161079407,
-0.4190930128097534,
0.5552347302436829,
0.6812252998352051,
-0.34119078516960144,
-0.3736591637134552,
-0.15067581832408905,
0.6759279370307922,
0.28472253680229187,
0.4877089858055115,
-0.13423478603363037,
-0.5975750684738159,
0.22185109555721283,
0.5693354606628418,
1.1091701984405518,
-0.7080507278442383,
0.058288875967264175,
0.587566614151001,
0.261488676071167,
0.19764573872089386,
1.3622114658355713,
-0.019565844908356667,
-0.1707104742527008,
-0.8310291171073914
] |
Comparison of Lattice Coulomb Gauge Wave Functions in Quenched Approximation and with Dynamical Fermions
|
We present a comparison of Coulomb gauge wave functions from $6/{g^2}=6.0$ quenched simulations with two simulations which include the effects of dynamical fermions: simulations with two flavors of dynamical staggered quarks and valence Wilson quarks at $6/{g^2}=5.6$ and simulations with two flavors of dynamical Wilson quarks and Wilson valence quarks, at $6/{g^2}=5.3$. The spectroscopy of these systems is essentially identical. Parameterizations of the wave functions are presented which can be used as interpolating fields for spectroscopy calculations. The sizes of particles are calculated using these parameterized wave functions. The resulting sizes are small, approximately half the sizes of the physical states. The charge radius of the neutron, which provides an indication of the asymmetries between the wave functions of up and down quarks, is calculated. Although the size of the nucleon in these simulations is small, the ratio of the charge radius of the neutron to that of the proton is consistent with the physical value. We find no significant differences between the quenched and dynamical simulations.
|
M. Hecht, et al. (High Energy Monte Carlo Grand Challenge)
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208005
|
hep-lat/9208006
|
[
-0.5340456366539001,
-0.8742520809173584,
-0.06668438762426376,
-0.7665058970451355,
-0.20916026830673218,
-0.20848341286182404,
-0.31537294387817383,
-0.7554929852485657,
-0.40714558959007263,
1.2120155096054077,
0.6889760494232178,
-0.17863112688064575,
0.8134078979492188,
-0.902275025844574,
-0.009563636034727097,
0.5121414065361023,
-0.5938639044761658,
-0.7412881255149841,
-1.5994716882705688,
0.7560614943504333,
0.7363629341125488,
-0.11825274676084518,
-0.9259632229804993,
-1.0137207508087158,
-0.02708074450492859,
0.9047500491142273,
0.23019015789031982,
0.47499552369117737,
1.0671645402908325,
0.9923299551010132,
-0.048095718026161194,
-0.0557655468583107,
-0.7507860660552979,
-0.7779549956321716,
-0.5392126441001892,
-0.18077579140663147,
-0.48647788166999817,
-0.8567228317260742,
0.6265780329704285,
-0.09972706437110901,
0.6704411506652832,
-0.5572996139526367,
-0.5245887041091919,
-0.35692596435546875,
-0.509287416934967,
0.35120856761932373,
0.15278983116149902,
-0.07819143682718277,
-0.036424022167921066,
-1.0578022003173828,
0.5760064125061035,
0.502012312412262,
0.45390042662620544,
-0.5639678835868835,
-0.44773542881011963,
-0.38776272535324097,
0.5645570755004883,
-0.20455783605575562,
-0.38195550441741943,
-0.137466162443161,
0.2016964703798294,
-0.2813001573085785,
-0.034248750656843185,
-0.6125774383544922,
-0.04238261282444,
0.7383302450180054,
-0.43378013372421265,
0.45318174362182617,
0.004489630926400423,
-0.8244964480400085,
0.11950723826885223,
-0.3351622223854065,
-1.2484779357910156,
0.2051793932914734,
-0.4388677179813385,
0.04879490286111832,
-0.5336107611656189,
-0.5606399774551392,
-0.6761550307273865,
-0.4596741795539856,
-0.09155506640672684,
0.23453328013420105,
-0.12539970874786377,
0.6258772611618042,
-0.7814325094223022,
-0.010966263711452484,
-0.2951200604438782,
-0.47283342480659485,
0.5218648910522461,
0.1267743706703186,
0.23985040187835693,
0.8559183478355408,
-0.1073075607419014,
-0.36360639333724976,
0.30028036236763,
0.7090054750442505,
0.22836577892303467,
0.8636617660522461,
0.42465782165527344,
0.014612480998039246,
-0.02414322830736637,
1.444674015045166,
-0.8719833493232727,
0.5310245156288147,
-0.4975319802761078,
0.5451700687408447,
-0.8245663046836853,
-0.34320545196533203,
-0.23464617133140564,
-0.3555944263935089,
0.5788076519966125,
-0.2306898832321167,
0.5575632452964783,
0.524182140827179,
0.34184369444847107,
0.650591254234314,
-0.45700716972351074,
0.11446274071931839,
-0.5354510545730591,
-0.29516154527664185,
0.43781140446662903,
0.40800940990448,
0.5092706680297852,
0.45525169372558594,
-0.36027681827545166,
-0.14069271087646484,
0.5413302183151245,
0.6387391090393066,
-0.5204594731330872,
0.32869675755500793,
0.4230835735797882,
-0.36596688628196716,
-0.3106687068939209,
0.10314351320266724,
-0.3137184679508209,
-0.45464029908180237,
-0.5083393454551697,
-0.20772895216941833,
0.3179331421852112,
-0.21289001405239105,
0.3752347230911255,
-0.42102906107902527,
0.21777872741222382,
0.911879301071167,
0.5461939573287964,
0.3221884071826935,
-0.08110207319259644,
0.39644482731819153,
-0.6595933437347412,
-0.1919165700674057,
-0.5098931789398193,
0.058349061757326126,
0.3591320216655731,
0.15229588747024536,
0.1414085030555725,
0.7554646134376526,
-1.0359313488006592,
0.037468064576387405,
-0.39695820212364197,
-0.17148080468177795,
-0.18978212773799896,
-0.5350274443626404,
-0.3749964237213135,
0.60688316822052,
-0.7339356541633606,
0.14908070862293243,
-0.5943582057952881,
-0.8014699220657349,
0.14165176451206207,
-0.4412361979484558,
-0.32210230827331543,
0.40677914023399353,
-0.3818809986114502,
0.4400317072868347,
0.8878339529037476,
0.7254059910774231,
0.6407737731933594,
-0.5032680630683899,
-0.14898467063903809,
0.09751664102077484,
-0.3835170865058899,
-0.3858831822872162,
0.18228282034397125,
0.3298279941082001,
-0.889105498790741,
-0.2877967953681946,
-0.2743954062461853,
-0.3482780456542969,
0.4525887370109558,
0.16489849984645844,
0.22137756645679474,
0.2107262909412384,
-0.14861367642879486,
0.8592010736465454,
-0.3673865795135498,
0.5470399856567383,
-0.8367233276367188,
0.5305765271186829,
-0.2827390134334564,
-0.4002176821231842,
-0.25251123309135437,
0.15619328618049622,
-0.9423500895500183,
-0.03885493054986,
-1.5987809896469116,
0.15965330600738525,
0.8776388764381409,
0.43703433871269226,
-0.3187442421913147,
-0.33832237124443054,
0.38216713070869446,
0.2893909215927124,
0.3175468444824219,
-0.5996070504188538,
0.7343032360076904,
0.4476357698440552,
0.26488828659057617,
0.33459436893463135,
-0.05800206959247589,
0.30799973011016846,
0.32263273000717163,
0.9768940210342407,
-0.2514188289642334,
-0.0012981424806639552,
-1.0142967700958252,
-0.3804391622543335,
0.41032731533050537,
0.8457108736038208,
0.11067339777946472,
0.16830654442310333,
0.09440185129642487,
0.059382736682891846,
-0.48453348875045776,
0.8763609528541565,
0.5578144192695618,
0.45791274309158325,
0.3794008791446686,
0.6958500146865845,
0.4652101397514343,
0.7634615302085876,
-0.12654118239879608,
-0.026745472103357315,
0.9517185688018799,
-0.4519781172275543,
-0.5647143721580505,
-0.21782708168029785,
-0.3770654499530792,
0.7047353982925415,
-1.2367137670516968,
0.2711266577243805,
-0.7074827551841736,
0.09615838527679443,
0.20933856070041656,
0.3109310567378998,
-1.4359129667282104,
-0.4139980375766754,
-0.07214505225419998,
-0.06768298149108887,
0.13535025715827942,
-0.46993428468704224,
0.7323122620582581,
0.5731131434440613,
-0.035913459956645966,
-0.5462746620178223,
-0.12700031697750092,
0.9871006608009338,
-0.10374046862125397,
0.23735809326171875,
0.28020450472831726,
-0.34226927161216736,
-0.8253215551376343,
-0.2122960388660431,
-0.9289180040359497,
0.1786354035139084,
-0.648801326751709,
0.15480558574199677,
0.28176915645599365,
-0.6829928159713745,
0.9612372517585754,
0.7078704833984375,
-0.41966933012008667,
0.33920472860336304,
-0.6468357443809509,
0.3291471600532532,
0.6073792576789856,
-0.1582329273223877,
-0.8449553847312927,
0.48123589158058167,
-0.44374191761016846,
-0.25818774104118347,
0.2262878566980362,
-0.06505027413368225,
1.1075866222381592,
-0.47860947251319885,
0.4192063808441162,
0.011150887235999107,
0.0010016232263296843,
0.11004992574453354,
-0.3181565999984741,
-0.8578012585639954,
-0.35379451513290405,
0.30075329542160034,
0.10444775968790054,
0.3284837007522583,
-0.7683794498443604,
0.9355179071426392,
-0.07922592014074326,
0.01838064193725586,
-0.1426745504140854,
0.005629758816212416,
-0.6208847761154175,
0.539847195148468,
0.3669402003288269,
0.021223196759819984,
0.08493064343929291,
1.3667497634887695,
0.8295199871063232,
-0.35941603779792786,
-0.6706183552742004,
-0.1311330795288086,
-0.20305190980434418,
0.02619575522840023,
-0.11142010241746902,
-0.6004500389099121,
0.10950586944818497,
0.39007821679115295,
-0.22123491764068604,
-0.8021528124809265,
0.7687051296234131,
-0.41259753704071045,
-1.022918701171875,
0.5292377471923828,
-0.4674592614173889,
0.20368386805057526,
-0.38080674409866333,
0.14225724339485168,
-0.9784910082817078,
-0.03789524734020233,
0.4141664206981659,
0.21775288879871368,
0.31984958052635193,
0.12280160933732986,
0.805111289024353,
0.0409909226000309,
0.49138039350509644,
0.027577757835388184,
-0.43819618225097656,
-0.3635159134864807,
-0.26953503489494324,
0.30388665199279785,
-0.4377795159816742,
0.655562162399292,
-0.21400918066501617,
-0.19211961328983307,
-0.2448207437992096,
0.3767988383769989,
-0.8485961556434631,
-0.3592343032360077,
-0.17711946368217468,
0.06467186659574509,
0.46249625086784363,
0.9359579682350159,
-0.0050599658861756325,
-0.924601137638092,
-0.7357308268547058,
-0.5921472311019897,
-0.10813960433006287,
-0.03631841018795967,
0.6640034317970276,
-0.8018220067024231,
0.4816957116127014,
0.31120359897613525,
-0.3235650956630707,
-0.02816643752157688,
-0.2888328433036804,
-0.14077012240886688,
0.5397014617919922,
0.278385728597641,
0.843294084072113,
-0.4040919244289398,
-0.7142401933670044,
-0.0758623331785202,
0.7469180822372437,
0.17610397934913635,
0.8468378782272339,
0.014128868468105793,
-0.2708454728126526,
0.17368347942829132,
-0.511587917804718,
-0.6487808227539062,
0.01531088724732399,
0.20484617352485657,
0.09200665354728699,
0.3125515878200531,
0.21686778962612152,
0.13174432516098022,
0.367058128118515,
0.6493834853172302,
0.43898671865463257,
0.1265718638896942,
0.07979266345500946,
0.6384385824203491,
0.5229299664497375,
0.46338319778442383,
-0.3403950035572052,
0.3465435206890106,
-0.4750868082046509,
0.21704275906085968,
0.32509109377861023,
0.1237155944108963,
0.012676918879151344,
-0.5286563634872437,
0.06194932386279106,
-0.46009573340415955,
0.06282365322113037,
0.30148765444755554,
-0.9709773659706116,
0.1391909122467041,
0.33938130736351013,
0.8201135993003845,
-0.08702503144741058,
-0.3096601963043213,
1.2142528295516968,
0.507892906665802,
0.5809113383293152,
-1.282728672027588,
0.006287728901952505,
-0.7006120681762695,
-0.25045013427734375,
-0.15305909514427185,
-0.6787281036376953,
-0.5731632709503174,
-1.032297968864441,
0.1419614851474762,
-0.4998762607574463,
0.83304363489151,
0.9292196035385132,
0.11294516175985336,
0.18762534856796265,
-0.8118414878845215,
-0.3577377498149872,
0.7765430212020874,
-0.6013547778129578,
-0.27182459831237793,
0.0027444264851510525,
0.1131773591041565,
0.31045228242874146,
0.6272960901260376,
-0.5674098134040833,
-0.4162697494029999,
-0.0020628829952329397,
-0.300430029630661,
0.09084243327379227,
-0.3406303822994232,
-0.46022146940231323,
-0.28016984462738037,
-0.4700278341770172,
-0.44830912351608276,
0.6484746932983398,
0.8930495381355286,
-0.4270288646221161,
0.07401074469089508,
0.2418070137500763,
0.35676634311676025,
0.107124462723732,
0.10152754932641983,
0.3440222442150116,
1.0074888467788696,
0.47997185587882996,
0.48052212595939636,
0.40514296293258667,
-0.5643355250358582,
0.03399491310119629,
-0.39087459444999695,
0.16285304725170135,
0.10039754956960678,
-0.6646973490715027,
-0.44982245564460754,
-0.29954710602760315,
-0.2999544143676758,
-0.30091848969459534,
-0.15673145651817322,
-0.1569053828716278,
1.0511902570724487,
-0.5230933427810669,
-0.7467119693756104,
-0.37586021423339844,
-0.6458961367607117,
-0.6380022764205933,
0.6182736754417419,
0.4611941874027252,
-0.19705525040626526,
0.8554737567901611,
-0.30392226576805115,
0.31037434935569763,
-0.42988771200180054,
-0.1682662069797516,
-0.8073855638504028,
-0.010334068909287453,
0.9271461963653564,
0.3557819724082947,
1.1981916427612305,
-0.570934534072876,
0.050838470458984375,
-0.24649271368980408,
0.3851170837879181,
-0.009838993661105633,
-0.19107560813426971,
-0.38111722469329834,
-0.573032796382904,
0.16351261734962463,
-0.26214924454689026,
0.5478280186653137,
0.35564953088760376,
0.4680609405040741,
0.10294723510742188,
-0.48677027225494385,
-0.07252893596887589,
-0.39873552322387695,
0.4687974750995636,
0.2631664574146271,
-0.12724128365516663,
-0.1359446942806244,
0.5023438334465027,
-0.1427830457687378,
0.627851665019989,
0.14483526349067688,
-0.04098265618085861,
-0.250600129365921,
-0.24072426557540894,
1.1189731359481812,
-0.935469388961792,
-0.754386842250824,
-0.414657860994339,
-0.19057710468769073,
0.8690544962882996,
1.0348490476608276,
-0.3176058828830719,
-0.4252983033657074,
-0.9407181739807129,
-0.5020653009414673,
-0.07218097895383835,
-0.6380699872970581,
0.1365303248167038,
-0.44495949149131775,
-0.4497113525867462,
-0.7082782983779907,
0.585382342338562,
-0.5934574604034424,
0.10408776998519897,
0.11495283246040344,
0.3548431396484375,
0.28779637813568115,
0.57430499792099,
0.603672981262207,
0.12923583388328552,
-0.3699616491794586,
-0.10659633576869965,
0.16476894915103912,
0.4000614285469055,
-0.12606357038021088,
0.3158744275569916,
-0.9470635056495667,
0.5354868173599243,
-0.7883248329162598,
-0.2692631781101227,
0.1152333989739418,
0.18188194930553436,
1.0282502174377441,
-1.1601626873016357,
-0.16834937036037445,
0.4384436309337616,
-0.10635820031166077,
-0.038235124200582504,
-0.05325350910425186,
-0.32282453775405884,
-0.28573477268218994,
-0.5742964148521423,
-0.8400792479515076,
0.0592297725379467,
0.25830549001693726,
-0.6061502695083618,
-0.7457324266433716,
-0.6698230504989624,
0.18101273477077484,
0.13335025310516357,
0.16494563221931458,
0.450509637594223,
-0.2039322406053543,
-0.13044323027133942,
-0.13827937841415405,
-0.2828322649002075,
-0.5115894079208374,
0.5483534336090088,
0.18302668631076813,
-0.1227920800447464,
0.1005280613899231,
0.16334883868694305,
-0.429353803396225,
-0.6059884428977966,
-0.13860806822776794,
0.3269047439098358,
-0.3979937434196472,
-0.4633733034133911,
0.5285102128982544,
-0.04366357624530792,
-0.14659585058689117,
0.25143641233444214,
-0.10357949882745743,
0.5937963128089905,
0.04244816675782204,
0.22942572832107544,
0.9586771726608276,
0.5135195255279541,
-0.0386229045689106,
0.19301718473434448,
-0.6710724830627441,
0.3777150511741638,
1.0159056186676025,
-0.5994923710823059,
-0.22218362987041473,
0.5292249917984009,
-0.2134108543395996,
-0.527921199798584,
-0.2711271643638611,
-0.5760184526443481,
0.42533397674560547,
-0.41802266240119934,
-0.5949722528457642,
0.010543943382799625,
-0.22195737063884735,
0.05796641483902931,
0.36015230417251587,
1.1016019582748413,
-0.034036785364151,
-0.05050026625394821,
0.5753409266471863,
-0.6352931261062622,
-0.171929270029068,
-0.11209588497877121,
1.2143034934997559,
0.11973167955875397,
-1.0663578510284424,
0.5127621293067932,
-0.19557695090770721,
-0.1422160565853119,
0.19981259107589722,
0.9427164196968079,
0.19664901494979858,
0.42888930439949036,
0.1603115350008011,
0.11167726665735245,
0.24006761610507965,
0.424108624458313,
0.14147605001926422,
-0.24072490632534027,
-0.2509184181690216,
-0.7457655072212219,
-0.1046799048781395,
-0.1904771625995636,
0.08294427394866943,
0.8008186221122742,
-0.10462784767150879,
-0.027526557445526123,
0.18907266855239868,
-0.5501924753189087,
-0.4788537621498108,
-0.46960875391960144,
-0.614290714263916,
-0.9842529296875,
-0.05199763551354408,
-0.6097965836524963,
-0.39960789680480957,
-0.00909129623323679,
0.3066520392894745,
0.060626253485679626,
0.13496458530426025,
-0.4009281396865845,
0.023021869361400604,
0.30296945571899414,
0.8132035136222839,
-0.43094685673713684,
-0.8812295198440552,
-0.5093646049499512,
-0.7145329713821411,
0.1586645543575287,
-0.23392093181610107,
0.16554497182369232,
-0.18552236258983612,
-0.12393981218338013,
0.5789288282394409,
-0.17598211765289307,
0.9043962955474854,
-0.8466218709945679,
-0.7864395976066589,
-0.10343518853187561,
-0.017845697700977325,
-0.851262629032135,
0.7231109142303467,
0.2542988061904907,
0.37615805864334106,
0.431426465511322,
0.5025460720062256,
-0.3659091591835022,
0.28204968571662903,
-1.0656955242156982,
-0.04814053326845169,
0.1929541826248169,
0.9140025973320007,
-0.44989755749702454,
-0.769220232963562,
-0.061665333807468414,
0.3227085769176483,
-1.0218428373336792,
0.11498362571001053,
0.2219172865152359,
0.19510523974895477,
-0.2414671927690506,
0.46945637464523315,
0.5575031638145447,
0.5940815806388855,
-0.345815509557724,
0.664447546005249,
-0.16699013113975525,
-0.2249155193567276,
-0.05898464843630791,
0.4581387937068939,
-0.11673849821090698,
0.06885472685098648,
0.26036760210990906,
-0.7237834930419922,
0.12464437633752823,
-0.153702974319458,
-0.11422877758741379,
0.40840625762939453,
-0.42731741070747375,
-0.604421854019165,
-0.6691171526908875,
-0.42326146364212036,
-0.04103834927082062,
0.4935184419155121,
0.47568967938423157,
0.039574142545461655,
0.16912466287612915,
-0.9103649854660034,
-0.2787102162837982,
-0.02969963662326336,
-0.7002696394920349,
-0.6027411818504333,
0.3931535482406616,
-0.3567129075527191,
-0.5766105055809021,
0.03503863140940666,
-0.33934134244918823,
0.17891010642051697,
-0.5116637945175171,
0.4720144271850586,
-0.05130805820226669,
-0.38509708642959595,
-0.4531789720058441,
-0.2789498269557953,
-0.9092109203338623,
-0.3674016296863556,
-0.2325538992881775,
0.5408123731613159,
-0.5007625222206116,
-0.8983321189880371,
0.387808233499527,
0.07392478734254837,
0.11715491116046906,
-0.06795334815979004,
-0.1790764331817627,
-0.40265321731567383,
-0.24398094415664673,
0.4180711805820465,
0.012807495892047882,
-0.009365779347717762,
-1.513901948928833,
-0.03460397943854332,
-0.006620950996875763,
-0.5167028307914734,
0.12477728724479675,
0.6666860580444336,
0.13826656341552734,
-0.10181599110364914,
0.1382850557565689,
1.701771855354309,
-0.1163267269730568,
-0.2451057881116867,
0.9561160206794739,
-0.5985092520713806,
0.015202932059764862,
-0.311962366104126,
-0.5172410607337952,
-0.06959734857082367,
0.48271629214286804,
0.5351517796516418,
0.6886678338050842,
0.543571949005127,
0.2455516904592514,
0.5942516922950745,
0.15113969147205353,
0.09806554019451141,
0.004769365303218365,
0.005364398006349802,
0.7441524863243103,
0.34513187408447266,
-0.18037275969982147,
0.04893095791339874,
0.005807844921946526,
0.1436324268579483,
0.40076062083244324,
-0.12055874615907669,
-0.4913160502910614,
-0.16145440936088562,
0.09059281647205353,
0.42805686593055725,
0.006702677346765995,
-0.18211281299591064,
-0.4672529697418213,
0.0225283931940794,
0.5777265429496765,
0.7844528555870056,
-0.22805002331733704,
0.16816020011901855,
0.6661494970321655,
-0.060840826481580734,
-0.9257034659385681,
0.6731021404266357,
-0.07678436487913132,
0.5397194623947144,
0.656011164188385,
0.648485004901886,
0.6255240440368652,
0.49961981177330017,
0.40001776814460754,
-1.1513997316360474,
0.45320865511894226,
0.26405417919158936,
-0.47684037685394287,
0.21815530955791473,
-0.4447230398654938,
0.2742869555950165,
-0.3109722435474396,
-0.3664707839488983,
0.4897763431072235,
-0.02472468838095665,
-0.055187564343214035,
-0.13065731525421143,
-0.2818658947944641,
-0.18030454218387604,
0.4848316013813019,
0.30638378858566284,
0.12804333865642548,
0.19452576339244843,
-0.27674177289009094,
0.4467878043651581,
0.8252244591712952,
1.4410172700881958,
0.28285184502601624,
0.3736250698566437,
0.11894293129444122,
-0.13985837996006012,
0.2884120047092438,
0.5727134346961975,
-0.5244430303573608,
0.1969764679670334,
-0.8806486129760742,
-0.27509769797325134,
0.5189070701599121,
0.6301317811012268,
-0.02537119761109352,
-0.02879403904080391,
0.039193298667669296,
0.13047592341899872,
-0.8307835459709167,
-0.5881988406181335,
1.1380566358566284,
0.23600155115127563,
-0.5301610231399536,
-0.5047118663787842,
-0.026086702942848206,
-0.8935674428939819,
-0.2397925704717636,
-1.2326220273971558,
0.3268807828426361,
-0.648989200592041,
0.1779591143131256,
-0.6066165566444397,
-0.19693708419799805,
-0.28011149168014526,
-0.5985000729560852,
0.3430834710597992,
0.005658263340592384,
0.29911017417907715,
0.183545783162117,
0.08176402002573013,
-0.008060939610004425,
-0.5952030420303345,
-0.46677905321121216,
-0.49770867824554443,
0.9122054576873779,
0.8263707756996155,
0.03821369633078575,
1.0433807373046875,
0.2547401785850525,
-0.3348783552646637,
0.4914688766002655,
0.7239197492599487,
-0.6850911974906921,
0.8565036654472351,
-0.32154136896133423,
-0.3096522390842438,
0.4162086844444275,
0.04205648601055145,
0.03297017142176628,
0.3878996968269348,
0.24588429927825928,
0.5821958184242249,
0.3177832067012787,
0.19521208107471466,
-0.11185400187969208,
0.17931322753429413,
-0.6863888502120972,
-0.126544788479805,
0.4530658423900604,
0.039489515125751495,
0.32150334119796753,
-0.6252443194389343,
4.214452266693115,
0.47198688983917236,
0.35890811681747437,
0.29614874720573425,
1.1322267055511475,
1.5241639614105225,
-0.5405344367027283,
0.34767836332321167,
0.4870090186595917,
-1.1384235620498657,
-0.586834728717804,
-0.10506155341863632,
-0.35683417320251465,
0.17541594803333282,
0.024956317618489265,
0.9718499183654785,
-0.035946041345596313,
-0.05684144049882889,
-0.5807164907455444,
-0.6565179824829102,
-0.5274820327758789,
0.32536542415618896,
0.33577579259872437,
0.4049889147281647,
0.23641647398471832,
-0.2738932967185974,
-0.06287217140197754,
-0.7759479880332947,
-0.9223395586013794,
-0.4383396804332733,
-0.8074899911880493,
-0.6635468602180481,
-0.29697176814079285,
-0.06130145862698555,
-0.8505476117134094,
0.0726899653673172,
0.005674251355230808,
-0.40338411927223206,
0.010782464407384396,
0.26089030504226685,
-0.426920086145401,
-0.37326425313949585,
0.4779151678085327,
0.06712236255407333,
-0.3044755458831787,
1.1024504899978638,
0.011209222488105297,
0.6840646266937256,
0.741010844707489,
-0.5264297723770142,
0.5646623373031616,
0.07821249961853027,
0.388785719871521,
-0.5182563066482544,
-0.6980007886886597,
-0.08451732248067856,
-0.42277419567108154,
-0.030138222500681877,
0.654766857624054,
-0.1876569390296936,
-0.17794574797153473,
-0.22409671545028687,
-0.33754420280456543,
0.23288749158382416,
0.051727086305618286,
0.20523856580257416,
0.3658894896507263,
0.06153232231736183,
-0.10816175490617752,
-0.22450067102909088,
0.223606139421463,
0.21136535704135895,
-0.16014179587364197,
0.32825419306755066,
0.12672321498394012,
0.10823054611682892,
-0.3813167214393616,
0.7736838459968567,
0.4182772636413574,
0.043651554733514786,
-0.148829385638237,
-0.4843435287475586,
0.07701577991247177,
0.0051222797483205795,
0.12447567284107208,
0.6631268262863159,
-0.34525585174560547,
-0.0634637176990509,
-0.7839675545692444,
0.14427264034748077,
0.347759872674942,
1.508586049079895,
-0.01901295594871044,
0.14846745133399963,
-0.36984947323799133
] |
Continuum Gauge Fields from Lattice Gauge Fields
|
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the $U(1)$ theory in two dimensions, where it leads to simple results.
|
M. Goeckeler, A. S. Kronfeld, G. Schierholz and U.-J. Wiese
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208006
|
hep-lat/9208007
|
[
0.13975635170936584,
-0.8051380515098572,
-0.3028484284877777,
0.3032912611961365,
-0.42647939920425415,
0.22508753836154938,
-0.5512164831161499,
-0.7685750722885132,
-0.40088748931884766,
1.0695996284484863,
0.06505963951349258,
-0.0878128707408905,
0.2326962798833847,
-0.42824357748031616,
0.27226170897483826,
0.9522278308868408,
-0.29557836055755615,
-0.8022497892379761,
-1.3420528173446655,
1.1385186910629272,
0.2340073436498642,
0.13772301375865936,
-0.9351160526275635,
-0.7833142280578613,
-0.02046031691133976,
1.0358799695968628,
0.6486657857894897,
-0.1036820113658905,
1.0468071699142456,
0.3625035881996155,
0.33914685249328613,
-0.42830297350883484,
-0.5850792527198792,
-0.3493480384349823,
-0.8341135382652283,
-0.340586394071579,
-0.40853723883628845,
-0.07486077398061752,
0.5677944421768188,
0.1204088106751442,
0.6845453977584839,
-0.7154856324195862,
-0.5364543199539185,
-0.28519105911254883,
-0.16333556175231934,
0.08039538562297821,
-0.2643854320049286,
-0.46761322021484375,
0.41935819387435913,
-1.1643658876419067,
0.2959595322608948,
0.4613613486289978,
0.2074035108089447,
-1.2240955829620361,
-0.8299618363380432,
-0.032272666692733765,
0.12896959483623505,
-0.08973352611064911,
-1.3028699159622192,
-0.2927536368370056,
0.5986902117729187,
-0.09364975243806839,
0.24476173520088196,
-0.7562159895896912,
0.13288778066635132,
0.5264415144920349,
-0.5436918139457703,
1.0262084007263184,
-0.5282802581787109,
-0.48377183079719543,
0.21725668013095856,
-0.33625781536102295,
-1.2396801710128784,
0.6863133311271667,
-1.064879298210144,
-0.08618344366550446,
0.08198070526123047,
-0.4772871434688568,
-1.0581204891204834,
-0.539680004119873,
-0.26395198702812195,
-0.3937821686267853,
-0.33279550075531006,
0.40978777408599854,
-0.668889582157135,
0.07560226321220398,
-0.40841472148895264,
-0.8911252021789551,
-0.11712919175624847,
0.3068453371524811,
0.19701719284057617,
0.8791351914405823,
-0.641342043876648,
-0.06225854530930519,
-0.07144929468631744,
0.32124924659729004,
-0.05082639679312706,
0.6444924473762512,
0.06703458726406097,
0.02518872544169426,
0.15650531649589539,
0.7053177356719971,
-1.124484896659851,
0.15320026874542236,
-0.8610232472419739,
0.5861721038818359,
-0.3606168329715729,
-0.24992036819458008,
-0.2903512418270111,
-0.4013461172580719,
0.2811063230037689,
-0.2701776623725891,
0.08264176547527313,
1.0041378736495972,
0.20324687659740448,
0.29251110553741455,
-0.40975531935691833,
0.16442136466503143,
-0.15214936435222626,
-0.2524385452270508,
0.40367788076400757,
-0.09598482400178909,
0.15547356009483337,
-0.0518982857465744,
0.3321864902973175,
-0.32629773020744324,
0.018951207399368286,
0.6708300113677979,
-0.5361814498901367,
0.19231410324573517,
0.22685982286930084,
0.3076893091201782,
-0.38532188534736633,
0.44470229744911194,
-0.37720176577568054,
-0.06269413232803345,
-0.3314669728279114,
0.21449364721775055,
-0.15303915739059448,
0.1382518708705902,
0.8537649512290955,
-0.7527218461036682,
0.27351316809654236,
1.115061640739441,
0.4797336459159851,
0.09848149120807648,
-0.05991677939891815,
0.4596942067146301,
-0.35523340106010437,
0.321126788854599,
-0.5309537649154663,
0.4986950159072876,
0.1776251196861267,
0.10304762423038483,
-0.054767534136772156,
0.6390540599822998,
-0.418582946062088,
-0.11663907021284103,
-0.4493367671966553,
-0.13389338552951813,
0.08502437174320221,
-0.18102207779884338,
-0.816718578338623,
0.024297252297401428,
-0.8071601986885071,
-0.12618134915828705,
-0.3148754835128784,
-0.38012388348579407,
0.7256057262420654,
-0.45025306940078735,
-0.6265193819999695,
0.4162183701992035,
-0.2810637652873993,
0.7260705232620239,
0.34148523211479187,
0.646595299243927,
0.38974353671073914,
-0.18202762305736542,
0.3665578365325928,
0.06726696342229843,
0.10623863339424133,
0.08922631293535233,
0.11238075792789459,
-0.32461899518966675,
0.22594811022281647,
-0.1449168622493744,
0.23905207216739655,
-0.23973947763442993,
0.5264312028884888,
0.4236390292644501,
-0.12739796936511993,
0.01890275627374649,
-0.4844151437282562,
1.3964872360229492,
-0.6398912072181702,
-0.3025467097759247,
-0.9720343351364136,
-0.21690361201763153,
-0.42723241448402405,
-0.3672003448009491,
0.4588616192340851,
-0.14536909759044647,
-1.2580708265304565,
-0.031024806201457977,
-1.14338219165802,
0.19454677402973175,
0.858698308467865,
0.31034499406814575,
-0.7274292707443237,
-0.15086837112903595,
0.04515325650572777,
-0.4281816780567169,
0.4056948125362396,
-0.6551485061645508,
0.834430992603302,
0.3837825655937195,
0.5623687505722046,
0.7137584090232849,
0.5945766568183899,
0.3577468991279602,
0.5929359197616577,
0.19719965755939484,
0.08976086229085922,
0.7462893128395081,
-0.7503223419189453,
-0.49713334441185,
0.12675276398658752,
0.22445961833000183,
0.13345463573932648,
-0.14244762063026428,
-0.2809082269668579,
0.30795979499816895,
-0.2769372761249542,
0.8516653180122375,
0.15448318421840668,
0.5403777360916138,
0.5677435994148254,
0.11575882881879807,
0.5905711054801941,
0.6748151779174805,
-0.018273908644914627,
-0.017037708312273026,
0.33810245990753174,
-0.8220177888870239,
-0.12052574008703232,
0.0111996503546834,
-0.6154451966285706,
-0.02297421358525753,
-1.0248956680297852,
0.10041939467191696,
0.12551434338092804,
0.24205352365970612,
0.17865942418575287,
0.7650513648986816,
-1.1656354665756226,
0.058121196925640106,
-0.28909844160079956,
-0.012449086643755436,
0.06461591273546219,
-0.03690561652183533,
1.1705329418182373,
0.09193066507577896,
-0.31828927993774414,
-0.8267149329185486,
0.06993928551673889,
1.282872200012207,
-0.3399164080619812,
0.2323027104139328,
0.9616712927818298,
0.12462784349918365,
-0.8200807571411133,
-0.2564256489276886,
-0.7786688208580017,
0.02312343940138817,
-0.875566840171814,
-0.1820879578590393,
0.6012535691261292,
-0.7022587656974792,
0.14662832021713257,
0.3766435980796814,
-0.3593485355377197,
0.6595624089241028,
-0.8371043801307678,
0.09402292221784592,
0.5106318593025208,
0.24837638437747955,
-0.5277789831161499,
0.28246429562568665,
-0.5927630066871643,
-0.06140880286693573,
-0.07751906663179398,
0.35786041617393494,
0.8693222999572754,
-0.38286375999450684,
0.5948665142059326,
-0.2560519576072693,
-0.6776179671287537,
-0.15643425285816193,
0.009516770020127296,
-0.9867424964904785,
0.10456990450620651,
0.4102451801300049,
-0.15914121270179749,
-0.1392347514629364,
-0.8918291926383972,
0.5016641616821289,
0.05682331696152687,
-0.27975374460220337,
0.31585031747817993,
-0.32438814640045166,
-0.3845500946044922,
0.9296015501022339,
0.4576217830181122,
-0.11637013405561447,
0.24320942163467407,
1.3136299848556519,
1.1481083631515503,
-0.1292886734008789,
-0.5742350816726685,
-0.38601821660995483,
-0.2528655230998993,
0.17676261067390442,
-0.04266059771180153,
-0.5286824107170105,
-0.3895415663719177,
0.6502088904380798,
0.0312421265989542,
-0.09261657297611237,
0.6399627327919006,
-0.8869666457176208,
-1.0249266624450684,
0.1959710568189621,
-0.4520241618156433,
0.2490973323583603,
-0.004830388352274895,
-0.03846712037920952,
-0.7762189507484436,
0.22276143729686737,
0.5348981618881226,
-0.12816739082336426,
0.22833576798439026,
-0.15118110179901123,
0.7495324015617371,
-0.03426792472600937,
0.5383355617523193,
-0.093269482254982,
-0.28627875447273254,
-0.7034561038017273,
-0.36803102493286133,
0.39187851548194885,
-0.668633222579956,
0.09198231995105743,
-0.37897157669067383,
0.29728826880455017,
-0.24656513333320618,
0.46078944206237793,
-0.6047132015228271,
-0.14170321822166443,
-0.5803744196891785,
-0.465658038854599,
0.2889891564846039,
0.709607720375061,
0.16883239150047302,
-0.7811799049377441,
-0.4723886251449585,
-0.024685518816113472,
0.1506168395280838,
0.02596825547516346,
0.5252578854560852,
-0.5659545063972473,
0.34262558817863464,
-0.29076215624809265,
-0.7251806855201721,
-0.22415360808372498,
0.1002960205078125,
0.30009832978248596,
0.49095386266708374,
0.43708711862564087,
0.8593204021453857,
-0.21880438923835754,
-0.6172579526901245,
0.23927384614944458,
0.6278748512268066,
0.5418151617050171,
0.888171911239624,
0.12332475930452347,
-0.21026654541492462,
0.25445303320884705,
-0.13568778336048126,
-0.5085472464561462,
-0.0795782059431076,
0.1854250282049179,
0.46963223814964294,
-0.14484067261219025,
0.42733484506607056,
0.035928837954998016,
0.7116192579269409,
0.3011256158351898,
-0.017316671088337898,
0.0017628506757318974,
0.13350887596607208,
-0.08633817732334137,
0.8664388656616211,
0.0711900070309639,
0.26597172021865845,
0.4424087405204773,
-0.9091624021530151,
0.22160333395004272,
0.6819422245025635,
0.7914796471595764,
-0.458299458026886,
-0.2531736493110657,
0.050592705607414246,
-0.8586472868919373,
0.30059465765953064,
0.4105847179889679,
-0.8875829577445984,
0.43207573890686035,
0.17963631451129913,
1.1400146484375,
-0.26915088295936584,
-0.11007377505302429,
0.9388872385025024,
0.441209077835083,
0.5493319630622864,
-1.2661784887313843,
0.7553139925003052,
-0.06252480298280716,
0.013155531138181686,
0.3385705053806305,
-0.6096699237823486,
-0.23772014677524567,
-0.7722524404525757,
-0.033513836562633514,
-0.5769256353378296,
0.618948757648468,
1.1344048976898193,
0.24566121399402618,
0.01674262061715126,
-0.642109215259552,
-0.31128600239753723,
0.8864615559577942,
-0.1713651418685913,
-0.26080915331840515,
0.6557258367538452,
0.16705799102783203,
-0.2735743224620819,
0.44083523750305176,
-0.28102847933769226,
-0.3077700138092041,
0.1306939721107483,
-1.1126155853271484,
0.756778359413147,
-0.28512316942214966,
-0.4358609914779663,
-0.11109308898448944,
-0.183146134018898,
-0.4793635904788971,
0.5438427925109863,
0.3775815963745117,
-0.6581818461418152,
-0.46693670749664307,
-0.08865590393543243,
0.09148669242858887,
-0.020658858120441437,
-0.2384360432624817,
0.0030651609413325787,
0.8064342141151428,
0.8210654854774475,
0.24578414857387543,
0.7335020899772644,
0.2482140064239502,
-0.3855297565460205,
-0.17713037133216858,
0.3729720413684845,
0.2889000177383423,
-0.31197071075439453,
-0.40826454758644104,
-0.2481374442577362,
-0.5566163063049316,
-0.5064655542373657,
0.16230954229831696,
-0.1075451523065567,
0.8900574445724487,
0.40511101484298706,
-0.6654444932937622,
-0.6968953609466553,
-0.861126720905304,
-1.1079456806182861,
0.661134660243988,
0.6299495100975037,
-0.36618611216545105,
0.9146170020103455,
-0.5789507627487183,
0.5092634558677673,
-0.7598040103912354,
-0.19515980780124664,
-0.3982178866863251,
0.46547964215278625,
1.0042341947555542,
0.5076183676719666,
-0.3553861677646637,
-1.3956221342086792,
0.6133026480674744,
-0.6764383912086487,
-0.12202820926904678,
-0.43881839513778687,
-0.48332443833351135,
0.1459268480539322,
-0.12563571333885193,
0.6053720712661743,
0.11293879896402359,
-0.05614401400089264,
0.16402848064899445,
0.30055493116378784,
-0.6057534217834473,
-0.05643144249916077,
-0.20057186484336853,
0.21726012229919434,
0.2879442572593689,
-0.20682281255722046,
-0.5790053606033325,
-0.20943884551525116,
0.1535680741071701,
0.20952434837818146,
0.20004205405712128,
0.2953389286994934,
-0.7191036939620972,
-0.21517139673233032,
-0.2953658401966095,
0.3674144148826599,
-0.6105920672416687,
-0.7327083349227905,
-0.11930711567401886,
-0.516870379447937,
0.7707953453063965,
0.24856407940387726,
0.4021219313144684,
-0.029496530070900917,
-0.5072352290153503,
-0.15547272562980652,
0.45195072889328003,
-0.6441770195960999,
-0.028052911162376404,
-0.5918685793876648,
-0.373970627784729,
-0.26149600744247437,
0.6776816844940186,
-0.06175108626484871,
0.5846441388130188,
-0.13453495502471924,
-0.15609484910964966,
0.17831461131572723,
0.5192938446998596,
0.04936846345663071,
-0.29259541630744934,
0.2558545470237732,
0.668834924697876,
-0.005894242320209742,
0.5786731839179993,
-0.6660001277923584,
0.4212246239185333,
-0.6493907570838928,
1.088196039199829,
-0.7262641191482544,
-0.10373645275831223,
0.0022073634900152683,
-0.4029293358325958,
0.582099437713623,
-0.8200475573539734,
0.3478296995162964,
0.7947911024093628,
-0.23172427713871002,
0.1807006150484085,
0.1924094706773758,
-0.6400026082992554,
0.09769441187381744,
-0.8865251541137695,
-0.38540613651275635,
0.26007363200187683,
0.14662013947963715,
-0.2963401973247528,
-0.7936844825744629,
-0.7831078767776489,
0.16918468475341797,
0.3079785704612732,
0.4769246280193329,
0.9610071182250977,
0.0344337522983551,
0.26387813687324524,
-0.20191971957683563,
-0.1575963944196701,
-0.6655315160751343,
0.40353265404701233,
0.1940983235836029,
-0.21003317832946777,
0.20793424546718597,
0.08819800615310669,
-0.37414291501045227,
-0.44141244888305664,
0.1136312261223793,
0.4799691438674927,
0.23601825535297394,
-0.3727445900440216,
1.0733976364135742,
-0.15142273902893066,
-0.47106361389160156,
-0.4527190923690796,
0.2934485375881195,
0.21980918943881989,
0.5139349102973938,
0.4054238200187683,
0.2377973049879074,
0.0948563888669014,
0.2635704278945923,
0.1819152534008026,
-0.2887458801269531,
-0.6451056599617004,
0.3084696829319,
-0.9376257658004761,
-0.3789382874965668,
0.7373594641685486,
0.31692370772361755,
-0.5123555660247803,
-0.200169175863266,
-0.8845727443695068,
0.2063133865594864,
-0.7248678803443909,
0.174758180975914,
-0.35322901606559753,
-0.14755912125110626,
-0.35430899262428284,
0.5677281618118286,
0.548396110534668,
0.05851657688617706,
-0.17875106632709503,
-0.13128556311130524,
-0.5152687430381775,
-0.30424758791923523,
-0.2477118968963623,
1.390978455543518,
-0.029689237475395203,
-0.5961559414863586,
0.2764670252799988,
0.40291696786880493,
0.2156442105770111,
-0.40584826469421387,
0.5430018901824951,
-0.6723275184631348,
0.29176896810531616,
-0.1485797017812729,
-0.3681434988975525,
0.2826520800590515,
1.2022475004196167,
0.5085418820381165,
-0.4893951117992401,
-0.11353357136249542,
-0.9878272414207458,
-0.24348106980323792,
-0.5024033188819885,
0.38791829347610474,
0.6136822700500488,
0.2180503010749817,
0.3030044734477997,
0.2318921834230423,
-0.5729256272315979,
-0.16766107082366943,
-0.8068748116493225,
0.4119011163711548,
-1.0319483280181885,
-0.06579889357089996,
-0.1133769154548645,
-0.30256447196006775,
0.1579403132200241,
0.8614150285720825,
-0.19624574482440948,
-0.23676487803459167,
-0.8062624335289001,
-0.19471022486686707,
0.32883256673812866,
0.1075906902551651,
-0.29138198494911194,
-0.6219295859336853,
-0.11498040705919266,
-0.41017013788223267,
-0.5779513716697693,
-0.4331078827381134,
0.24569126963615417,
-0.23879601061344147,
0.16961392760276794,
0.3939586579799652,
-0.22140908241271973,
0.7195547819137573,
-0.9868152141571045,
-1.1734395027160645,
0.22895307838916779,
-0.15822210907936096,
-0.799338161945343,
0.5545815825462341,
-0.09370557218790054,
0.8926959037780762,
0.777761697769165,
0.07566129416227341,
-0.984278678894043,
0.5926393270492554,
-1.190960168838501,
0.2046615481376648,
0.46029818058013916,
0.4598095715045929,
-0.02424597553908825,
-0.7823200225830078,
-0.6077991724014282,
0.20995232462882996,
-0.7772833108901978,
-0.05217514932155609,
-0.4821581542491913,
0.27346116304397583,
-0.592435359954834,
0.6006262302398682,
0.1627626121044159,
0.0928259938955307,
0.7404209971427917,
1.2506989240646362,
-0.1444864273071289,
-0.08322206139564514,
0.38628435134887695,
0.13110113143920898,
-0.36168426275253296,
-0.33335649967193604,
0.08450699597597122,
-0.3027326464653015,
-0.23403537273406982,
0.9005482792854309,
0.00947549007833004,
0.14536678791046143,
0.19407762587070465,
-0.3306443989276886,
-0.16872525215148926,
-0.18368397653102875,
-1.0984848737716675,
0.2193160355091095,
0.7551581859588623,
-0.8520829677581787,
-0.17891645431518555,
-0.9134248495101929,
-0.9126352667808533,
0.5825982093811035,
-0.19241924583911896,
-0.4676682651042938,
0.2647644281387329,
-0.0751311257481575,
0.4230313301086426,
0.5214561223983765,
-0.13632279634475708,
0.2817472219467163,
-0.07073244452476501,
0.08697318285703659,
-0.3875715732574463,
-0.11865530908107758,
-0.6108465790748596,
0.20347347855567932,
-0.8148108720779419,
-0.01029885932803154,
-0.6030216217041016,
0.26702940464019775,
-0.9804744720458984,
-0.8418601751327515,
-0.17570136487483978,
0.24349260330200195,
0.127444788813591,
0.2103085070848465,
-0.26817917823791504,
-0.2865374684333801,
-0.6323357820510864,
-0.08729783445596695,
-0.6123538613319397,
-0.04290205240249634,
-0.8567134141921997,
0.09928974509239197,
-0.06374570727348328,
-0.4709228575229645,
-0.2822771966457367,
0.005966233089566231,
0.4226618707180023,
-0.15887589752674103,
0.5492306351661682,
1.5398831367492676,
0.44098278880119324,
-0.3905319571495056,
0.0637957751750946,
0.12486568838357925,
0.10484587401151657,
0.09708774089813232,
-1.074671745300293,
0.12954701483249664,
0.15102680027484894,
0.16869735717773438,
0.4670536518096924,
0.5109917521476746,
0.4645999073982239,
0.5889970064163208,
0.0185975544154644,
0.757483959197998,
-0.28809747099876404,
0.24661977589130402,
0.7298915982246399,
0.1795899122953415,
-0.3518165946006775,
0.17630495131015778,
-0.33262553811073303,
-0.4461859464645386,
0.19289402663707733,
-0.40537697076797485,
-0.5663735270500183,
-0.510225772857666,
0.10762760043144226,
-0.07569873332977295,
-0.923393726348877,
-0.4074232578277588,
-0.012487317435443401,
-0.3250710368156433,
1.2625150680541992,
0.38592252135276794,
-0.128497913479805,
0.7027917504310608,
-0.11711148917675018,
0.16373255848884583,
0.12235774844884872,
0.20953801274299622,
-0.09567658603191376,
1.1740891933441162,
0.5494703650474548,
0.3621464669704437,
0.5142059922218323,
0.3559075891971588,
0.48747727274894714,
-0.8561252951622009,
0.3808524012565613,
0.5338369607925415,
-0.8080199360847473,
0.3226732909679413,
-0.7888150811195374,
0.14067582786083221,
-0.2443045675754547,
-0.26233217120170593,
0.5462983846664429,
-0.9205318689346313,
-0.34311559796333313,
0.44401779770851135,
-0.5290857553482056,
0.3620627820491791,
0.9290811419487,
0.0827314704656601,
0.003423101268708706,
0.09960557520389557,
0.19220465421676636,
-0.383759468793869,
1.0041606426239014,
1.7130460739135742,
0.11253318935632706,
0.6267756223678589,
0.39062032103538513,
-0.6340722441673279,
0.15732860565185547,
0.5739401578903198,
-0.2541022300720215,
0.44041019678115845,
-0.6550637483596802,
-0.6561986207962036,
0.6124325394630432,
0.28757619857788086,
0.15643419325351715,
-0.41932064294815063,
0.43228551745414734,
-0.11864757537841797,
-0.46720993518829346,
-0.6032498478889465,
1.7034707069396973,
0.694604218006134,
-0.7707465887069702,
-0.2040654718875885,
0.12955696880817413,
-0.043266523629426956,
-0.147287055850029,
-0.710955023765564,
0.6179269552230835,
-0.4307703673839569,
-0.5489732623100281,
-0.12539979815483093,
-0.5909221172332764,
-0.6702021360397339,
-0.5442466735839844,
0.23407867550849915,
-0.1902545839548111,
0.4912952780723572,
0.4755573272705078,
-0.05913635343313217,
0.3434877395629883,
-0.06122095137834549,
-0.26011067628860474,
0.2466464787721634,
0.13208982348442078,
0.01999804936349392,
0.24879170954227448,
1.0520126819610596,
0.2595897316932678,
-0.5198508501052856,
0.2688386142253876,
0.7538739442825317,
-0.6828584671020508,
0.3776956796646118,
-0.7453480958938599,
0.8398333787918091,
0.3897920846939087,
-0.037364471703767776,
0.0651899129152298,
0.319944828748703,
0.3236938416957855,
0.3342760503292084,
-0.16390497982501984,
0.04589467868208885,
-0.6359891891479492,
0.11467903852462769,
-0.31687960028648376,
0.4630448520183563,
0.11118730157613754,
0.07030747830867767,
0.2548285722732544,
-0.7313930988311768,
4.154717922210693,
0.324448823928833,
0.77497798204422,
0.5008907318115234,
0.8318869471549988,
0.901289165019989,
-0.37851542234420776,
-0.5978825688362122,
0.12904421985149384,
-0.3603998124599457,
-0.8075045943260193,
0.08057721704244614,
0.2733740508556366,
-0.14441446959972382,
0.38787585496902466,
0.5586799383163452,
-0.33083897829055786,
-0.4807169735431671,
0.4225200414657593,
-0.7253780364990234,
-0.6436977386474609,
-0.3233063519001007,
0.6456906199455261,
0.6338933706283569,
0.7573635578155518,
0.13975544273853302,
0.20236018300056458,
-1.0117645263671875,
-0.43912699818611145,
-0.6632543206214905,
-0.658650279045105,
-0.48061496019363403,
0.8831806182861328,
0.003246074775233865,
-0.7329792380332947,
0.7454787492752075,
0.5276346802711487,
-0.2005312293767929,
-0.2148277312517166,
0.2653517723083496,
-0.06739719957113266,
-0.7943145036697388,
0.5063907504081726,
-0.45910170674324036,
-0.08246748894453049,
1.0711264610290527,
0.012037659995257854,
0.9842478036880493,
0.4863722622394562,
-0.49645087122917175,
0.5073453187942505,
-0.023565104231238365,
0.3681972026824951,
-0.4719219207763672,
-0.45310086011886597,
0.4518832266330719,
-0.30366960167884827,
0.12217311561107635,
0.27844443917274475,
-0.24033308029174805,
0.17808061838150024,
-0.055440280586481094,
-0.13157206773757935,
-0.29438069462776184,
0.48176681995391846,
-0.3058816194534302,
0.1113508939743042,
0.12498298287391663,
-0.18475964665412903,
-0.08444324135780334,
0.15637840330600739,
-0.441339373588562,
0.18615852296352386,
0.4087296724319458,
0.4590325355529785,
-0.10834991186857224,
-0.44605839252471924,
0.13380496203899384,
0.4194433093070984,
-0.38687947392463684,
0.3938627243041992,
-0.6439007520675659,
-0.5991455316543579,
-0.5450069904327393,
-0.3226707875728607,
0.6577049493789673,
-0.5655613541603088,
-0.34160545468330383,
-0.030001651495695114,
0.2292822003364563,
0.24663597345352173,
1.2402476072311401,
0.10327272862195969,
0.5623379945755005,
-0.5959987640380859
] |
Introduction to Lattice Gaugefixing and Effective Quark and Gluon Masses
|
This talk was presented to a non-lattice audience at the June, 1992 Paris Workshop on QCD Vacuum Structure. We report on the status of quark and gluon propagators in quenched, gaugefixed lattice QCD. In Landau gauge we find that the effective quark mass in the chiral limit is $M_q \sim 350(40)MeV$. Quark and gluon propagators, the slope of the quark dispersion relation, and effective masses all appear to depend on gauge. A link-chain picture of lattice gaugefixing in the color $N\to\infty$ and strong coupling limit, where the system becomes almost solvable, supports the gauge variance of these numerical results. Subscribers will be given one Postscript file, the Figure included. Latex and Axis versions available from KY at [email protected] on request.
|
Claude Bernard, Amarjit Soni, Ken Yee
|
hep-lat cond-mat hep-ph
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208007
|
hep-lat/9208008
|
[
0.15157999098300934,
-0.6950017213821411,
0.29144543409347534,
0.3865605592727661,
-0.10762302577495575,
-0.6890183687210083,
-0.44015172123908997,
-0.34262531995773315,
-0.8514539003372192,
1.7110939025878906,
0.43153414130210876,
-0.05523834004998207,
0.6104677319526672,
-0.6649722456932068,
-0.2144327461719513,
0.8266696929931641,
-0.3972749710083008,
-0.8708834052085876,
-1.6467500925064087,
0.3219904899597168,
-0.11643471568822861,
-0.1964987963438034,
-1.5856672525405884,
-0.4415925443172455,
-0.5937567949295044,
1.1564812660217285,
0.17842265963554382,
0.2538470923900604,
0.8671883344650269,
0.27598705887794495,
0.01895187422633171,
-0.4869120717048645,
-0.012843683362007141,
-0.7776401042938232,
-0.48888516426086426,
-0.45609599351882935,
-0.2055811882019043,
-0.6105852723121643,
0.4653152525424957,
0.3969923257827759,
0.5853108167648315,
-0.47768858075141907,
-0.22036771476268768,
-0.7527843713760376,
-0.7117940187454224,
-0.017394818365573883,
-0.7564535737037659,
-0.30540645122528076,
0.09824389964342117,
-1.2640314102172852,
-0.08313735574483871,
0.7319989204406738,
0.40024667978286743,
-0.5605270266532898,
-0.2173338532447815,
0.16999436914920807,
0.21848207712173462,
0.17119288444519043,
-0.6335017681121826,
-0.17400416731834412,
0.041896358132362366,
0.34069329500198364,
0.5588125586509705,
-0.3479403257369995,
-0.24641931056976318,
0.7328166961669922,
-0.2712983191013336,
1.0901944637298584,
0.33050820231437683,
-0.19011123478412628,
-0.6163698434829712,
-1.003618597984314,
-0.45467910170555115,
0.5252716541290283,
-0.910063624382019,
0.12430235743522644,
-0.35370343923568726,
-0.549507737159729,
-0.7304527163505554,
-0.43400031328201294,
-0.2770564556121826,
-0.08090747892856598,
-0.5288408398628235,
0.3755357563495636,
-0.040634993463754654,
0.12845996022224426,
-0.2862938344478607,
-0.26392436027526855,
-0.37048327922821045,
0.7244243621826172,
0.3382246196269989,
0.5877208709716797,
0.192013218998909,
0.07768161594867706,
-0.05327305942773819,
0.7531130313873291,
-0.10554405301809311,
0.6481744050979614,
0.20607703924179077,
0.0072049652226269245,
0.16814635694026947,
0.685408890247345,
-0.7287291288375854,
-0.06940018385648727,
-0.23020431399345398,
0.7450205683708191,
-0.23268762230873108,
0.6637189984321594,
-0.6282197833061218,
-0.5717802047729492,
-0.30121028423309326,
-0.530027449131012,
0.6735450029373169,
0.592811644077301,
0.42091599106788635,
0.8645308613777161,
-0.2749834954738617,
-0.08062147349119186,
-1.0600993633270264,
-0.5279380679130554,
0.15553706884384155,
1.0326858758926392,
-0.13316233456134796,
-0.040207743644714355,
0.37690407037734985,
-0.3310110867023468,
0.2451440989971161,
0.9702097773551941,
-0.6153791546821594,
0.4733213484287262,
0.05780913680791855,
-0.16863791644573212,
-0.2999708354473114,
0.9065590500831604,
-0.8427712321281433,
0.4834870398044586,
-0.23809604346752167,
0.24296407401561737,
-0.17023645341396332,
-0.04995175451040268,
0.757036566734314,
-0.1900792419910431,
-0.35351240634918213,
1.173726201057434,
0.4575894773006439,
-0.22619928419589996,
0.5658144354820251,
0.09907925873994827,
-0.22922471165657043,
0.6236079931259155,
-1.1923083066940308,
-0.3057215213775635,
0.2676701247692108,
-0.3219794034957886,
-0.2301468700170517,
0.6647200584411621,
-0.7526359558105469,
0.6546339988708496,
-0.5590626001358032,
-0.727688729763031,
0.6556863188743591,
-0.145524263381958,
-0.4313754141330719,
0.5523857474327087,
0.17585788667201996,
-0.22361449897289276,
-0.922073245048523,
0.15270164608955383,
0.460065633058548,
-0.6237988471984863,
-0.2646508514881134,
1.0371816158294678,
-0.3668919503688812,
0.8840933442115784,
1.0903438329696655,
-0.13618749380111694,
0.6422640085220337,
-0.5123825669288635,
0.01835091970860958,
0.3994799852371216,
-0.3249688148498535,
-0.26132866740226746,
-0.04901893436908722,
-0.27276647090911865,
0.225619837641716,
0.0032927687279880047,
-0.1299174278974533,
-0.0936259925365448,
0.33704593777656555,
0.5626543164253235,
0.13851730525493622,
0.4037143588066101,
-0.40255871415138245,
0.7004927396774292,
-0.5913828015327454,
-0.19851011037826538,
-1.3094180822372437,
0.06690862774848938,
-0.5419749617576599,
0.027026571333408356,
0.28722915053367615,
-0.07547453790903091,
-1.1317367553710938,
0.1914573311805725,
-1.652786135673523,
0.12562324106693268,
0.439860075712204,
0.24947531521320343,
-0.8338250517845154,
-0.5031293034553528,
0.20908711850643158,
-0.1695084124803543,
0.15763801336288452,
-0.14318405091762543,
0.06493227183818817,
0.11546708643436432,
-0.32250189781188965,
-0.14198003709316254,
0.6763871312141418,
0.24347984790802002,
0.7660898566246033,
0.14587940275669098,
0.25855764746665955,
1.0399229526519775,
-0.41985777020454407,
-0.5647968053817749,
-0.2561592161655426,
0.4793980121612549,
0.5955142378807068,
-0.30073973536491394,
0.15717388689517975,
0.6157972812652588,
-0.005155058111995459,
0.6746904850006104,
0.17496570944786072,
0.06113084405660629,
0.38446247577667236,
0.6975393295288086,
0.6074769496917725,
0.4687986373901367,
-0.21100027859210968,
-0.12406748533248901,
0.6108659505844116,
0.2819189429283142,
-0.6002737283706665,
0.13958370685577393,
-0.6356881260871887,
0.22746232151985168,
-0.24487151205539703,
0.09954646229743958,
0.22664332389831543,
1.0173499584197998,
0.32593411207199097,
0.2184300571680069,
-1.2325669527053833,
-0.1606677770614624,
0.2917223274707794,
0.48632410168647766,
-0.1038307324051857,
-0.24872422218322754,
0.23835916817188263,
-0.26781582832336426,
0.0896378755569458,
-0.29540836811065674,
-0.14340783655643463,
1.1977057456970215,
-0.09226982295513153,
-0.052324358373880386,
0.5294311046600342,
-0.5065897107124329,
-0.8701998591423035,
-0.08304914832115173,
-0.40395206212997437,
-0.10231054574251175,
-0.3442971110343933,
0.6742062568664551,
0.4740379750728607,
-0.8861899375915527,
0.16243241727352142,
0.5656989216804504,
-0.09876840561628342,
0.6029759645462036,
-0.9840575456619263,
-0.020243681967258453,
0.24532295763492584,
0.6935551166534424,
-1.0656630992889404,
0.36697840690612793,
-1.082521915435791,
-0.372745156288147,
-0.18535549938678741,
-0.17513249814510345,
0.9809576869010925,
-0.519767165184021,
0.4305764436721802,
0.37380075454711914,
-0.4125421345233917,
-0.5594357252120972,
-0.07731308043003082,
-0.6612935662269592,
0.2653807997703552,
0.7366114258766174,
-0.11944904178380966,
-0.2683895528316498,
-0.8320472836494446,
0.4650839865207672,
0.02763071097433567,
-0.4982917010784149,
0.3566717207431793,
0.4375879168510437,
-0.40639403462409973,
0.2551852762699127,
0.2522740960121155,
0.2797308564186096,
0.08176693320274353,
0.6096766591072083,
1.027547001838684,
-0.06822244077920914,
0.07280931621789932,
-0.4624899923801422,
-0.7987837195396423,
0.5273711085319519,
0.3363044261932373,
-0.3317580223083496,
-0.02555728331208229,
0.46946027874946594,
0.7579659223556519,
-0.32778212428092957,
0.6512983441352844,
-1.236713171005249,
-0.77449631690979,
-0.6279515624046326,
-0.34464138746261597,
0.13416993618011475,
0.4310707449913025,
0.16455043852329254,
-1.1465593576431274,
-0.20345662534236908,
-0.1656046062707901,
0.6478452682495117,
0.18480715155601501,
-0.2715511918067932,
0.051466941833496094,
-0.19650746881961823,
0.7629095911979675,
-0.08770571649074554,
0.5104111433029175,
-0.4322209656238556,
0.029703248292207718,
0.16192255914211273,
-0.4247201681137085,
-0.05329667404294014,
-0.21176078915596008,
0.6774571537971497,
-0.46400973200798035,
0.49430596828460693,
-0.4716073274612427,
-0.3137989342212677,
-0.5689123272895813,
-1.1643093824386597,
0.5238805413246155,
0.581701934337616,
-0.6087163090705872,
0.36941462755203247,
-0.2699897885322571,
-0.7745481133460999,
0.5387117266654968,
0.1848175823688507,
0.1847829669713974,
-0.434682697057724,
0.049350664019584656,
0.061628490686416626,
-0.371610552072525,
0.2842724621295929,
-0.4648521840572357,
0.03377242758870125,
0.6700210571289062,
0.2046377807855606,
0.771131694316864,
-0.5543903112411499,
-0.7136576771736145,
-0.1243365928530693,
0.697898805141449,
1.4553391933441162,
0.8920606970787048,
0.40176141262054443,
-0.8064658045768738,
0.5711016654968262,
-0.5943312048912048,
-0.2086144983768463,
-0.11283719539642334,
-0.2590596377849579,
0.29624512791633606,
-0.5260027050971985,
0.3551267683506012,
0.3594006299972534,
0.5268956422805786,
0.657073438167572,
-0.17593145370483398,
0.29589152336120605,
0.37548765540122986,
0.1295015811920166,
0.3824804127216339,
0.2195706069469452,
0.15910284221172333,
0.4539888799190521,
-0.616488516330719,
0.41667109727859497,
0.5049493312835693,
0.21681813895702362,
-0.07182420790195465,
-0.3201029598712921,
-0.3232172429561615,
-0.4620135426521301,
0.5249391198158264,
0.7802754640579224,
-1.143091082572937,
0.8164501190185547,
-0.010476380586624146,
0.6470853686332703,
-0.5186482071876526,
-0.22604282200336456,
0.6890260577201843,
0.5114378929138184,
0.5146365761756897,
-0.9163835644721985,
0.1477082520723343,
-0.605388879776001,
0.1987428069114685,
0.12089822441339493,
-0.6562418937683105,
-0.8510251045227051,
-0.39985013008117676,
0.16950488090515137,
-0.2840534746646881,
0.4733668267726898,
1.1568922996520996,
-0.006425336003303528,
0.16787832975387573,
-0.18121036887168884,
-0.65891432762146,
0.835903525352478,
-0.45852261781692505,
-0.2510429620742798,
0.14125891029834747,
0.1821100264787674,
-0.34929633140563965,
0.43525636196136475,
-0.5057785511016846,
-0.8869581818580627,
-0.105242520570755,
-0.268693745136261,
0.4773956537246704,
0.1592417061328888,
-0.32798993587493896,
-0.2896541357040405,
-0.6753458380699158,
-0.30671271681785583,
0.47337159514427185,
-0.1887337863445282,
-0.2900608479976654,
0.24343378841876984,
-0.10525991022586823,
-0.757877767086029,
0.047981999814510345,
-0.15671353042125702,
-0.18306976556777954,
1.0395536422729492,
1.0525063276290894,
0.5716931819915771,
0.15402628481388092,
0.630238950252533,
-0.1963576376438141,
0.1969677060842514,
0.5003815293312073,
-0.5177527070045471,
-0.11981229484081268,
-0.1349036544561386,
-0.357354998588562,
-0.8614559769630432,
-0.6001103520393372,
0.11615388840436935,
-0.605549693107605,
0.8044324517250061,
-0.13422751426696777,
-0.6335288882255554,
-0.5379929542541504,
-0.60102379322052,
-0.27303293347358704,
0.543721079826355,
0.2620592713356018,
-0.4518240988254547,
0.6703835725784302,
-0.16661228239536285,
-0.12154070287942886,
-0.42679011821746826,
0.2755003571510315,
-0.4905644655227661,
-0.2334749400615692,
0.7377539873123169,
-0.21866342425346375,
0.01540346909314394,
-1.243302583694458,
-0.05366170033812523,
-0.4298146963119507,
0.016029980033636093,
-0.803648054599762,
-0.25640010833740234,
-0.009526928886771202,
-0.5752381682395935,
0.3598784804344177,
-0.22155626118183136,
-0.6357018947601318,
-0.09420885145664215,
-0.36945661902427673,
0.16939440369606018,
-0.08922543376684189,
-0.3800655007362366,
0.3693120777606964,
0.4311259984970093,
0.10327450931072235,
-0.3819926083087921,
0.10359440743923187,
0.4755135178565979,
0.14989714324474335,
0.4194983243942261,
-0.2787530720233917,
-0.7115157246589661,
0.5765430331230164,
-0.30639350414276123,
0.9327215552330017,
-0.9008511900901794,
-0.17280039191246033,
0.323469340801239,
-0.0785779356956482,
0.039497703313827515,
0.7614763379096985,
0.4267111122608185,
-0.30514276027679443,
-0.47593289613723755,
-0.13927893340587616,
0.37533804774284363,
-0.1794007420539856,
-0.3903628885746002,
-0.21171854436397552,
-0.2798192501068115,
-0.5670040249824524,
0.7630234956741333,
-0.11573895812034607,
0.6337074637413025,
0.3583340346813202,
-0.03178594261407852,
0.2846856117248535,
0.3475993573665619,
0.19635052978992462,
0.3986686170101166,
0.12307797372341156,
0.08527199178934097,
0.19151553511619568,
1.0997363328933716,
-0.3802746832370758,
0.5475068688392639,
-0.7846894264221191,
1.2159357070922852,
-1.2150120735168457,
-0.2509779632091522,
0.1589449942111969,
0.02060610242187977,
0.8335431814193726,
-0.9152474403381348,
0.6830517649650574,
0.3828813433647156,
-0.1000811755657196,
0.9945369362831116,
0.6698977947235107,
-0.7798150181770325,
0.10946637392044067,
-0.6884651780128479,
-1.3487300872802734,
0.5754952430725098,
0.20671233534812927,
-0.20475022494792938,
-0.6912362575531006,
-0.3345959782600403,
0.12170381844043732,
-0.20544110238552094,
0.13281691074371338,
0.5606054067611694,
-0.0820406824350357,
-0.17442817986011505,
0.11272858828306198,
0.011959165334701538,
0.18445102870464325,
-0.013821562752127647,
0.3465001583099365,
0.4581432044506073,
-0.12701071798801422,
0.23573912680149078,
-0.4987042546272278,
0.014126956462860107,
-0.35892510414123535,
0.22820208966732025,
0.24907025694847107,
-0.7449670433998108,
0.7386051416397095,
-0.5401920676231384,
-0.5509798526763916,
-0.39778977632522583,
-0.2441016286611557,
-0.0063562169671058655,
0.021870501339435577,
0.45846259593963623,
0.4577597975730896,
0.419173002243042,
-0.04333501309156418,
0.3291180729866028,
-0.3284345269203186,
-0.6743069887161255,
0.18947459757328033,
-0.6745339632034302,
-0.7244902849197388,
-0.07472319900989532,
0.2612987160682678,
-0.6381245851516724,
-0.09296197444200516,
-0.9258409142494202,
0.3155145049095154,
-0.5007469058036804,
-0.64539635181427,
-0.022502899169921875,
-0.2054825872182846,
-0.07051131874322891,
0.4324491024017334,
0.507885754108429,
0.027095379307866096,
-0.27430495619773865,
0.45681244134902954,
-0.47404539585113525,
-0.35339611768722534,
0.3434436321258545,
0.8942998051643372,
0.21864435076713562,
-0.8863433003425598,
-0.37938565015792847,
0.7433822751045227,
-0.08873822540044785,
-0.11459014564752579,
0.008327972143888474,
-0.023823192343115807,
0.3143308162689209,
-0.13512711226940155,
-0.160723477602005,
0.023447901010513306,
0.765270471572876,
-0.09687663614749908,
-0.03184166178107262,
-0.45774805545806885,
-1.0107375383377075,
-0.15937194228172302,
-0.7475796341896057,
0.2326802909374237,
0.8129662275314331,
0.23128391802310944,
0.3706379234790802,
-0.28962239623069763,
-0.6665962338447571,
-0.3463842272758484,
-0.6669764518737793,
0.31625238060951233,
-1.3447825908660889,
-0.7273931503295898,
-0.11533058434724808,
-0.3026553690433502,
-0.06524305790662766,
0.4758911430835724,
-0.20551975071430206,
0.5264742970466614,
-0.5485853552818298,
-0.28298208117485046,
0.018613437190651894,
0.7157037258148193,
-0.2959011495113373,
-1.071932077407837,
-0.23432479798793793,
0.14406272768974304,
-0.35233786702156067,
-0.43264055252075195,
-0.0012103384360671043,
0.16459888219833374,
-0.29342690110206604,
0.5775461196899414,
-0.05863242968916893,
0.4189000427722931,
-1.454815149307251,
-0.8862277269363403,
0.387790709733963,
0.1395450234413147,
0.5157650709152222,
0.3239627778530121,
-0.04076327383518219,
1.1126316785812378,
0.35081106424331665,
-0.2145264744758606,
-0.6899535059928894,
0.3950902223587036,
-1.2730623483657837,
-0.15978358685970306,
0.9361515641212463,
0.4767620265483856,
0.20249620079994202,
-0.8742091655731201,
-0.4266473054885864,
0.128260999917984,
-0.8989463448524475,
0.5353510975837708,
-0.5060581564903259,
0.64553302526474,
-0.5895113348960876,
0.35738664865493774,
0.5279812812805176,
0.21466413140296936,
-0.16026504337787628,
1.516301155090332,
-0.2910412847995758,
-0.17769482731819153,
0.28892698884010315,
0.19360296428203583,
-0.40852656960487366,
0.19458432495594025,
0.14797116816043854,
-0.2706565856933594,
-0.380605548620224,
0.3211468458175659,
-0.14180052280426025,
-0.08671560883522034,
0.18144968152046204,
-0.8410072326660156,
-0.10004645586013794,
-0.2895960509777069,
-0.18359529972076416,
0.6339693069458008,
-0.007205150555819273,
-0.9304946660995483,
0.4937155246734619,
-1.0556814670562744,
-0.7929936647415161,
0.05259149149060249,
-0.572630763053894,
-0.18070738017559052,
-0.27239900827407837,
-0.34399908781051636,
-0.4924654960632324,
0.8183204531669617,
-0.00954633392393589,
0.17308452725410461,
-0.096793994307518,
0.3872884511947632,
-0.4941850006580353,
-0.04009822756052017,
-0.253428190946579,
-0.3931294083595276,
-0.9619650840759277,
-0.16187536716461182,
0.07077805697917938,
0.9324469566345215,
-0.6225448846817017,
-0.27173343300819397,
-0.10538293421268463,
0.012428145855665207,
0.02491835318505764,
0.35134357213974,
0.20514033734798431,
-0.601768970489502,
-0.8277531862258911,
-0.37693554162979126,
-0.29040977358818054,
0.015206185169517994,
-0.8437455892562866,
0.30519863963127136,
-0.2558758854866028,
-0.8112367391586304,
0.17263969779014587,
-0.3031502664089203,
-0.1901848167181015,
0.2815169095993042,
-0.19573332369327545,
1.0394959449768066,
0.3476519286632538,
-0.31280601024627686,
0.3580508828163147,
0.3652595281600952,
-0.09988459199666977,
0.3311555087566376,
-0.6807249188423157,
-0.013482760637998581,
0.2066354900598526,
0.5946981310844421,
0.674781322479248,
0.24936801195144653,
0.28397616744041443,
0.7201439142227173,
1.0208303928375244,
0.2552434802055359,
-0.2767848074436188,
0.451576828956604,
0.22259315848350525,
0.4551372826099396,
0.06688275933265686,
0.010552078485488892,
-0.3660048246383667,
-0.28783950209617615,
0.30998972058296204,
-0.09023924171924591,
-0.3263688385486603,
0.18701337277889252,
-0.12575776875019073,
0.040280845016241074,
-0.950067400932312,
-0.7465807199478149,
0.16587400436401367,
-0.25491616129875183,
0.8146259188652039,
0.348889023065567,
0.2240915298461914,
0.6747181415557861,
0.463026762008667,
0.10998242348432541,
-0.4348103404045105,
0.2307009994983673,
-0.11999710649251938,
0.780940592288971,
1.113529920578003,
0.5194080471992493,
0.39654383063316345,
0.2211347073316574,
0.1599806249141693,
-0.543630063533783,
-0.2085997611284256,
0.2165742963552475,
-0.9426705837249756,
0.13528747856616974,
-0.10546556115150452,
0.5597386956214905,
-0.35573509335517883,
-0.46095341444015503,
0.5219680666923523,
-0.8644562363624573,
-0.06274887919425964,
0.5418747067451477,
-0.6589614748954773,
0.5600603818893433,
0.9227309226989746,
0.0880909338593483,
0.31845203042030334,
0.186119943857193,
0.21163010597229004,
-0.2670011818408966,
1.0333302021026611,
1.6544982194900513,
-0.665367841720581,
0.29673075675964355,
0.34485363960266113,
-0.5779839754104614,
0.14813031256198883,
0.04037037864327431,
-0.26970338821411133,
0.4190314710140228,
-0.9398043155670166,
-0.4274739921092987,
0.33425959944725037,
0.27668121457099915,
0.3887079358100891,
-0.32171502709388733,
-0.0011461022077128291,
-0.17355114221572876,
-0.2543765604496002,
-0.560710608959198,
1.3185548782348633,
0.6838871836662292,
-0.6356011033058167,
-0.1525610387325287,
0.16387775540351868,
-0.5552929043769836,
0.028972763568162918,
-0.47106435894966125,
0.5057858824729919,
0.24526971578598022,
-0.25383663177490234,
0.05013877525925636,
-0.09468824416399002,
-0.2563525140285492,
-0.960000216960907,
-0.5165377855300903,
-0.361244797706604,
0.6164495348930359,
0.27554211020469666,
0.08486657589673996,
0.6130015254020691,
-0.8883051872253418,
0.5024373531341553,
0.5709731578826904,
1.2142800092697144,
0.18330401182174683,
-0.005798286758363247,
0.7778769135475159,
0.4693388044834137,
-0.6481119394302368,
0.4693112075328827,
1.2032874822616577,
0.0442747063934803,
0.37961360812187195,
-0.5137386918067932,
0.27666017413139343,
0.3229154646396637,
-0.012697814032435417,
0.8693537712097168,
0.305660218000412,
-0.1319650411605835,
-0.09112118929624557,
-0.7698027491569519,
0.023348232731223106,
-0.996414303779602,
-0.38052091002464294,
-0.6273740530014038,
0.779381513595581,
0.11298022419214249,
-0.00564132584258914,
0.8969290852546692,
-0.4632985293865204,
4.1074419021606445,
0.9869149327278137,
0.4133239984512329,
-0.25754889845848083,
0.48185935616493225,
0.5296425223350525,
-0.1674930453300476,
-0.5732994675636292,
0.45285406708717346,
-1.0802557468414307,
-0.4499521553516388,
-0.011541574262082577,
0.06245977431535721,
-0.1551973670721054,
0.09391798079013824,
0.855665922164917,
-0.10010992735624313,
-0.42851701378822327,
0.0012448109919205308,
-1.1879935264587402,
-0.5962635278701782,
0.4614916145801544,
0.4932093024253845,
0.119712695479393,
-0.1668214201927185,
0.20267608761787415,
0.41959258913993835,
-0.6013771295547485,
-0.27237042784690857,
-0.018940676003694534,
-1.6116169691085815,
-1.2254421710968018,
0.17288856208324432,
0.5092293620109558,
-0.9923365116119385,
0.4927736222743988,
0.4390598237514496,
-0.26319512724876404,
-0.03703481703996658,
0.14867337048053741,
0.45207831263542175,
-0.8831522464752197,
0.3993544578552246,
-0.166571706533432,
-0.4516292214393616,
0.9504247903823853,
-0.04121365025639534,
0.8583829998970032,
-0.21772617101669312,
-0.07217630743980408,
0.2389388233423233,
-0.0507199652493,
0.49558764696121216,
-0.06127862259745598,
-0.7670519948005676,
0.361741840839386,
-0.4443728029727936,
-0.07996676862239838,
-0.17665506899356842,
-0.1811571717262268,
0.38533785939216614,
-0.311972439289093,
0.4542827308177948,
0.24471622705459595,
0.09117884933948517,
0.6568618416786194,
0.3914673328399658,
0.10921349376440048,
-0.19318288564682007,
0.2571694552898407,
-0.37273794412612915,
-0.5217568278312683,
0.007253082934767008,
-0.04654943570494652,
-0.13665913045406342,
-0.39511001110076904,
0.4840620160102844,
-0.05680140480399132,
-0.006655487697571516,
-0.0026834073942154646,
0.31537267565727234,
-0.4398761987686157,
-0.33573848009109497,
-0.1516721397638321,
0.06703724712133408,
0.3146313726902008,
-0.5109789371490479,
0.24720844626426697,
-0.06719861924648285,
0.05560003221035004,
0.5028294920921326,
1.0333952903747559,
0.300957590341568,
0.5580549836158752,
-0.47456711530685425
] |
Phase Transitions in Induced QCD
|
The variety of the phase transitions in Induced QCD are studied. Depending upon the parameters in the scalar field potential, there could be infinite number of fixed points, with different critical behavior. The integral equation for the density of the eigenvalues of the scalar field are generalized to the weak coupling phases, with the gap at the origin. We find a wide class of the massive solutions of these integral equations in the strong coupling phases, and derive an explicit eigenvalue equation for the scalar branch of the mass spectrum.
|
A.A.Migdal
|
hep-lat hep-th
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208008
|
hep-lat/9208009
|
[
0.3860890865325928,
-0.11205468326807022,
-0.4653671979904175,
-0.27107733488082886,
-0.5162307024002075,
-0.08365888148546219,
-0.2141026258468628,
-0.5492551326751709,
-0.5043011903762817,
0.7766392230987549,
0.565087616443634,
-0.27656233310699463,
-0.22394488751888275,
-1.5457290410995483,
-0.46793919801712036,
0.2739209234714508,
-0.2873603403568268,
-0.6527292728424072,
-0.8344590663909912,
0.3895902931690216,
0.6340954303741455,
-0.44312700629234314,
-1.1656179428100586,
-0.7797887921333313,
-0.29291415214538574,
0.36912739276885986,
-0.3417202830314636,
-0.34533366560935974,
0.6632204651832581,
0.32669487595558167,
0.35080525279045105,
-0.056962013244628906,
-0.46831515431404114,
-0.859385073184967,
-0.006190324667841196,
-0.6723763942718506,
-0.05077465996146202,
-0.36502769589424133,
0.8534961938858032,
-0.3482416570186615,
0.15408837795257568,
0.2891032099723816,
-0.6930696964263916,
0.043695997446775436,
0.07591163367033005,
-0.41197484731674194,
-0.7036615610122681,
-0.37844178080558777,
0.7276149392127991,
-1.2466462850570679,
0.48498275876045227,
0.40882858633995056,
0.5818306803703308,
-0.2829868495464325,
-0.13258032500743866,
-0.9311434030532837,
0.06550697237253189,
0.8362718224525452,
-0.7554898858070374,
-0.048450637608766556,
0.8949032425880432,
0.2357722669839859,
0.058255717158317566,
-0.8671733736991882,
0.17919078469276428,
0.3488948941230774,
-0.5315694212913513,
0.5349410772323608,
-0.2649332284927368,
-0.2938932776451111,
0.033774808049201965,
-0.27639615535736084,
-0.7361302375793457,
0.06176762282848358,
-0.9305972456932068,
0.28883618116378784,
0.041169423609972,
-0.10257594287395477,
-1.7480335235595703,
-0.49647045135498047,
-0.428531289100647,
-0.33973270654678345,
-0.5056244134902954,
0.31320929527282715,
-0.21711567044258118,
-0.5931973457336426,
-0.07167990505695343,
-0.30755436420440674,
0.20364786684513092,
0.21573175489902496,
0.33745408058166504,
0.9902607798576355,
0.04408221319317818,
-0.24389657378196716,
0.5864876508712769,
0.06991606950759888,
0.011876325123012066,
0.21211126446723938,
0.14738386869430542,
0.40368589758872986,
-0.4679516553878784,
0.20469725131988525,
-0.9194048643112183,
0.379819393157959,
0.2434239685535431,
0.22927533090114594,
0.3845433294773102,
-0.07924860715866089,
0.06504299491643906,
-0.6717343926429749,
0.3124612867832184,
-0.31109485030174255,
-0.09949962049722672,
0.3441051244735718,
-0.20664235949516296,
0.9151023626327515,
0.3410794734954834,
0.18200820684432983,
-0.44169554114341736,
-0.514381468296051,
0.0832558125257492,
-0.35755613446235657,
-0.024326499551534653,
0.579230546951294,
0.2876608967781067,
-0.06332124024629593,
0.3639410436153412,
0.3471563160419464,
-0.777603805065155,
-0.00787646509706974,
-0.15930478274822235,
-0.09722046554088593,
-0.45058968663215637,
0.5098795890808105,
-0.16814909875392914,
-0.6429694890975952,
-0.6297383308410645,
0.6641113758087158,
0.3685299754142761,
-0.37266331911087036,
0.46535366773605347,
-0.26763221621513367,
0.7746327519416809,
1.122567892074585,
-0.5317189693450928,
0.28964146971702576,
0.028793739154934883,
0.6796543598175049,
0.022711217403411865,
0.3348734974861145,
-0.865347146987915,
-0.4114025831222534,
-0.25931522250175476,
1.0793647766113281,
-0.2540213465690613,
0.16618433594703674,
0.06759854406118393,
-0.19186973571777344,
-0.5674034953117371,
-0.32976701855659485,
-0.34081125259399414,
0.028479021042585373,
0.37753063440322876,
-0.010129554197192192,
-0.5024596452713013,
0.29988953471183777,
-0.5108740925788879,
-0.5176001787185669,
0.018473684787750244,
-1.00295889377594,
-0.018693167716264725,
0.15763233602046967,
-0.3857291638851166,
0.7136971354484558,
0.24647122621536255,
0.740922212600708,
0.19192653894424438,
-0.19745604693889618,
0.4984464645385742,
-0.17221666872501373,
-0.3611706793308258,
-0.06441211700439453,
0.7646443247795105,
0.14988316595554352,
0.11262659728527069,
-0.41109585762023926,
-0.6146085262298584,
-0.7125588655471802,
0.14005468785762787,
0.1424446403980255,
-0.36301615834236145,
-0.07833459228277206,
-0.23987077176570892,
0.4713325500488281,
-0.559238612651825,
-0.3145582973957062,
-0.9176433682441711,
-0.5214674472808838,
0.10431031882762909,
-0.9930757284164429,
-0.2407313883304596,
0.11859128624200821,
-0.190245121717453,
0.42391255497932434,
-0.6790780425071716,
-0.13425855338573456,
1.146435022354126,
0.5346400141716003,
-0.35119369626045227,
-0.2894994616508484,
0.08761323988437653,
-0.03850340470671654,
0.3443901538848877,
-0.2679738402366638,
-0.051660191267728806,
0.716607928276062,
0.23006345331668854,
0.3392057716846466,
0.08377201855182648,
1.0065183639526367,
-0.23788605630397797,
0.6866005063056946,
0.35916441679000854,
0.5641250014305115,
-0.2592196762561798,
-0.15370860695838928,
-0.5448941588401794,
0.4347385764122009,
0.35884976387023926,
-0.06156807020306587,
-0.608562707901001,
0.5536397695541382,
0.05331204831600189,
0.3757398724555969,
0.3271569013595581,
-0.11204291135072708,
0.001989746233448386,
-0.3074245750904083,
0.4952118694782257,
0.7843925952911377,
-0.486378937959671,
-0.6898166537284851,
0.45617398619651794,
-0.2666684687137604,
0.09892065823078156,
0.8754811882972717,
-0.24182358384132385,
0.1535768359899521,
-0.5474815964698792,
0.4456561803817749,
-0.3185991048812866,
0.14690206944942474,
0.28171804547309875,
0.40881815552711487,
-0.4035130739212036,
-0.07912146300077438,
0.21693077683448792,
0.6022869348526001,
-0.03875848650932312,
-0.49177443981170654,
0.13607214391231537,
0.35922810435295105,
-0.014347008429467678,
-0.41087818145751953,
-0.2527598440647125,
1.139260172843933,
0.2556425631046295,
-0.18106842041015625,
0.3994002044200897,
-0.10358606278896332,
-1.0774180889129639,
0.07449791580438614,
-1.250835657119751,
0.05100370571017265,
-0.6780108213424683,
-0.4199689030647278,
0.29708409309387207,
-0.8833782076835632,
0.5887435674667358,
-0.5986825227737427,
-0.23743079602718353,
0.2676754295825958,
-0.016932034865021706,
0.7601134777069092,
0.16295789182186127,
-0.2202327698469162,
-0.33214977383613586,
1.1582530736923218,
-0.26146575808525085,
-0.28179943561553955,
-0.809076726436615,
0.3970474302768707,
0.7046335935592651,
-1.0277053117752075,
0.17035578191280365,
-0.6030475497245789,
-0.25072968006134033,
0.3103398084640503,
0.431241512298584,
-0.5408068895339966,
-0.23077812790870667,
0.6895934343338013,
-0.29581183195114136,
-0.2773978114128113,
-1.4496396780014038,
0.2504407465457916,
0.4697548449039459,
-0.35283002257347107,
0.09525838494300842,
0.22419339418411255,
-0.23317654430866241,
0.6709359884262085,
0.16909123957157135,
-0.3442547917366028,
-0.14017122983932495,
0.8153671026229858,
0.5029554963111877,
-0.0903884544968605,
0.14180514216423035,
-0.32998260855674744,
-0.8399286866188049,
0.08734723180532455,
-0.4441818594932556,
-0.7211428880691528,
-0.5388393402099609,
0.6833022832870483,
0.3261755704879761,
-0.19665668904781342,
0.5191466808319092,
-0.32026052474975586,
-0.6513344049453735,
0.44428640604019165,
-0.40857937932014465,
0.745631992816925,
-0.38759559392929077,
-0.00919796247035265,
-0.7638986706733704,
0.11080286651849747,
0.40950196981430054,
0.5539838075637817,
0.35142162442207336,
0.07476910203695297,
0.17683541774749756,
0.43563687801361084,
0.2739831805229187,
0.06589006632566452,
-0.36235499382019043,
-0.4342207908630371,
-0.6910276412963867,
0.1483096182346344,
-0.5480598211288452,
0.0045749731361866,
-0.020289979875087738,
0.6072471737861633,
0.5297979116439819,
0.7848008871078491,
-0.09984862804412842,
0.32423922419548035,
-0.06271303445100784,
-0.5976036190986633,
0.49233245849609375,
0.544045090675354,
0.47082802653312683,
-0.6822137832641602,
-0.8042957186698914,
-0.31051331758499146,
-0.12104184180498123,
-0.4837181568145752,
-0.07912544906139374,
-0.4705493748188019,
0.21293535828590393,
0.07478044927120209,
-0.8185254335403442,
0.666650116443634,
-0.32537782192230225,
-0.0425601564347744,
0.6796771287918091,
0.11803704500198364,
1.265486240386963,
-0.8523374795913696,
-0.057880595326423645,
0.4704941213130951,
0.34223195910453796,
0.03819756954908371,
0.2813356816768646,
0.10432523488998413,
-0.07537321001291275,
-0.23585145175457,
0.4074028432369232,
-0.6163685917854309,
-1.0570564270019531,
0.10331369191408157,
-0.0564308799803257,
0.03594323247671127,
-0.31492742896080017,
-0.1681220829486847,
0.6962898373603821,
0.12879103422164917,
0.3975052237510681,
0.1859297901391983,
1.011408805847168,
0.27479106187820435,
0.5312470197677612,
0.7641851902008057,
0.5130984783172607,
0.4510059952735901,
-0.5946888327598572,
0.10002496838569641,
0.24973775446414948,
0.1375265121459961,
-0.08069148659706116,
0.30958127975463867,
-0.31206825375556946,
-0.26195839047431946,
0.31981831789016724,
0.2271200567483902,
-0.3322256803512573,
0.023572375997900963,
-0.020387256518006325,
0.561435878276825,
-0.41449177265167236,
0.09449377655982971,
0.18706893920898438,
-0.1625021994113922,
0.7284877300262451,
-1.0188696384429932,
0.15027877688407898,
-0.7142676711082458,
0.35610073804855347,
0.5554565191268921,
-1.157060146331787,
-0.6550848484039307,
-0.7730394005775452,
-0.008222459815442562,
-0.1591901034116745,
-0.08240479975938797,
0.6122532486915588,
0.6370600461959839,
-0.10527526587247849,
-0.7191914319992065,
-0.1693534106016159,
0.3403504192829132,
-0.015302133746445179,
-0.5849994421005249,
0.5318494439125061,
-0.1242368072271347,
0.06286374479532242,
0.8719642758369446,
0.06728973984718323,
-0.5634663105010986,
-0.13572129607200623,
-0.8872342109680176,
0.9001489281654358,
-0.5407198071479797,
0.14746986329555511,
0.02570168301463127,
-0.10316070169210434,
-0.9557861089706421,
0.5364671349525452,
0.33261898159980774,
-0.06528853625059128,
-0.4340860843658447,
0.014428926631808281,
-0.7490230798721313,
0.14531898498535156,
0.01999378390610218,
0.15662521123886108,
1.1796354055404663,
0.6785159707069397,
0.5154166221618652,
0.23755139112472534,
0.4481349587440491,
0.25655731558799744,
-0.41443005204200745,
0.4938291907310486,
-0.18880507349967957,
0.0479852519929409,
-0.03521667793393135,
-0.21251225471496582,
-0.4964313507080078,
-0.564315915107727,
0.03249324485659599,
-0.3375358283519745,
0.2650279998779297,
-0.16287867724895477,
-0.8329951763153076,
0.02553037740290165,
-0.19127687811851501,
-0.7638497352600098,
0.5504790544509888,
0.4151729941368103,
-0.3908367156982422,
0.5899768471717834,
-0.3468664884567261,
0.4625675678253174,
0.03794386237859726,
-0.8350608348846436,
-0.5739399790763855,
0.9735487103462219,
0.7242662906646729,
0.6561145782470703,
0.1555923968553543,
-0.7094951868057251,
0.3828311264514923,
-0.7152971029281616,
-0.12536326050758362,
-0.5342477560043335,
-0.020745621994137764,
0.3088575601577759,
-0.5151726007461548,
0.15164892375469208,
0.019609522074460983,
0.010950226336717606,
0.3049233853816986,
-0.27482733130455017,
-0.3035212457180023,
0.5452468395233154,
-0.35586509108543396,
-0.10629525035619736,
0.1786264032125473,
0.4727291166782379,
-0.3645744025707245,
0.04025029391050339,
0.21961480379104614,
-0.6412125825881958,
0.38672834634780884,
0.9075126647949219,
-1.2207043170928955,
0.555777907371521,
-0.06467963755130768,
0.2827732563018799,
-0.5623382329940796,
-0.2133944034576416,
-0.4845416843891144,
-0.641487181186676,
-0.32535961270332336,
0.3020390570163727,
0.15962153673171997,
-0.519051194190979,
-1.0673820972442627,
0.18944984674453735,
0.5024199485778809,
0.07485882192850113,
-0.19268912076950073,
-0.3979127109050751,
-0.745098888874054,
-0.4132488965988159,
0.9978119730949402,
-0.6430284976959229,
-0.31735384464263916,
0.09980017691850662,
-0.19785617291927338,
0.10089799016714096,
0.7495185136795044,
0.012132066302001476,
-0.3626655638217926,
0.2795596718788147,
0.723296046257019,
-0.20513267815113068,
1.3156282901763916,
-0.5992960333824158,
0.759704053401947,
-0.7885624170303345,
0.6274561882019043,
-0.12968599796295166,
-0.13483619689941406,
0.0361863449215889,
-0.2629648447036743,
0.6688398122787476,
-1.0098750591278076,
0.33236780762672424,
0.7043527960777283,
0.08958809077739716,
0.3503097891807556,
0.013784840703010559,
-0.6298465132713318,
0.08877915889024734,
-0.6091527938842773,
-0.5799403190612793,
0.3085395097732544,
-0.1361224353313446,
-0.38744428753852844,
-0.09478525072336197,
-0.09173434972763062,
-0.13515296578407288,
-0.17972435057163239,
0.6151923537254333,
0.9046061038970947,
0.3735976815223694,
0.39731842279434204,
-0.42732685804367065,
-0.3804038166999817,
-0.5125128626823425,
0.2877432703971863,
0.3294062912464142,
-0.48214656114578247,
-0.23100332915782928,
0.4324271082878113,
-0.22517162561416626,
-1.34395170211792,
-0.5892497301101685,
0.27018752694129944,
0.36715468764305115,
-0.5775899291038513,
0.9037594795227051,
0.09436971694231033,
-0.069966159760952,
-0.4249526560306549,
0.22315917909145355,
0.19073866307735443,
0.7599392533302307,
0.536170482635498,
0.5921951532363892,
0.5126384496688843,
-0.2986126244068146,
1.0997017621994019,
-0.08693698793649673,
-0.2853121757507324,
0.49241897463798523,
-0.3009907007217407,
-0.6679069399833679,
0.4937155842781067,
0.8849913477897644,
-1.0538735389709473,
-0.11306049674749374,
-0.3469099700450897,
0.08232452720403671,
-0.5181505680084229,
-0.34196966886520386,
-0.07174380123615265,
-0.3192814588546753,
-0.5665090680122375,
0.05998483672738075,
0.7852636575698853,
-0.32499298453330994,
-0.10537341982126236,
-0.13423146307468414,
-0.21714752912521362,
-0.5073009133338928,
-0.5159295201301575,
1.2371636629104614,
-0.4545539915561676,
-0.7057503461837769,
0.012319046072661877,
-0.03893933445215225,
-0.2970793843269348,
-0.11719076335430145,
0.6182417869567871,
-0.3992404341697693,
0.7744513750076294,
0.6080545783042908,
0.19345150887966156,
0.4404310882091522,
0.6101006865501404,
-0.06522146612405777,
0.64113849401474,
0.32584646344184875,
-0.6600379943847656,
-0.8608049154281616,
0.1532081514596939,
-0.005472355987876654,
0.43087056279182434,
0.34712323546409607,
0.14493830502033234,
0.04450821876525879,
-0.29387637972831726,
0.3934567868709564,
-0.48861682415008545,
-0.43031972646713257,
-0.5111836791038513,
-0.9541317224502563,
-0.14758968353271484,
0.3316267132759094,
-0.23414970934391022,
0.8141470551490784,
-0.2855881154537201,
-0.7801666855812073,
-0.29073861241340637,
-0.07476923614740372,
-0.05976681783795357,
0.5260001420974731,
-0.12256356328725815,
-0.4849836230278015,
-0.09020838886499405,
-0.7772171497344971,
0.0110433679074049,
-0.7977681159973145,
0.2974647283554077,
-0.30103635787963867,
0.16012132167816162,
0.4266416132450104,
-0.24294956028461456,
1.0151702165603638,
-0.5860615968704224,
-0.9405324459075928,
-0.21835650503635406,
-0.5378225445747375,
-0.5268363356590271,
0.870340883731842,
-0.1338454782962799,
0.780876636505127,
0.3938579857349396,
0.5615507364273071,
0.18324105441570282,
0.03676437586545944,
-0.28750720620155334,
0.2254389524459839,
0.3809005320072174,
0.5473634004592896,
-0.11561930924654007,
-0.9071688055992126,
-0.3081687092781067,
0.32533079385757446,
-0.6498740911483765,
-0.0023355288431048393,
-0.4759487509727478,
0.519576370716095,
0.43297767639160156,
0.3595551550388336,
0.23721987009048462,
1.1033272743225098,
0.29861098527908325,
0.4926000237464905,
0.01533166877925396,
-0.23875774443149567,
0.5946483612060547,
0.0952301174402237,
0.3442762494087219,
0.14969387650489807,
-0.7802416086196899,
-0.2587697505950928,
-0.6812292337417603,
0.3624497652053833,
-0.04468550160527229,
0.09691030532121658,
-0.14030063152313232,
-0.09829960763454437,
-0.01455032080411911,
-0.28268808126449585,
-0.64341139793396,
0.614500105381012,
0.018146898597478867,
-1.2130980491638184,
0.024364659562706947,
-0.34538573026657104,
-0.5956679582595825,
0.8375906348228455,
-0.5070459842681885,
-0.0341518260538578,
0.5115890502929688,
-0.4235783815383911,
-0.007718733511865139,
-0.17362935841083527,
-0.9453019499778748,
0.06271424889564514,
0.4801422357559204,
0.669206976890564,
-0.35904234647750854,
-0.2423330694437027,
-0.1860361397266388,
-0.1642477810382843,
-0.22146075963974,
0.1884477734565735,
-1.3689351081848145,
0.3434547185897827,
-1.0862433910369873,
-1.1322448253631592,
-0.15044090151786804,
0.3063439428806305,
0.09454265981912613,
-0.656435489654541,
0.0011192187666893005,
0.2567015290260315,
-0.007350747007876635,
-0.04161207750439644,
-0.4458909332752228,
-0.6215082406997681,
-0.35840222239494324,
0.23758715391159058,
0.1132943332195282,
-0.18346385657787323,
0.40013188123703003,
0.17589065432548523,
0.40957581996917725,
0.07477205246686935,
-0.13502465188503265,
0.9059000611305237,
0.4323209822177887,
-0.10274577885866165,
0.3672597110271454,
0.4998771846294403,
0.20385846495628357,
-0.15854570269584656,
-0.40028175711631775,
0.34623828530311584,
0.21028481423854828,
0.06353902816772461,
0.7350117564201355,
0.3300636112689972,
-0.01039407029747963,
0.14751704037189484,
0.0929081067442894,
0.36719223856925964,
-0.7941655516624451,
0.20446360111236572,
0.44480839371681213,
0.5032973885536194,
0.19217932224273682,
-0.4607611298561096,
0.12040336430072784,
0.30188390612602234,
0.6549822092056274,
0.24832089245319366,
-0.3629882037639618,
-0.4574263095855713,
-0.05244306102395058,
0.08081025630235672,
-0.3599857687950134,
-0.2231741100549698,
0.028574960306286812,
0.3747461140155792,
1.101249098777771,
0.4326762557029724,
-0.21038301289081573,
0.21330775320529938,
0.577405571937561,
0.2753084599971771,
0.11995931714773178,
0.3281638026237488,
-0.05091597139835358,
0.5733789205551147,
0.3656155467033386,
0.5129066109657288,
0.22089135646820068,
0.5691867470741272,
0.030268987640738487,
-1.233362078666687,
0.024469660595059395,
0.21398229897022247,
-0.3349876403808594,
0.16234448552131653,
-0.5246357917785645,
0.22162188589572906,
0.2969914972782135,
-0.5088839530944824,
0.5119620561599731,
-0.9571402668952942,
-0.037489891052246094,
0.7044095993041992,
-0.3739272654056549,
0.028851743787527084,
0.5558600425720215,
-0.0019138817442581058,
0.440096378326416,
0.3405987322330475,
0.42648911476135254,
0.23260143399238586,
1.280424952507019,
1.4300792217254639,
-0.11994406580924988,
-0.13828200101852417,
0.37734338641166687,
-0.31458988785743713,
-0.09608098864555359,
0.006063250359147787,
-0.5170283913612366,
0.8193544745445251,
-0.08578807860612869,
-0.07066083699464798,
-0.05176008865237236,
0.18320001661777496,
-0.06782065331935883,
-0.15355879068374634,
0.7802978754043579,
0.40472733974456787,
0.3729279935359955,
-0.6876130104064941,
1.3802876472473145,
0.2582395374774933,
-0.32938647270202637,
-0.3183854818344116,
0.23664803802967072,
-0.009399267844855785,
-0.8103760480880737,
-0.32104602456092834,
0.331959068775177,
-0.51142418384552,
0.16750426590442657,
-0.2603316307067871,
-0.3154367506504059,
-0.4826682209968567,
-0.3446846902370453,
0.427886426448822,
-0.8074964880943298,
0.4886813461780548,
0.2771990895271301,
0.10668910294771194,
0.5713207721710205,
-0.6434816122055054,
-0.21093504130840302,
0.38325393199920654,
0.8944503664970398,
-0.06389158219099045,
0.6747233867645264,
0.31996044516563416,
0.7641716003417969,
-0.12033647298812866,
-0.09567507356405258,
0.8873758912086487,
-0.9282429814338684,
0.3443959057331085,
-0.6447983980178833,
-0.05863584578037262,
0.6738373637199402,
-0.2862332761287689,
0.3694611191749573,
1.1162744760513306,
0.3818272054195404,
0.3046783208847046,
-0.2697235941886902,
0.09270180016756058,
-0.9091277718544006,
0.7548232078552246,
-1.0116089582443237,
0.4788052439689636,
-0.21846863627433777,
0.18052947521209717,
-0.12953446805477142,
-0.7546771168708801,
4.324425220489502,
0.24015910923480988,
0.6048532724380493,
0.2444048970937729,
0.04303669556975365,
0.9633655548095703,
-0.20984140038490295,
-0.7603326439857483,
-0.0689350888133049,
-0.6665131449699402,
0.02773781679570675,
0.4982660412788391,
0.024442806839942932,
0.44249576330184937,
0.2723441421985626,
1.241428017616272,
-0.5330925583839417,
-0.11564548313617706,
0.3449925482273102,
-0.6426746845245361,
-0.36483967304229736,
0.03346015512943268,
-0.3413184881210327,
0.0745445266366005,
0.2687053978443146,
0.6752920150756836,
-0.02670590952038765,
-0.10165929794311523,
-0.16483326256275177,
0.036933671683073044,
-0.5466209650039673,
-0.499311625957489,
0.3383973240852356,
0.24187463521957397,
-0.7951570749282837,
0.2468622773885727,
-0.10182331502437592,
-0.5464818477630615,
-0.07964879274368286,
-0.3555768132209778,
-0.3790166676044464,
-0.644893229007721,
0.17746518552303314,
-0.4077058434486389,
-0.9131665825843811,
1.1336568593978882,
-0.5679495334625244,
0.46446865797042847,
0.5572136640548706,
-0.9718961715698242,
0.3129807412624359,
0.0006442193989641964,
0.30328795313835144,
-0.36711472272872925,
-0.18332700431346893,
0.5240187048912048,
-0.2117801457643509,
-0.16994412243366241,
0.07453178614377975,
0.7148436307907104,
0.11917778104543686,
-0.8820962309837341,
-1.0071532726287842,
0.24925066530704498,
0.137291818857193,
0.040243733674287796,
-0.333853155374527,
0.33746564388275146,
-0.5037798881530762,
0.18760816752910614,
-0.09935439378023148,
0.4585614800453186,
-0.5524194240570068,
0.697039783000946,
0.4579252004623413,
0.03513561189174652,
-0.7494692802429199,
-0.39895159006118774,
-0.06613772362470627,
-0.41856101155281067,
0.41094639897346497,
-0.3612660765647888,
-0.5972883105278015,
-0.03899850696325302,
0.02433394268155098,
0.49933478236198425,
0.1727079153060913,
-0.10953973978757858,
-0.34816521406173706,
0.805023729801178,
0.1714797019958496,
0.5418927073478699,
0.4589638113975525,
-0.10485000163316727,
-0.774906575679779
] |
A New Technique for Measuring the Strangemess Content of the Proton on the Lattice
|
A new technique for computing the strangeness content of the proton on the lattice is described. It is applied to the calculation of the strange quark contribution to the proton's spin, specifically to the evaluation of the proton matrix element of the strange quark axial current. Preliminary results are not in disagreement with the EMC experiment. NOTE: This paper is available only in postscript form.
|
Jeffrey E. Mandula and Michael C. Ogilvie
|
hep-lat hep-ph
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208009
|
hep-lat/9208010
|
[
0.8868435025215149,
-0.6233701705932617,
0.004898277577012777,
0.31325048208236694,
-0.4869615137577057,
-0.11065587401390076,
-0.16289973258972168,
-0.8143694996833801,
-0.7759321331977844,
0.9691042304039001,
0.5936384797096252,
-0.27365583181381226,
0.3728843927383423,
-0.5778270959854126,
-0.05963252857327461,
0.21941624581813812,
-0.5401260256767273,
-0.44613441824913025,
-1.7128928899765015,
0.5291796922683716,
0.8769700527191162,
-0.3572515547275543,
-0.662135899066925,
-0.2643308937549591,
-0.7315106391906738,
0.8267261385917664,
0.04951929301023483,
0.18902796506881714,
0.8468278050422668,
0.27569928765296936,
0.2647284269332886,
-0.36320996284484863,
-0.13099108636379242,
-0.7791697978973389,
0.46256357431411743,
-0.11365125328302383,
0.3348539471626282,
-0.06504393368959427,
0.8568406701087952,
-0.6093556880950928,
0.8125650882720947,
-0.2320621758699417,
-0.4752466380596161,
-0.3661144971847534,
-0.5549696683883667,
-0.09409400820732117,
-0.4077618718147278,
-0.1076073870062828,
0.29226571321487427,
-1.2128612995147705,
0.45222246646881104,
0.41780850291252136,
0.3274971544742584,
-0.6911277770996094,
-0.7506796717643738,
0.1315506249666214,
-0.16434480249881744,
-0.5376926064491272,
-0.586479127407074,
-0.2902791500091553,
0.9347018003463745,
-0.7778283953666687,
0.13292774558067322,
-1.065746784210205,
0.20426158607006073,
0.7821422815322876,
-0.20101682841777802,
0.567421019077301,
0.08930428326129913,
-0.006572145037353039,
0.7068375945091248,
-0.5772175788879395,
-0.9191724061965942,
0.10973488539457321,
-0.32442304491996765,
0.3382299542427063,
0.3031594455242157,
-0.2787092924118042,
-1.0992770195007324,
-0.18344490230083466,
-0.26827749609947205,
-0.10080332309007645,
-0.4896067678928375,
0.06709946691989899,
-0.3359288275241852,
-0.43508386611938477,
0.3967910706996918,
-0.42187657952308655,
-0.17849351465702057,
0.6831737160682678,
0.0944523811340332,
0.7415255904197693,
-0.6973047852516174,
0.27973538637161255,
0.014687176793813705,
0.07153958082199097,
0.030720748007297516,
0.3761073648929596,
-0.023868700489401817,
-0.014346998184919357,
-0.09560909122228622,
1.1600494384765625,
-0.7839323878288269,
0.5896911025047302,
-0.202668696641922,
0.22840429842472076,
0.20965591073036194,
-0.049572091549634933,
-0.7338703870773315,
-0.6063011884689331,
0.7148876190185547,
-0.025958441197872162,
0.4094322621822357,
1.0230121612548828,
0.5177156925201416,
0.35324570536613464,
0.15082648396492004,
0.10507380962371826,
-0.3107110559940338,
-0.4287417232990265,
-0.07108969986438751,
0.09210105240345001,
0.4169612228870392,
0.23072496056556702,
-0.262641042470932,
0.16891294717788696,
0.1368855983018875,
0.2725636065006256,
-0.6785011291503906,
-0.35693156719207764,
-0.05427555367350578,
0.04346716031432152,
-0.4774681329727173,
0.6110133528709412,
-0.6032722592353821,
-0.14345470070838928,
-0.00498617347329855,
-0.0909980982542038,
-0.24981103837490082,
-0.4341379404067993,
0.9637718796730042,
-1.0681536197662354,
0.2068391889333725,
0.9509962201118469,
-0.8275514841079712,
0.0618002824485302,
0.31709250807762146,
0.6997960805892944,
0.3235305845737457,
0.2390919178724289,
-0.6821101903915405,
0.36258363723754883,
0.22078777849674225,
0.010613725520670414,
-0.10862281918525696,
0.295766681432724,
-0.5175094604492188,
0.30324071645736694,
-0.6516727209091187,
-0.5939856767654419,
-0.306474894285202,
0.7408708930015564,
0.09343953430652618,
0.13845890760421753,
-0.6923004388809204,
0.2689129710197449,
-0.7021623253822327,
-0.8094886541366577,
0.4133532643318176,
-0.4383867084980011,
-0.22048906981945038,
0.4480360746383667,
-0.1488000601530075,
0.24806594848632812,
0.6107268333435059,
0.33660635352134705,
0.25996774435043335,
-0.3267957866191864,
0.07091803848743439,
0.6505844593048096,
-0.12965820729732513,
0.03808519244194031,
1.1073813438415527,
-0.1077202707529068,
-0.2347533106803894,
-0.5940423607826233,
-0.5566721558570862,
-0.2928577959537506,
0.25958266854286194,
0.19225777685642242,
0.13163898885250092,
0.3765900731086731,
-0.18150107562541962,
0.6675164103507996,
-0.43333539366722107,
-0.08654004335403442,
-0.9030347466468811,
0.21257448196411133,
-0.22410231828689575,
-0.6401073336601257,
0.34162792563438416,
0.09885839372873306,
-0.8630850911140442,
0.38185009360313416,
-1.0669734477996826,
-0.03072655200958252,
1.1205939054489136,
0.23665526509284973,
-0.5619415640830994,
0.1943027526140213,
-0.03491600602865219,
-0.24331620335578918,
0.12044389545917511,
-0.100516177713871,
0.35105493664741516,
0.03943273797631264,
0.2514875531196594,
0.09122546017169952,
0.3296905755996704,
0.4073368012905121,
-0.03237246349453926,
-0.050777748227119446,
0.15075063705444336,
0.3843088150024414,
0.3205980360507965,
-0.28084370493888855,
0.10373356938362122,
0.3664519488811493,
0.3135716915130615,
-0.4049805700778961,
-0.13195030391216278,
-0.07988058030605316,
0.03009738214313984,
0.061830803751945496,
-0.019485460594296455,
-0.05853484943509102,
0.7961956262588501,
-0.035023946315050125,
0.25504326820373535,
0.7921188473701477,
-0.7168115973472595,
-0.14151209592819214,
0.49490782618522644,
-0.2891558110713959,
-0.1787380576133728,
0.33469119668006897,
-0.11744221299886703,
0.2966596782207489,
-0.4814763069152832,
0.3468092083930969,
-0.364295095205307,
0.8965522646903992,
-0.057787105441093445,
1.021526575088501,
-1.0345580577850342,
-0.656586766242981,
0.1830054223537445,
0.37022167444229126,
-0.1238890290260315,
0.15197734534740448,
0.199504554271698,
0.3861500024795532,
-0.5446214079856873,
-1.0245102643966675,
0.2335582673549652,
0.9271098971366882,
-0.34370213747024536,
0.365464985370636,
0.7398068308830261,
-0.491142213344574,
-0.8635058403015137,
-0.016233088448643684,
-0.6670075058937073,
-0.3204852342605591,
-0.2560497224330902,
0.03586357459425926,
0.558340311050415,
-0.7923744320869446,
0.8240719437599182,
0.08883696794509888,
-0.6223752498626709,
0.24024826288223267,
0.000021284620743244886,
0.41667574644088745,
0.290335476398468,
0.16957688331604004,
-0.9050893783569336,
0.7368796467781067,
-0.14692425727844238,
-0.1222117617726326,
0.2680850923061371,
0.06175655871629715,
-0.14739221334457397,
-0.1551806479692459,
0.4563484787940979,
-0.1839565485715866,
-0.04483320191502571,
0.1339975893497467,
-0.1087135449051857,
-0.7479882836341858,
-0.17405739426612854,
0.6852839589118958,
-0.07783513516187668,
-0.583113968372345,
-1.1049079895019531,
0.09570048749446869,
0.09351851046085358,
-0.23607362806797028,
-0.014245226047933102,
0.3739200830459595,
-0.7151352167129517,
0.6840152144432068,
-0.47842302918434143,
0.19079557061195374,
0.12087681889533997,
0.4883487820625305,
0.8417215943336487,
-0.2400185465812683,
0.28183838725090027,
-0.3145686686038971,
-0.8718591332435608,
0.14859066903591156,
-0.0944247916340828,
-0.2757183909416199,
-0.5787286162376404,
0.9795963168144226,
0.24190691113471985,
-0.18244902789592743,
0.45751285552978516,
-0.7061676383018494,
-0.7349876165390015,
0.15291039645671844,
-0.5407522916793823,
0.20012496411800385,
-0.16447223722934723,
-0.36349427700042725,
-0.5543038845062256,
0.26770520210266113,
0.28662025928497314,
0.5520002841949463,
0.4082885980606079,
-0.2234884649515152,
0.5215557813644409,
0.5791952013969421,
0.009235747158527374,
-0.11185469478368759,
0.04113754630088806,
-0.08061320334672928,
-0.5154587030410767,
0.32497522234916687,
-0.32460644841194153,
0.6411165595054626,
-0.39493343234062195,
0.7633708119392395,
0.1083248034119606,
0.2764783501625061,
-0.42373546957969666,
0.4464299976825714,
-0.3187960088253021,
0.05112230032682419,
0.0768614411354065,
0.5131083726882935,
0.13441556692123413,
-0.12429669499397278,
-0.8022083640098572,
-0.08365342020988464,
-0.1944034993648529,
0.24556151032447815,
0.5166726112365723,
-0.4263247847557068,
0.4142376482486725,
-0.5317116975784302,
-0.6051890850067139,
-0.6359888911247253,
0.0764068141579628,
0.35270196199417114,
0.05137532949447632,
0.32298675179481506,
1.4258497953414917,
-0.45627644658088684,
-0.4580725133419037,
0.1447274386882782,
0.7477302551269531,
-0.008269498124718666,
0.660619854927063,
0.1544673591852188,
-0.1442037969827652,
0.3968042731285095,
-0.3676033318042755,
-0.5728433728218079,
-0.4734351634979248,
-0.8921284079551697,
-0.1758994162082672,
-0.5038426518440247,
-0.16684049367904663,
0.03396029770374298,
0.1672130674123764,
0.4375275671482086,
0.05366532877087593,
-0.21325422823429108,
0.24936823546886444,
0.39451783895492554,
0.4302947521209717,
0.4501216411590576,
0.2368321567773819,
0.3330753743648529,
-1.2129379510879517,
0.3136133551597595,
-0.16468921303749084,
0.49556034803390503,
-0.5833911299705505,
-0.031335264444351196,
-0.37538331747055054,
-0.4040694236755371,
0.1874106526374817,
0.21849468350410461,
-0.8814843893051147,
0.06936818361282349,
0.17417603731155396,
0.1717360019683838,
0.13113191723823547,
0.17571140825748444,
0.6640905737876892,
0.2771355211734772,
0.23038430511951447,
-0.9551268219947815,
0.820497453212738,
-0.12460599094629288,
0.2816859781742096,
1.0957528352737427,
-0.6633971333503723,
-0.34265241026878357,
-1.222439169883728,
-0.1265815794467926,
-0.24718454480171204,
0.27575191855430603,
1.3534644842147827,
-0.24165290594100952,
0.324063241481781,
-0.2715686857700348,
0.19862614572048187,
0.23205353319644928,
-0.6083332300186157,
-0.8576575517654419,
0.20943966507911682,
0.09449100494384766,
0.01142431516200304,
0.5369662046432495,
-0.05390331521630287,
-0.42609044909477234,
0.24641597270965576,
-0.5859740972518921,
-0.22669966518878937,
-0.7918272018432617,
-0.056840501725673676,
0.250669926404953,
-0.3821752667427063,
-0.6896687150001526,
0.4165970981121063,
0.6999531388282776,
0.39991602301597595,
-0.042694028466939926,
0.025340033695101738,
-0.3763694763183594,
-0.16471505165100098,
0.31886768341064453,
0.4053294062614441,
0.4886281192302704,
0.3498285412788391,
0.31754615902900696,
0.09880715608596802,
-0.008742348290979862,
-0.2613689601421356,
0.08937074989080429,
0.056956078857183456,
-0.02505299635231495,
-0.038784388452768326,
-0.1190502792596817,
-0.4827631115913391,
0.031144991517066956,
-0.14392927289009094,
0.5744161009788513,
0.3161081075668335,
0.6028184294700623,
-0.10620478540658951,
-0.9832888245582581,
-0.6868054270744324,
-0.4475553631782532,
-1.0342155694961548,
0.5455440282821655,
-0.25664374232292175,
-0.22623632848262787,
0.5132485628128052,
-0.8745372891426086,
0.17606130242347717,
0.02757168933749199,
-0.6974213719367981,
-0.14478328824043274,
0.7439320683479309,
0.6239609122276306,
0.36303842067718506,
0.2312922179698944,
-0.9950684309005737,
0.29516714811325073,
-0.3287268579006195,
0.028457656502723694,
-0.5485973954200745,
-0.8537107110023499,
-0.19282256066799164,
-0.003526070388033986,
-0.13741280138492584,
-0.11344014108181,
-0.18220964074134827,
-0.02083512954413891,
-0.05904209613800049,
-0.22218120098114014,
0.560581624507904,
-0.6655486226081848,
-0.22722077369689941,
0.27314847707748413,
0.5140923261642456,
-0.9303535223007202,
-0.6428943276405334,
0.008748944848775864,
-0.1321706920862198,
0.3105149567127228,
0.18345022201538086,
-0.8026654720306396,
0.07739531248807907,
-0.5825708508491516,
0.4154093563556671,
-0.5218588709831238,
-0.4420080780982971,
-0.19589515030384064,
-0.9548745155334473,
0.14303185045719147,
0.0440828800201416,
0.2610644996166229,
-0.32251235842704773,
-0.2322918176651001,
0.2501017153263092,
0.32998183369636536,
-0.17594178020954132,
0.29528719186782837,
-0.3143726587295532,
-1.1158967018127441,
-0.2793624699115753,
0.9086540341377258,
-0.2421521693468094,
-0.2006031572818756,
0.10666065663099289,
-0.029384518042206764,
0.3208877444267273,
0.5724356770515442,
0.4506220519542694,
-0.22300998866558075,
0.19322873651981354,
0.4695163071155548,
-0.26390841603279114,
0.3988680839538574,
-0.9440025687217712,
0.6230237483978271,
-0.8780403137207031,
0.8264820575714111,
-0.14456400275230408,
-0.23447062075138092,
0.024437280371785164,
0.5182414650917053,
0.13423092663288116,
-1.163399577140808,
0.40541398525238037,
-0.27410537004470825,
0.2540488541126251,
0.16448138654232025,
0.34691211581230164,
0.1857302188873291,
-0.5560910105705261,
-0.9985897541046143,
-0.5901530981063843,
0.5510181784629822,
-0.21840499341487885,
-0.1685725897550583,
-0.38063520193099976,
-0.531953752040863,
0.357023686170578,
-0.10560982674360275,
0.7196827530860901,
0.5002442002296448,
-0.016692791134119034,
-0.019956404343247414,
-0.03472726792097092,
-0.2747951149940491,
-0.43045103549957275,
-0.20792993903160095,
0.2817193567752838,
0.13012714684009552,
0.3174944818019867,
0.4398876428604126,
-0.18578630685806274,
-0.609934389591217,
0.13218270242214203,
-0.16695792973041534,
0.5043818950653076,
0.22854724526405334,
0.8421512842178345,
0.15121988952159882,
-0.3883526921272278,
-0.1530703455209732,
0.13246475160121918,
0.28534579277038574,
0.27272114157676697,
0.05233637988567352,
-0.10676586627960205,
0.3998410701751709,
-0.16435368359088898,
0.22281695902347565,
-0.47959691286087036,
-0.11966156959533691,
0.9873032569885254,
-0.5927057266235352,
-0.5594832301139832,
1.038773536682129,
0.15124015510082245,
-0.2419040948152542,
-0.24405132234096527,
-0.8128674030303955,
-0.08974597603082657,
-0.868506908416748,
-0.27941080927848816,
-0.4244503378868103,
-0.3166736662387848,
-0.3781873881816864,
0.599461555480957,
0.33592742681503296,
0.08769404143095016,
-0.5172168612480164,
-0.16118712723255157,
-0.6065094470977783,
-0.40181219577789307,
-0.5899856686592102,
1.6021368503570557,
-0.1428470015525818,
-0.6181920766830444,
-0.026076406240463257,
0.1549108475446701,
-0.7214990854263306,
0.004641354084014893,
0.6459565162658691,
-0.4569421410560608,
0.6964680552482605,
0.19660720229148865,
0.34375661611557007,
0.9045135974884033,
1.0504310131072998,
0.4107949435710907,
-0.17345595359802246,
-0.2739046514034271,
-0.9385281801223755,
-0.4767082631587982,
-0.4264300763607025,
0.5428386926651001,
0.2938319146633148,
-0.10227246582508087,
-0.14157187938690186,
0.03534615412354469,
-0.1158745139837265,
-0.08240557461977005,
-0.7100886106491089,
0.3355754315853119,
-0.1335689276456833,
-0.03725219517946243,
-0.23961564898490906,
-0.5173888206481934,
0.2601068913936615,
0.6690727472305298,
-0.6960008144378662,
-0.5561219453811646,
-0.8801300525665283,
0.1312796175479889,
0.39260777831077576,
0.482728511095047,
-0.4229714870452881,
-0.9951581358909607,
-0.7207176089286804,
-0.8396710753440857,
-0.46044525504112244,
-0.08750072121620178,
-0.5519049167633057,
-0.23354516923427582,
-0.41232985258102417,
0.4578160345554352,
0.18655161559581757,
0.6584619879722595,
-0.5250346064567566,
-0.6159064769744873,
0.2861667573451996,
-0.06368732452392578,
-0.6901159286499023,
0.15875105559825897,
0.20752392709255219,
0.9379327893257141,
0.4538244605064392,
0.267956405878067,
0.1859208196401596,
-0.5037493109703064,
-1.0325076580047607,
0.44512638449668884,
0.12586610019207,
1.2353477478027344,
-0.2402225136756897,
-0.4317629039287567,
0.2220008373260498,
0.3700759708881378,
-1.0688029527664185,
0.767113447189331,
-0.3162957429885864,
0.8194764852523804,
-0.14395776391029358,
0.549800455570221,
-0.007856572046875954,
0.5567757487297058,
0.30600517988204956,
0.23363851010799408,
-0.20465965569019318,
-0.5974811315536499,
0.1745603233575821,
0.2011592984199524,
0.04312090948224068,
0.007946383208036423,
0.07444517314434052,
-0.3720417618751526,
-0.3914196789264679,
0.1892130821943283,
-0.14113536477088928,
0.27351412177085876,
-0.15611369907855988,
0.5312758684158325,
-0.37110021710395813,
-0.32177215814590454,
-0.263450026512146,
0.322591096162796,
0.4505683481693268,
-0.39172667264938354,
-0.4766467213630676,
-0.5837422609329224,
-0.44283440709114075,
0.6647141575813293,
-0.9174173474311829,
-0.8241286277770996,
0.3769569396972656,
-0.14253270626068115,
-0.01624462753534317,
0.07814440131187439,
-0.2679053843021393,
0.010995284654200077,
0.37779340147972107,
0.07674716413021088,
-0.10826356709003448,
-0.33087629079818726,
-0.5067098140716553,
0.7339309453964233,
-0.5550903081893921,
-0.41437825560569763,
-0.8147945404052734,
0.75350022315979,
-0.8704147934913635,
-0.5391135215759277,
-0.05210119113326073,
1.0424131155014038,
-0.043168433010578156,
-0.490261048078537,
-0.347196102142334,
0.03891093283891678,
0.01533040963113308,
-0.43590018153190613,
-0.3573857247829437,
0.1864883452653885,
-0.43104591965675354,
0.513910710811615,
-0.5232510566711426,
-0.3666386902332306,
-0.017197517678141594,
0.283735066652298,
-0.03960577771067619,
0.5733522176742554,
-0.14035023748874664,
0.7447002530097961,
0.4171120524406433,
-0.24608738720417023,
0.41811227798461914,
0.23074890673160553,
0.49363166093826294,
0.03499728441238403,
-0.15180326998233795,
0.17358733713626862,
0.5109398365020752,
0.07428940385580063,
0.8083438873291016,
-0.22275295853614807,
0.3870069086551666,
0.2741073966026306,
-0.06107942759990692,
-0.14392977952957153,
0.1459851861000061,
0.5832085013389587,
0.18513637781143188,
0.6332720518112183,
0.37979328632354736,
-0.03463571146130562,
-0.12273668497800827,
-0.3313715159893036,
0.389571875333786,
0.24340364336967468,
-0.5143932104110718,
-0.21199291944503784,
-0.8263893127441406,
0.17940396070480347,
-0.7074717283248901,
-0.6338287591934204,
-0.05922938883304596,
-0.03226524218916893,
1.0843909978866577,
0.3808777332305908,
0.26754671335220337,
-0.49256497621536255,
0.6229059100151062,
0.1360364705324173,
-0.6929471492767334,
0.3923746347427368,
-0.03445371985435486,
1.5069268941879272,
0.31543412804603577,
0.8692816495895386,
0.7196038961410522,
0.699790894985199,
0.13744468986988068,
-1.0629656314849854,
-0.16366340219974518,
0.24785354733467102,
-0.4472231864929199,
0.5212035775184631,
-0.6514805555343628,
0.11659853160381317,
-0.16904906928539276,
-0.5163514614105225,
0.9103114604949951,
-0.9407913684844971,
-0.49141761660575867,
0.7818958759307861,
-1.0369932651519775,
-0.2674882113933563,
0.5325281023979187,
0.5924831628799438,
0.1957297921180725,
0.8348321318626404,
1.091535210609436,
0.16174203157424927,
0.9743717312812805,
0.7214778661727905,
-0.2479700744152069,
0.3710702955722809,
0.1900068074464798,
-0.38724446296691895,
-0.17844630777835846,
0.36883842945098877,
-0.5529248714447021,
0.9744773507118225,
0.24313077330589294,
-0.40129199624061584,
0.14186859130859375,
0.12486985325813293,
0.13492663204669952,
-0.16180013120174408,
0.6835170388221741,
-0.00811244547367096,
-0.8861748576164246,
-0.169197678565979,
1.2353835105895996,
0.03981664031744003,
-0.1251695603132248,
-0.3762485384941101,
0.2342287302017212,
-0.0500943586230278,
-0.20743660628795624,
-0.33664485812187195,
0.12709158658981323,
-0.1490074247121811,
-0.4257281720638275,
0.03759375587105751,
-0.3227715790271759,
-0.6933848261833191,
-0.15024589002132416,
-0.08311981707811356,
-0.5440966486930847,
0.5272135734558105,
0.33217525482177734,
0.65245121717453,
-0.08585546165704727,
-0.4795846939086914,
-0.10469774156808853,
-0.03298291936516762,
0.7824010252952576,
0.40353548526763916,
0.18895380198955536,
0.20550496876239777,
0.168084517121315,
-0.2695702016353607,
-0.07308432459831238,
0.870469868183136,
-0.11379490047693253,
0.7104238867759705,
-0.4275871515274048,
0.4144814610481262,
0.6273154616355896,
-0.30598825216293335,
-0.17873257398605347,
0.06823177635669708,
-0.04490650072693825,
0.643186628818512,
-0.11199040710926056,
-0.3391546905040741,
-0.7665104866027832,
0.3578503727912903,
-0.12452416867017746,
0.6201513409614563,
0.1301337331533432,
0.2448774129152298,
0.0964769572019577,
-1.2746471166610718,
4.37626838684082,
0.669462263584137,
0.862157940864563,
0.0053751966916024685,
0.7934677600860596,
0.8554412126541138,
-0.5270089507102966,
-0.3329963684082031,
-0.1459721475839615,
-0.18520809710025787,
-0.30898645520210266,
0.008239151909947395,
-0.489993155002594,
0.000276364415185526,
0.03282700851559639,
0.5482951998710632,
0.01580497995018959,
-0.5654325485229492,
0.5063393115997314,
-0.8987773060798645,
-0.2745790183544159,
-0.10654988884925842,
-0.20225638151168823,
-0.1234220415353775,
0.5240767598152161,
-0.601874828338623,
0.6734337210655212,
-0.9651479721069336,
-0.6090564727783203,
-0.2884629964828491,
-0.24279551208019257,
-0.34985044598579407,
0.15153880417346954,
-0.2511768341064453,
-0.9704594016075134,
0.3745644986629486,
-0.4723195433616638,
-0.34124743938446045,
-0.02142120525240898,
0.048057861626148224,
0.13913604617118835,
-0.5450368523597717,
-0.2688200771808624,
0.006479979958385229,
0.000030136725399643183,
0.6726899743080139,
-0.6524991989135742,
1.1297738552093506,
0.9926663637161255,
-0.5954850316047668,
0.7670099139213562,
-0.13968347012996674,
0.6290329098701477,
-0.4194088578224182,
-0.5053443312644958,
0.5595229864120483,
-0.9703109264373779,
0.026131540536880493,
-0.04214230179786682,
0.38923680782318115,
0.4956808388233185,
-0.5405479669570923,
0.0015646193642169237,
0.017741132527589798,
-0.03352350741624832,
-0.0446971170604229,
-0.10949394106864929,
0.8218300342559814,
-0.48595815896987915,
0.13866017758846283,
0.24518798291683197,
-0.1638818383216858,
-0.5968023538589478,
0.05983881652355194,
0.229806587100029,
-0.11357023566961288,
-0.4807910919189453,
0.12902240455150604,
-0.004154105670750141,
-0.2033630758523941,
0.12952230870723724,
-0.24151378870010376,
-0.13028942048549652,
-0.4173503816127777,
0.5239194631576538,
1.0145460367202759,
-0.18846915662288666,
-0.0856437236070633,
0.36044737696647644,
0.3021427094936371,
0.7394530177116394,
1.1947705745697021,
0.323957234621048,
-0.03790067508816719,
-0.45283111929893494
] |
Gribov Copies and Smeared Correlation Functions in Lattice QCD
|
We study the influence of Gribov copies in the Coulomb gauge on the smeared hadronic correlation functions that are involved in the determination of the B meson decay constant. We find that the residual gauge freedom associated to Gribov copies induces observable noise effects, though at the level of numerical accuracy of our simulation these effects are not relevant to the final determination of f_B. Our results indicate that such effects may become important on bigger lattices.
|
M.L. Paciello, C. Parrinello, S. Petrarca, B. Taglienti, A. Vladikas
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208010
|
hep-lat/9208011
|
[
0.18316775560379028,
0.23512351512908936,
-0.08779724687337875,
0.16362264752388,
-0.07148967683315277,
-0.16734915971755981,
-0.27276498079299927,
0.22533082962036133,
-0.2883165180683136,
1.2074958086013794,
0.7265008091926575,
-0.08412124961614609,
0.14800365269184113,
-0.7555984258651733,
-0.10163970291614532,
0.6788955926895142,
-0.3028869032859802,
-0.8122347593307495,
-0.7821707129478455,
-0.5373759865760803,
0.16024038195610046,
-0.15338987112045288,
-1.694678783416748,
-0.9022603631019592,
-0.11886979639530182,
0.12784893810749054,
1.0009528398513794,
-0.8006414175033569,
1.4517709016799927,
0.4528367221355438,
1.0387643575668335,
-0.2598051428794861,
0.5439051389694214,
-0.1533224731683731,
0.303291916847229,
-0.5015292763710022,
0.5418616533279419,
-0.017852379009127617,
0.09270453453063965,
-0.795595109462738,
1.1012027263641357,
-0.200667142868042,
-0.08217108994722366,
-0.11043566465377808,
-0.629950761795044,
-0.4907383322715759,
-0.6188257336616516,
-0.3074099123477936,
0.28314805030822754,
-0.9788720607757568,
0.21233856678009033,
0.02829291857779026,
0.07641297578811646,
-0.44262000918388367,
-0.4175507128238678,
-0.00921495072543621,
0.2501208782196045,
-0.023574763908982277,
-0.30052998661994934,
0.49628207087516785,
1.0471813678741455,
-0.23090563714504242,
0.3648477792739868,
-0.6213310956954956,
0.7284886837005615,
1.0873125791549683,
-0.19656836986541748,
0.5663157105445862,
-0.18863151967525482,
-0.6650739312171936,
-0.03498408570885658,
-0.38291436433792114,
-0.5770739912986755,
-0.055945876985788345,
-0.5914902091026306,
1.384004831314087,
0.2029598504304886,
-0.24468351900577545,
-1.0638272762298584,
0.11696860194206238,
0.15251265466213226,
-0.3146562874317169,
-0.37915459275245667,
0.34032362699508667,
-0.4275752305984497,
-0.2220643162727356,
0.7787417769432068,
-0.039576273411512375,
-0.6358655691146851,
-0.08899174630641937,
0.6860086917877197,
0.5883271098136902,
0.38266533613204956,
-0.17914392054080963,
0.09503882378339767,
0.2512476146221161,
-0.15953326225280762,
0.8568093776702881,
0.45529475808143616,
0.4418785572052002,
-0.3487423062324524,
1.3465816974639893,
-0.41036662459373474,
0.8345759510993958,
-0.08416919410228729,
-0.1891973912715912,
-0.052245792001485825,
-0.32905879616737366,
-0.006041352637112141,
-0.8253744840621948,
0.0552595853805542,
0.026793230324983597,
-0.25283756852149963,
0.43390953540802,
-0.2178671807050705,
1.210117220878601,
0.5598746538162231,
0.4301932454109192,
-0.5126346945762634,
0.2908722162246704,
-0.06149407476186752,
-0.026459315791726112,
0.36604002118110657,
0.21170704066753387,
0.5844892859458923,
-0.7156749963760376,
-0.6129217147827148,
0.2926853895187378,
-0.9187327027320862,
-0.3595203459262848,
-0.30691275000572205,
0.3139358460903168,
-0.40227559208869934,
0.9144079685211182,
-0.08805344998836517,
0.10290135443210602,
0.08815313875675201,
0.5596902370452881,
-0.05662146583199501,
-0.5057691335678101,
0.5479137897491455,
-0.5753414034843445,
0.6940174102783203,
1.1836796998977661,
-0.7353752255439758,
0.09177982062101364,
0.09495588392019272,
-0.050406165421009064,
0.08783795684576035,
0.41901713609695435,
-0.9792230725288391,
-0.09808605909347534,
-0.3720417022705078,
1.0723861455917358,
0.4040217697620392,
0.014636472798883915,
-0.25415170192718506,
0.7059851288795471,
-1.0608829259872437,
0.1279015988111496,
-0.5686086416244507,
0.5630795359611511,
-0.38811901211738586,
0.08274967223405838,
-0.017324717715382576,
0.07941659539937973,
-0.6428754925727844,
-0.43842339515686035,
-0.4820300042629242,
-0.6944072842597961,
-0.30442866683006287,
-0.25799062848091125,
0.2667219042778015,
0.17433986067771912,
0.4495508372783661,
0.8423193693161011,
0.40805158019065857,
-0.5542407035827637,
-0.314164400100708,
-0.005186641588807106,
-0.7584490776062012,
-0.40475842356681824,
0.7147265076637268,
0.3708359897136688,
0.3309180736541748,
-0.47919121384620667,
-0.3399723172187805,
0.2752212584018707,
-0.10751233994960785,
0.8242231011390686,
0.04018908739089966,
0.7717701196670532,
-0.4117778241634369,
0.9714634418487549,
-0.1298515498638153,
-0.057330422103405,
0.3691450357437134,
-0.21794432401657104,
-0.6134646534919739,
-0.9558397531509399,
-0.19847451150417328,
0.6598085761070251,
-0.28002429008483887,
0.32333850860595703,
-1.4187870025634766,
-0.14256374537944794,
0.36241427063941956,
0.17539286613464355,
-0.4117990732192993,
-0.03342008218169212,
-0.015927433967590332,
0.2970323860645294,
0.3842991888523102,
-0.35001426935195923,
0.0487992949783802,
-0.04857084900140762,
-0.0780777633190155,
0.14414134621620178,
0.7714346051216125,
-0.3901822566986084,
0.4533589780330658,
-0.3021353483200073,
-0.20014142990112305,
0.37094375491142273,
0.47777897119522095,
-0.1253574639558792,
0.3186497986316681,
1.0067579746246338,
0.12564247846603394,
0.6073802709579468,
0.01625635288655758,
0.8234401941299438,
-0.24555526673793793,
0.2736247777938843,
0.5257065296173096,
0.3696664273738861,
-0.21943016350269318,
0.19671301543712616,
0.768569827079773,
-0.5024265050888062,
0.36598992347717285,
0.46614986658096313,
1.121516227722168,
0.8236989378929138,
0.4269038438796997,
0.521977961063385,
-0.20158928632736206,
0.11786658316850662,
-0.18228930234909058,
0.08164795488119125,
-0.5383299589157104,
0.9439989328384399,
-0.18233656883239746,
0.408223032951355,
-0.4780956506729126,
0.09571239352226257,
0.11952465772628784,
0.5373806953430176,
0.018150275573134422,
-0.6309494376182556,
-0.2962745130062103,
0.390812486410141,
-0.3532620668411255,
-0.8250845670700073,
-0.14410804212093353,
1.2232717275619507,
-0.2301434874534607,
0.020530277863144875,
0.28512635827064514,
-0.8039501905441284,
-0.7840697765350342,
-0.7405217289924622,
-0.5638346076011658,
-0.19247876107692719,
-0.38395652174949646,
-0.7236140370368958,
0.8176618218421936,
-1.1366527080535889,
0.48606258630752563,
-0.6541051864624023,
-0.26346853375434875,
0.16106899082660675,
0.20984391868114471,
0.7988408803939819,
-0.24005159735679626,
-0.5645365118980408,
-0.7687220573425293,
0.46653640270233154,
-0.584883451461792,
0.5510386228561401,
-0.2087467461824417,
-0.24397923052310944,
-0.03936414793133736,
-0.5282991528511047,
0.15609560906887054,
-0.41398265957832336,
-0.019056309014558792,
0.22674040496349335,
-0.195888951420784,
0.14570583403110504,
-0.05811208859086037,
0.48192450404167175,
0.4341358542442322,
-0.13205070793628693,
-0.6319652795791626,
-0.16360238194465637,
0.3729008436203003,
-0.825256884098053,
0.1471242755651474,
0.48281368613243103,
-1.0174970626831055,
-0.10724417120218277,
-0.589162290096283,
-0.02091369964182377,
-0.1333642452955246,
0.5205503702163696,
0.7957088351249695,
-0.5091394782066345,
0.3207188844680786,
-0.6448318958282471,
0.04709398001432419,
-0.11021225899457932,
-0.08872384577989578,
-0.4247257113456726,
-0.22950269281864166,
0.7345690727233887,
0.408708393573761,
-0.25814107060432434,
0.527970552444458,
-0.8595625162124634,
-0.7238429188728333,
0.1676836758852005,
-0.39393725991249084,
0.4540351629257202,
0.27166548371315,
-0.039510685950517654,
0.025109559297561646,
0.08674731850624084,
0.9510276913642883,
0.4862005114555359,
0.06616784632205963,
-1.2971097230911255,
0.8770643472671509,
0.676204264163971,
0.39956676959991455,
0.07335811108350754,
0.9376223683357239,
-0.2258220911026001,
-0.6520218253135681,
0.043237634003162384,
-0.44638198614120483,
-0.09730018675327301,
0.21006545424461365,
-0.048391494899988174,
-0.04987665265798569,
0.1253889799118042,
-0.5437778830528259,
-0.056745920330286026,
0.19762368500232697,
-0.03960934281349182,
0.01734926551580429,
0.16111476719379425,
-0.16493089497089386,
0.6273468136787415,
-0.7402167320251465,
-0.35412636399269104,
0.6401258707046509,
0.22920256853103638,
0.45713651180267334,
-0.7298076152801514,
0.8593432307243347,
-0.4679955542087555,
-0.2389647364616394,
-0.12594148516654968,
-0.3024776577949524,
0.05944472923874855,
0.09707436710596085,
0.5326921343803406,
1.0008940696716309,
-0.6114271879196167,
-0.546315610408783,
0.013583852909505367,
0.27679699659347534,
0.37317726016044617,
0.7238142490386963,
0.0463402085006237,
0.22574855387210846,
-0.5597355365753174,
0.06077348068356514,
-0.2961955964565277,
-0.12750013172626495,
-0.5452441573143005,
-0.005041508935391903,
-0.8750877380371094,
-0.23370012640953064,
-0.49827325344085693,
0.8206177949905396,
0.3210318088531494,
0.18091750144958496,
-0.17245827615261078,
0.9747510552406311,
-0.364959716796875,
0.03879920393228531,
0.2964770793914795,
0.1977672576904297,
0.3189329504966736,
-0.8037633299827576,
0.27665045857429504,
0.03554986044764519,
-0.09798765182495117,
-0.9310367107391357,
0.046478599309921265,
-0.1420757919549942,
-0.3149583339691162,
0.36005833745002747,
0.42997613549232483,
-0.5825819969177246,
0.31525304913520813,
-0.7100890874862671,
0.22832483053207397,
-0.7608020901679993,
-0.31262123584747314,
0.12783518433570862,
1.2862608432769775,
0.4601573944091797,
-0.857020378112793,
-0.07358286529779434,
-1.1493669748306274,
0.33826687932014465,
-0.014173628762364388,
0.19088594615459442,
-0.6159841418266296,
-0.7186024188995361,
-0.48185181617736816,
-0.999998152256012,
0.13201113045215607,
1.5511828660964966,
-0.2784157991409302,
0.38131070137023926,
-0.26467204093933105,
0.0008807844715192914,
-0.3381205201148987,
-0.5868364572525024,
-0.5333502292633057,
0.8007799983024597,
0.45146095752716064,
-0.1310172826051712,
0.4103083908557892,
-0.570102334022522,
-0.1085675060749054,
0.1154104471206665,
-0.7309638261795044,
1.0297527313232422,
-0.48499810695648193,
0.10032141953706741,
-0.5488577485084534,
-0.011300629004836082,
-0.3489699065685272,
0.1112339124083519,
-0.32762107253074646,
0.3824104070663452,
-0.9439778923988342,
0.3978906571865082,
-0.8241117000579834,
-0.4231831133365631,
-0.277817964553833,
-0.22399578988552094,
0.174701988697052,
1.0606411695480347,
-0.5519869327545166,
-0.01204572431743145,
-0.08027210831642151,
-0.19285553693771362,
0.16559897363185883,
0.8512812852859497,
0.1324591338634491,
0.425334632396698,
-0.37863507866859436,
-0.3570500314235687,
-0.5316384434700012,
-0.9938774704933167,
0.23362165689468384,
0.09268122166395187,
0.3051113486289978,
-0.19881831109523773,
-0.6337398886680603,
-0.15695109963417053,
0.6365010142326355,
-0.16688930988311768,
-0.03900373727083206,
0.000407213723519817,
0.02460402622818947,
-0.34140199422836304,
-0.02404973655939102,
-0.3478356599807739,
0.2762336730957031,
-0.11723321676254272,
-0.05107000470161438,
0.15303084254264832,
0.498409628868103,
-0.32558053731918335,
0.13930709660053253,
-0.5874367356300354,
0.512052595615387,
-0.28850772976875305,
-0.48854511976242065,
-0.7846623063087463,
-0.8205228447914124,
-0.5724305510520935,
0.08248375356197357,
-0.49903714656829834,
-0.18802770972251892,
-0.26114216446876526,
0.03490918502211571,
-0.013750232756137848,
-0.1428832709789276,
-0.008101248182356358,
0.46263521909713745,
-0.5454563498497009,
0.716360867023468,
-0.5782686471939087,
-1.141147494316101,
-0.16584403812885284,
-0.23628832399845123,
-0.5285120606422424,
-0.2778147757053375,
0.08510491997003555,
-1.5221627950668335,
-0.2335548847913742,
-0.17780311405658722,
0.21555252373218536,
-0.7498041391372681,
-0.020447028800845146,
-0.6108502745628357,
-1.137980580329895,
-0.41044995188713074,
0.07665861397981644,
0.7785669565200806,
-0.17815406620502472,
-0.2087961882352829,
-0.01833205856382847,
0.013553960248827934,
-0.2198399007320404,
0.09481637179851532,
0.1259615123271942,
-0.0542500801384449,
-0.5140906572341919,
0.2661653459072113,
-0.09577398002147675,
-0.22861036658287048,
0.5632794499397278,
0.1370164304971695,
0.004796150140464306,
0.6022728085517883,
-0.2748858332633972,
-0.6611368656158447,
-0.36410000920295715,
0.2510477304458618,
-0.19951295852661133,
0.9397085309028625,
0.23618213832378387,
0.20175455510616302,
-1.0300521850585938,
0.7328781485557556,
-0.7454708218574524,
-0.09349758923053741,
0.11550673842430115,
-0.3789599537849426,
0.7171432971954346,
-0.4976176619529724,
0.6294769644737244,
0.4910956919193268,
0.2745949923992157,
0.8213745951652527,
0.050673726946115494,
-0.7926956415176392,
0.019233975559473038,
-0.5708938837051392,
-0.940263032913208,
0.7302400469779968,
-0.0696849673986435,
-0.16474898159503937,
-0.6021239757537842,
-0.21917009353637695,
0.7183108925819397,
-0.8703487515449524,
0.3264305591583252,
0.8253846168518066,
-0.025384731590747833,
0.2773649990558624,
-0.27270540595054626,
-0.6216790080070496,
0.12480058521032333,
-0.10516110807657242,
0.5389982461929321,
-0.00595521368086338,
-0.36843323707580566,
0.573639452457428,
-0.9660173058509827,
-1.014929175376892,
-0.17765523493289948,
0.3902832865715027,
-0.019868360832333565,
0.33628129959106445,
0.75445955991745,
-0.8476656675338745,
-0.2438303679227829,
-0.325837105512619,
0.3270796239376068,
0.4388450086116791,
-0.023392755538225174,
0.6334711909294128,
0.8133254647254944,
0.14286845922470093,
-0.272905558347702,
0.08114861696958542,
-0.2460731565952301,
-0.6157045960426331,
1.0937507152557373,
0.009753057733178139,
-0.5578430891036987,
0.46795937418937683,
0.24561990797519684,
-0.5903549790382385,
-0.5923323631286621,
-0.4718291461467743,
0.19349132478237152,
0.11429224908351898,
-0.3606627881526947,
-0.513388454914093,
-0.35141292214393616,
-0.41334784030914307,
0.11990058422088623,
0.5298475027084351,
-0.9808371067047119,
0.08959105610847473,
0.08882764726877213,
0.10539654642343521,
-1.072121024131775,
0.21293893456459045,
1.012342929840088,
0.10075382143259048,
-0.46513617038726807,
-0.9146508574485779,
-0.7920548915863037,
0.026055697351694107,
-0.613153874874115,
0.15923164784908295,
-0.4846336245536804,
0.4047650396823883,
0.47298532724380493,
0.37506768107414246,
0.2718948721885681,
0.5580190420150757,
0.7941359877586365,
0.37294137477874756,
-0.4474853277206421,
-0.6952220797538757,
-0.6756923198699951,
0.5776512026786804,
-0.12030376493930817,
0.9796054363250732,
0.007915806956589222,
0.08216123282909393,
0.5198043584823608,
-0.08853230625391006,
-0.1813032478094101,
-1.3929046392440796,
0.11041144281625748,
-0.9046627879142761,
-0.7988635301589966,
-0.418501079082489,
-0.15973782539367676,
-0.018381603062152863,
0.7181060910224915,
0.09941074997186661,
0.024356096982955933,
-0.1302684098482132,
0.31094175577163696,
0.06008027493953705,
-0.12293067574501038,
-0.3334181308746338,
-0.5765660405158997,
-1.0047261714935303,
-0.10122306644916534,
-0.7075012922286987,
-0.18654179573059082,
0.006476016715168953,
0.7666056752204895,
0.36026594042778015,
0.19751352071762085,
-0.6098724007606506,
0.7420434951782227,
-0.7742326855659485,
-0.1806439310312271,
0.36822420358657837,
0.03811489790678024,
-0.8201227784156799,
0.2722570300102234,
-0.2626664638519287,
0.5288192629814148,
0.1769479364156723,
0.2267976552248001,
0.1786007136106491,
-0.35581547021865845,
-0.33320921659469604,
-0.13303105533123016,
-0.1419823169708252,
0.811822235584259,
0.09945013374090195,
-0.4512915313243866,
0.6919381618499756,
0.6484618782997131,
-1.0612059831619263,
0.19781316816806793,
0.3014446794986725,
-0.056518811732530594,
-0.303350567817688,
-0.0014276114525273442,
0.3118954598903656,
0.9547003507614136,
-0.04511918127536774,
1.0732375383377075,
0.015218769200146198,
0.011875472962856293,
0.05256190896034241,
-0.21084269881248474,
-0.24303489923477173,
0.7780856490135193,
0.011688980273902416,
-1.120950698852539,
0.16974690556526184,
0.6748335957527161,
-0.33261555433273315,
-0.098798006772995,
-0.10995937883853912,
-0.04355810955166817,
-0.6088884472846985,
-0.2530748248100281,
-0.501120924949646,
0.5770805478096008,
0.18069486320018768,
-0.5472230911254883,
-0.030209152027964592,
-0.1558573693037033,
-0.20578880608081818,
0.3202093839645386,
-1.216415286064148,
-0.49556079506874084,
-0.24485856294631958,
-0.21842937171459198,
0.27870041131973267,
0.5067099332809448,
-0.1176929697394371,
-0.16139104962348938,
0.13819994032382965,
0.21539190411567688,
0.05087507516145706,
0.2916455864906311,
-0.30907803773880005,
0.8451662659645081,
-0.6614456176757812,
-0.42098936438560486,
-0.24120183289051056,
0.47094857692718506,
-0.5422421097755432,
-0.8673463463783264,
-0.2979554235935211,
1.361096978187561,
-0.5283175110816956,
-0.3929136395454407,
-0.8348380327224731,
0.7083415389060974,
0.11635894328355789,
0.20634900033473969,
-0.6218276619911194,
0.22518591582775116,
-0.05655844509601593,
0.35660144686698914,
-0.4982666075229645,
0.12532800436019897,
0.056009989231824875,
1.1051735877990723,
0.4302493631839752,
0.21468044817447662,
-0.18238721787929535,
0.07872959971427917,
-0.2961578071117401,
-0.7543631792068481,
0.959513783454895,
0.15423187613487244,
1.0069360733032227,
0.3491631746292114,
0.6936661601066589,
0.3399471044540405,
0.061086684465408325,
0.6748008131980896,
1.0059908628463745,
-0.04775833338499069,
-0.11749427020549774,
0.12049999833106995,
-0.3708316683769226,
-0.2913905680179596,
0.7709141969680786,
0.6550249457359314,
-0.3979707956314087,
0.726636528968811,
-0.7849782705307007,
0.6424487829208374,
-1.0149531364440918,
0.24078354239463806,
0.07316680252552032,
-0.17790400981903076,
0.25320425629615784,
0.3956387937068939,
-0.42989957332611084,
0.8878278136253357,
-0.42958149313926697,
-0.579641580581665,
-0.5544971227645874,
0.7790544033050537,
0.4475443661212921,
-0.054644886404275894,
-0.3845832645893097,
-0.42110055685043335,
0.673596203327179,
0.5540854930877686,
-0.056660816073417664,
0.8102148771286011,
0.03173210844397545,
0.11931967735290527,
0.29448533058166504,
1.23787522315979,
0.37180793285369873,
0.361156702041626,
-0.07870802283287048,
-0.40917548537254333,
-0.19042623043060303,
0.17145618796348572,
-0.7206088900566101,
-0.6997992396354675,
-0.4769746661186218,
-0.020772166550159454,
0.2649492621421814,
-0.5738591551780701,
0.2612512707710266,
-0.7388737201690674,
0.033067572861909866,
0.9495794773101807,
-0.21130500733852386,
-0.6664500832557678,
0.6970074772834778,
-0.03386484086513519,
0.6768540740013123,
0.6882826685905457,
0.7849165201187134,
-0.1721796989440918,
1.3200467824935913,
0.8894765973091125,
-0.033246107399463654,
0.12892447412014008,
0.44027021527290344,
-0.3215537667274475,
0.19705508649349213,
-0.020187372341752052,
-0.3471767008304596,
0.33355987071990967,
-0.1188407689332962,
-0.6981721520423889,
-0.36137932538986206,
0.08969635516405106,
-0.8619885444641113,
-0.1308974325656891,
0.4862871766090393,
0.6477795243263245,
-0.6259349584579468,
-0.10612636804580688,
0.4800463318824768,
0.6319645643234253,
0.031001586467027664,
-0.17287994921207428,
0.009728369303047657,
-0.4373116195201874,
-0.29838860034942627,
-0.8079999685287476,
0.2909901440143585,
-0.46420300006866455,
-0.5197879672050476,
-0.15369324386119843,
-0.56429123878479,
-0.14001700282096863,
-0.2222479283809662,
-0.5408186912536621,
-0.05578386411070824,
0.6592216491699219,
0.6295875906944275,
0.862648606300354,
0.4811486005783081,
-0.5242911577224731,
0.3202532231807709,
0.3877098858356476,
0.6287177205085754,
0.004036734811961651,
0.42790457606315613,
0.9794195890426636,
0.3801161050796509,
-0.03739623725414276,
-0.053527869284152985,
0.3026811182498932,
-0.229320228099823,
0.47481569647789,
0.1932803988456726,
0.3962253928184509,
-0.7088909149169922,
-0.25643259286880493,
-0.18105220794677734,
0.13810749351978302,
0.1847194880247116,
-0.25724107027053833,
-0.8817504048347473,
-0.09318754822015762,
-1.353866696357727,
0.07814324647188187,
-0.7891132235527039,
0.4941116273403168,
-0.2453232854604721,
0.18817758560180664,
-0.5041143894195557,
0.09562631696462631,
4.110594272613525,
0.797868549823761,
0.7819151282310486,
-0.5031316876411438,
0.8182075619697571,
0.5632908344268799,
0.29678136110305786,
-0.8360029458999634,
0.28595152497291565,
-0.17660149931907654,
0.37445229291915894,
0.04117581993341446,
0.4014057219028473,
0.2790561020374298,
-0.5247437357902527,
0.2267531007528305,
-1.006882667541504,
-0.030728379264473915,
0.5872974395751953,
-1.3435523509979248,
-0.5106737017631531,
0.4335094392299652,
-0.14487311244010925,
-0.22257240116596222,
0.25461626052856445,
0.39103689789772034,
0.5361238121986389,
-0.5184088349342346,
-0.008215520530939102,
-0.6335890293121338,
-0.688671350479126,
-0.4928496181964874,
0.1791527271270752,
0.518653154373169,
-0.35309380292892456,
0.5683963298797607,
0.6053008437156677,
-0.019995657727122307,
-0.46621453762054443,
-0.2136656790971756,
0.6899510622024536,
0.2659963071346283,
-0.22621043026447296,
-0.24278061091899872,
-0.8560349941253662,
0.46127933263778687,
-0.26750972867012024,
0.8664149045944214,
0.575303852558136,
-0.8685970306396484,
0.26465505361557007,
-0.054980430752038956,
1.2399823665618896,
-0.014096728526055813,
-1.3506300449371338,
0.12687121331691742,
-0.43579405546188354,
-0.519826352596283,
-0.509169340133667,
0.4105246961116791,
1.1687558889389038,
0.138223335146904,
-0.5456472635269165,
-0.2133353352546692,
-1.0210741758346558,
0.33741331100463867,
0.12946848571300507,
-0.14642955362796783,
-0.25214701890945435,
0.8288741707801819,
-0.31965622305870056,
-0.32829225063323975,
-0.31222063302993774,
-0.05878391116857529,
0.2945092022418976,
0.3584097623825073,
-0.5288548469543457,
0.3420686721801758,
0.41610583662986755,
-0.5921542048454285,
0.27056416869163513,
-0.14141394197940826,
0.5047593116760254,
-0.1787535399198532,
0.2538764476776123,
0.8602681159973145,
-0.031236015260219574,
0.16783776879310608,
-0.2258330136537552,
0.6340978741645813,
0.6460496783256531,
1.0550765991210938,
0.07034064084291458,
0.21650095283985138,
-0.7858879566192627
] |
An Improved Acceptance Procedure for the Hybrid Monte Carlo Algorithm
|
The probability of accepting a candidate move in the hybrid Monte Carlo algorithm can be increased by considering a transition to be between windows of several states at the beginning and end of the trajectory, with a state within the selected window being chosen according to the Boltzmann probabilities. The detailed balance condition used to justify the algorithm still holds with this procedure, provided the start state is randomly positioned within its window. The new procedure is shown empirically to significantly improve performance for a test system of uncoupled oscillators.
|
R. M. Neal
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208011
|
hep-lat/9208012
|
[
0.3247639536857605,
-0.056667670607566833,
0.4706684947013855,
0.6195893883705139,
-0.21016983687877655,
-0.2944352328777313,
-0.2202068567276001,
-0.45872700214385986,
-0.8625533580780029,
1.552924633026123,
0.4464516341686249,
0.07917366176843643,
0.14360255002975464,
-0.8769891262054443,
0.28546661138534546,
0.3693944811820984,
-0.13023874163627625,
-0.1567424088716507,
-1.6699260473251343,
0.7608288526535034,
0.2055070698261261,
0.011823389679193497,
-1.2944457530975342,
-0.511677622795105,
-0.15721134841442108,
1.2217094898223877,
0.041068483144044876,
0.40540340542793274,
1.0449594259262085,
0.18780940771102905,
0.30025333166122437,
-0.5802609920501709,
-0.429497092962265,
-0.4120963215827942,
-0.5161951780319214,
-0.12120243161916733,
-0.45229440927505493,
-0.04426764324307442,
0.7374613285064697,
-0.48313501477241516,
0.5192857980728149,
-0.7525737285614014,
0.2022211104631424,
-0.4373360574245453,
-0.33679574728012085,
0.57853102684021,
0.21401463449001312,
-0.22263871133327484,
-0.21586979925632477,
-0.9376417994499207,
0.16924364864826202,
0.7458348274230957,
0.6692802309989929,
-1.0523515939712524,
-0.2883000373840332,
-0.15815849602222443,
0.09106431901454926,
0.37389594316482544,
-0.6358588337898254,
-0.10247021168470383,
0.4004988670349121,
0.041096024215221405,
0.6067476272583008,
-0.41218945384025574,
-0.03218517079949379,
1.1674247980117798,
-0.5982874631881714,
0.672080934047699,
-0.17700758576393127,
-0.17001664638519287,
-0.4552159309387207,
-0.4952518045902252,
-0.7800605297088623,
0.2757498323917389,
-0.8531005382537842,
-0.29741525650024414,
-0.2765389680862427,
-0.3703499138355255,
-0.7789484858512878,
-0.32719942927360535,
0.013178986497223377,
0.7899091243743896,
-0.21134312450885773,
0.35321947932243347,
-0.3380250036716461,
-0.30942320823669434,
-0.18013930320739746,
-0.09928479045629501,
0.023261064663529396,
0.6541039943695068,
0.10316026955842972,
0.7172028422355652,
-0.20186837017536163,
0.07473033666610718,
0.16416651010513306,
0.5110312700271606,
0.021788233891129494,
0.17680113017559052,
0.4771544337272644,
0.4276757538318634,
0.5865128636360168,
0.5532808303833008,
-0.30333298444747925,
0.07380570471286774,
-0.6549723148345947,
0.5761752128601074,
0.24525293707847595,
-0.30087247490882874,
-0.28104034066200256,
-0.5230119228363037,
0.2028779536485672,
0.01623397134244442,
0.8701454997062683,
0.5360414981842041,
0.18371260166168213,
0.7214152812957764,
-0.60627281665802,
-0.3256487548351288,
-0.8735979795455933,
-0.26876622438430786,
0.2559000253677368,
0.17993655800819397,
-0.23910027742385864,
0.7605419754981995,
0.17736878991127014,
-0.015934184193611145,
1.0290710926055908,
0.5762225389480591,
-0.2822023630142212,
0.510604202747345,
-0.08634410053491592,
-0.08485814929008484,
-0.37761127948760986,
0.4989820718765259,
-0.5997287631034851,
-0.08646784722805023,
-0.2594141960144043,
0.36661088466644287,
-0.6136881113052368,
-0.26896265149116516,
0.5990722179412842,
-0.42092758417129517,
0.08269966393709183,
1.039705514907837,
0.32199257612228394,
0.01217834185808897,
0.2362768054008484,
0.1398804485797882,
-0.057166535407304764,
0.6524161100387573,
-0.7781543135643005,
0.15915894508361816,
-0.045838769525289536,
0.08381000906229019,
-0.07618308067321777,
0.31792327761650085,
-0.7826562523841858,
0.2948109805583954,
-0.7472382187843323,
-0.47571176290512085,
0.7172120213508606,
0.08623722940683365,
-0.5211953520774841,
0.2691330313682556,
-0.5820336937904358,
-0.13964056968688965,
-0.1675591617822647,
-0.4424009919166565,
0.1655552238225937,
-0.6490963697433472,
0.19215869903564453,
0.9521881341934204,
-0.17167386412620544,
1.0593239068984985,
0.9069860577583313,
0.1539485901594162,
0.3384803831577301,
-0.6631619334220886,
0.04347355291247368,
0.6418408751487732,
-0.28517961502075195,
-0.6034373044967651,
0.6425747275352478,
-0.16601401567459106,
-0.5270439386367798,
0.2370627373456955,
0.10138526558876038,
-0.7153013944625854,
0.19377321004867554,
0.2652393877506256,
-0.47091808915138245,
0.3871230185031891,
-0.6700728535652161,
0.1836816817522049,
-0.8507831692695618,
-0.480442613363266,
-1.0163663625717163,
0.12828664481639862,
-0.37194734811782837,
-0.23772042989730835,
-0.24622058868408203,
0.43809401988983154,
-0.6959777474403381,
0.16060850024223328,
-1.7277750968933105,
-0.3384748101234436,
1.0774058103561401,
-0.19295217096805573,
-0.47262465953826904,
-0.04518861323595047,
0.7017726302146912,
-0.44042035937309265,
0.00903566274791956,
-0.4665418863296509,
0.31600555777549744,
0.16096580028533936,
-0.6222512722015381,
-0.06041457876563072,
0.487038791179657,
0.42059850692749023,
0.4558730721473694,
0.13404354453086853,
0.15781822800636292,
0.7070788741111755,
-0.5109092593193054,
-0.7677139639854431,
0.09470490366220474,
0.5971095561981201,
0.6714814305305481,
-0.24317429959774017,
0.1781609207391739,
0.8802153468132019,
-0.03948361799120903,
0.6803808808326721,
0.9092431664466858,
0.18324311077594757,
0.7144715785980225,
0.6858699321746826,
0.5680304169654846,
0.7690069675445557,
-0.37773722410202026,
0.4006887376308441,
0.31093305349349976,
0.16037020087242126,
-0.46772539615631104,
0.25046950578689575,
-1.0554170608520508,
0.009494747966527939,
-1.0249921083450317,
-0.13348761200904846,
-0.09458854794502258,
0.48247867822647095,
0.31321561336517334,
0.21493583917617798,
-1.1490122079849243,
-0.3940621614456177,
-0.7021207213401794,
0.10175550729036331,
0.009227355010807514,
0.0867268368601799,
-0.23519478738307953,
0.11987969279289246,
-0.13622701168060303,
-0.45326054096221924,
-0.2354336529970169,
0.9684292674064636,
-0.4057071805000305,
0.058716557919979095,
1.1182068586349487,
-0.16542454063892365,
-1.0305391550064087,
0.3507365584373474,
-0.8675260543823242,
-0.02524949051439762,
-0.6820307970046997,
0.5312251448631287,
1.0243276357650757,
-0.7018884420394897,
0.08033286780118942,
0.3915861248970032,
-0.3347585201263428,
0.356398344039917,
-0.3708716034889221,
0.24726618826389313,
0.5649610757827759,
0.23969408869743347,
-0.9507054686546326,
0.1990644484758377,
-0.9110931754112244,
-0.20635993778705597,
-0.3236798048019409,
-0.12906266748905182,
0.8711850047111511,
-0.3834538459777832,
0.19198285043239594,
0.1135471984744072,
-0.7068530321121216,
0.14574922621250153,
-0.07354532182216644,
-0.9791396856307983,
0.23455967009067535,
-0.06672070920467377,
-0.227370947599411,
-0.1508205235004425,
-0.840043842792511,
0.7659865021705627,
-0.059216178953647614,
0.06451988965272903,
0.5732588768005371,
0.3478546142578125,
-0.31948158144950867,
0.2641051709651947,
-0.2496446818113327,
0.07644055783748627,
0.24863484501838684,
1.1814520359039307,
0.5016337037086487,
0.10931245237588882,
-0.22389276325702667,
-0.3732237219810486,
-0.21199220418930054,
0.27758368849754333,
0.029025640338659286,
-0.5530214309692383,
-0.06454237550497055,
0.6081008315086365,
-0.1784939020872116,
-0.47740963101387024,
0.3986668586730957,
-0.7949103713035583,
-0.9681810736656189,
0.439703106880188,
-0.5714085698127747,
0.29145389795303345,
0.10086960345506668,
0.4484347403049469,
-1.198433518409729,
0.07134247571229935,
-0.8464589715003967,
0.0156941507011652,
0.09838758409023285,
-0.26660865545272827,
0.33953630924224854,
0.23829030990600586,
0.5063627362251282,
-0.39772725105285645,
0.37212473154067993,
-0.17425385117530823,
-0.32576683163642883,
0.36164817214012146,
-1.0755555629730225,
0.07695279270410538,
0.42186084389686584,
0.43840324878692627,
-0.4092404842376709,
0.5932648777961731,
-0.3705575168132782,
-0.24041645228862762,
-0.4901389181613922,
-0.772047221660614,
0.3587532937526703,
0.6441259980201721,
-0.02771519497036934,
0.134721577167511,
-1.1622354984283447,
-0.34057217836380005,
0.4220508337020874,
0.08733479678630829,
0.48875364661216736,
-0.6646435260772705,
0.08557187765836716,
0.6693392992019653,
-0.02330510877072811,
-0.05131565406918526,
0.14911925792694092,
0.5368757247924805,
0.520965576171875,
0.029109973460435867,
0.5642140507698059,
-0.3901979625225067,
-0.8763841986656189,
0.010388617403805256,
1.1582931280136108,
0.885832667350769,
0.8564863801002502,
0.22268185019493103,
-0.4068080186843872,
0.4247630536556244,
-0.5650848150253296,
-0.29713866114616394,
-0.1064344197511673,
-0.2392081618309021,
-0.14531363546848297,
-0.2649195194244385,
0.5288621783256531,
0.38862091302871704,
0.28768283128738403,
0.6059868335723877,
0.4422478675842285,
0.08381813019514084,
0.3643518388271332,
0.2877119481563568,
0.7665188908576965,
0.971420168876648,
0.2704595923423767,
0.006462849676609039,
-0.5509723424911499,
0.44518110156059265,
0.20868606865406036,
0.279702752828598,
-0.0896826907992363,
-0.683977484703064,
-0.041337139904499054,
-0.7456254363059998,
0.898701548576355,
0.4504314064979553,
-0.8503940105438232,
0.10444553196430206,
0.026738829910755157,
0.1867809295654297,
-0.3449954688549042,
-0.3099420368671417,
0.874843180179596,
0.41744789481163025,
0.14928790926933289,
-0.3709592819213867,
0.6664304137229919,
-0.5849937200546265,
-0.09155958145856857,
0.27777010202407837,
-0.8816607594490051,
-0.6364789605140686,
-0.6452466249465942,
-0.26734817028045654,
-0.6416118741035461,
0.2784520387649536,
1.148939847946167,
0.41692692041397095,
-0.625166118144989,
-0.612217903137207,
-0.521446943283081,
0.7067726850509644,
-0.5398731231689453,
-0.815873384475708,
0.638440728187561,
0.24514171481132507,
0.011432301253080368,
0.7864425182342529,
-0.16638319194316864,
-0.6996845006942749,
-0.08461512625217438,
-0.3793185353279114,
0.2842901051044464,
-0.031887128949165344,
-0.26606589555740356,
-0.9578432440757751,
-0.6853203773498535,
0.13047626614570618,
0.6596627831459045,
0.05911487340927124,
-0.38366177678108215,
0.35602909326553345,
-0.026622654870152473,
-0.1734744906425476,
0.4592286944389343,
-0.016463352367281914,
0.19734641909599304,
1.2402286529541016,
1.2209506034851074,
0.3259633481502533,
0.18845680356025696,
0.392213374376297,
0.08613532036542892,
0.17607571184635162,
0.08273978531360626,
0.1553533673286438,
-0.0024425783194601536,
-0.5956287980079651,
0.10565353184938431,
-0.9104133248329163,
-0.4768531322479248,
0.636272668838501,
-0.4859854280948639,
0.7682662606239319,
0.13132436573505402,
-0.575491726398468,
-0.5325571894645691,
-0.7889142632484436,
-0.48403114080429077,
0.7133943438529968,
-0.21001023054122925,
-0.4760480523109436,
0.4010254442691803,
-0.24479113519191742,
-0.19076105952262878,
-0.06768744438886642,
0.1061561331152916,
-0.6526605486869812,
-0.09789584577083588,
0.8967167735099792,
0.14882494509220123,
0.11150942742824554,
-0.8005760312080383,
0.3916425108909607,
-0.36632561683654785,
-0.23881693184375763,
-0.4532853066921234,
-0.2691885828971863,
0.1133934035897255,
-0.8257195353507996,
0.8158087134361267,
0.17585164308547974,
-0.2884046733379364,
-0.23174022138118744,
-0.20535877346992493,
-0.29960739612579346,
-0.03868945688009262,
-0.5970430374145508,
-0.2005130648612976,
0.3629867434501648,
0.12542085349559784,
-0.3336048424243927,
0.6345362663269043,
0.6296374797821045,
0.7689033150672913,
0.23409338295459747,
-0.3065842390060425,
-0.349595844745636,
-0.07748584449291229,
-0.3089795410633087,
0.24401475489139557,
-0.3993610143661499,
-0.0990557000041008,
0.35749703645706177,
-0.13683567941188812,
0.3433443307876587,
0.6893722414970398,
-0.2653923034667969,
0.069351926445961,
-0.684444785118103,
-0.6758472323417664,
0.4350415766239166,
-0.2575085759162903,
-0.06446264684200287,
-0.6984688639640808,
-0.2147483080625534,
-0.3768770694732666,
0.8853182196617126,
-0.0746467188000679,
0.7850231528282166,
0.4585654139518738,
0.12922360002994537,
0.052812911570072174,
0.3871936500072479,
0.5442368984222412,
-0.11720657348632812,
0.21830904483795166,
0.7535588145256042,
-0.3613167405128479,
0.08788593113422394,
-0.7495762705802917,
0.2534201741218567,
-0.8935547471046448,
0.9238981008529663,
-1.0748400688171387,
-0.14653758704662323,
-0.07012108713388443,
0.3504093587398529,
0.8226416707038879,
-0.8360080122947693,
0.7430860996246338,
0.96891188621521,
-0.2925901710987091,
0.4318109452724457,
0.384018212556839,
-0.6165806651115417,
-0.3934384286403656,
-0.6974751949310303,
-0.9390600323677063,
0.3458738327026367,
0.4778921902179718,
-0.3291032612323761,
-0.8090148568153381,
-0.853400468826294,
-0.18864957988262177,
-0.5785186290740967,
0.33385732769966125,
0.008006599731743336,
-0.5361945629119873,
0.5762537717819214,
0.15248610079288483,
0.30984044075012207,
-0.4662633538246155,
-0.25144678354263306,
-0.25236794352531433,
-0.6804540157318115,
0.27367910742759705,
0.039887189865112305,
-0.6549241542816162,
-0.3243318498134613,
0.17696145176887512,
0.38768911361694336,
0.4824233055114746,
-0.49487966299057007,
0.6714445948600769,
-0.05498979240655899,
-0.9319794178009033,
-0.5034891366958618,
0.008842915296554565,
0.3805087208747864,
0.4370272755622864,
0.4814629554748535,
0.09841182827949524,
0.17530520260334015,
-0.08875928819179535,
0.5826246738433838,
-0.48410168290138245,
-0.12409041076898575,
0.4402428865432739,
-0.4299580454826355,
-0.7212669253349304,
0.4345471262931824,
-0.3555052876472473,
-0.27112430334091187,
-0.5824976563453674,
-1.349029302597046,
-0.19350524246692657,
-0.5374518632888794,
-0.3159394860267639,
0.32904675602912903,
-0.09960898011922836,
-0.007518473081290722,
0.44149309396743774,
0.7810692191123962,
0.20895066857337952,
-0.5302952527999878,
0.12666645646095276,
-0.45491793751716614,
-0.6032483577728271,
-0.3526327610015869,
1.4290064573287964,
0.2261505275964737,
-0.6739360094070435,
-0.21454288065433502,
0.10834470391273499,
-0.3100959360599518,
0.3159297704696655,
0.6005332469940186,
-0.696247935295105,
0.23359154164791107,
-0.03468400985002518,
-0.0064347716979682446,
0.3154698312282562,
0.41203901171684265,
0.3458230197429657,
0.5256555080413818,
-0.040894556790590286,
-0.6989558935165405,
-0.07068262994289398,
-0.5987606048583984,
0.07478424906730652,
0.5958040356636047,
0.2927602529525757,
0.46684256196022034,
-0.3805849850177765,
-0.4304869472980499,
0.10552912205457687,
-0.5677770972251892,
0.12324637919664383,
-0.891072154045105,
0.11168648302555084,
-0.2354789525270462,
-0.5650233626365662,
-0.10927210748195648,
0.39170992374420166,
-0.37073805928230286,
-0.2075699120759964,
-0.7157713174819946,
-0.04913920909166336,
0.7587019205093384,
0.7193619012832642,
-0.40161558985710144,
-0.8694267272949219,
-0.7176353931427002,
-0.023598916828632355,
-0.0765237957239151,
-0.5155812501907349,
0.06058511883020401,
0.14224769175052643,
-0.2085925042629242,
0.053322017192840576,
-0.007872717455029488,
0.6216803193092346,
-1.048188328742981,
-0.7711787223815918,
-0.28590667247772217,
0.006682416889816523,
-0.18359458446502686,
0.5332056283950806,
0.14767839014530182,
0.6121402382850647,
0.4022729992866516,
0.1848997175693512,
-0.843989908695221,
0.4848572909832001,
-1.2281913757324219,
0.05334213748574257,
0.4970472455024719,
0.42975178360939026,
0.537763237953186,
-0.37744495272636414,
-0.1814676821231842,
0.09176594018936157,
-0.8722296357154846,
-0.017653243616223335,
-1.0795934200286865,
-0.3100448250770569,
-0.2202896773815155,
0.6347585916519165,
0.623981237411499,
0.3751853406429291,
-0.2987845838069916,
0.7747876048088074,
-0.49026888608932495,
-0.041657816618680954,
0.21719111502170563,
0.09984779357910156,
-0.425540953874588,
-0.20311710238456726,
0.30478644371032715,
-0.11293088644742966,
-0.07245739549398422,
0.5269510746002197,
-0.2645336389541626,
0.0660814717411995,
-0.13854561746120453,
-0.5109384655952454,
0.09124339371919632,
-0.12428898364305496,
-0.3337569832801819,
0.4939471483230591,
0.09028831124305725,
-0.7098938226699829,
-0.13566097617149353,
-0.7092188000679016,
-0.5581257343292236,
0.3041548430919647,
-0.14570443332195282,
-0.37534332275390625,
-0.1476273536682129,
0.43732669949531555,
-0.7454890608787537,
0.5119618773460388,
0.08393436670303345,
0.6281147003173828,
-0.3866012394428253,
-0.12049911916255951,
0.12631285190582275,
-0.15502440929412842,
-0.2647564709186554,
0.03881128504872322,
-0.6892417073249817,
-0.31184855103492737,
0.056635014712810516,
0.8736804723739624,
-0.702434778213501,
-0.44279158115386963,
-0.5737153887748718,
0.44790735840797424,
0.15330778062343597,
0.2830904722213745,
-0.35386958718299866,
-0.14402887225151062,
0.028540192171931267,
0.12731556594371796,
-0.4720463454723358,
-0.2314477413892746,
-0.41403886675834656,
0.448392391204834,
-0.26715144515037537,
-1.0187904834747314,
0.3995860815048218,
0.0970100685954094,
0.1994795799255371,
-0.22172464430332184,
-0.16918884217739105,
0.5867764949798584,
0.400600403547287,
-0.4777453541755676,
0.5639324188232422,
-0.06095977872610092,
0.22747206687927246,
0.5508548617362976,
-0.7227162718772888,
0.4860483705997467,
0.1662137359380722,
-0.4159448742866516,
0.7297507524490356,
0.3284769058227539,
0.24567483365535736,
0.37680748105049133,
0.160314679145813,
0.10088831186294556,
-0.3600548803806305,
-0.3240964114665985,
0.06837774813175201,
0.5495964288711548,
-0.5156443119049072,
-0.18045319616794586,
0.11766758561134338,
-0.06806986033916473,
-0.06808491051197052,
-0.22223982214927673,
-0.22583037614822388,
0.1118442490696907,
0.13916853070259094,
0.47948896884918213,
-1.0188854932785034,
-0.6660028100013733,
0.2552717328071594,
0.2882997691631317,
0.3234110176563263,
-0.07235664874315262,
0.23084059357643127,
1.0306174755096436,
0.4985451102256775,
0.20679029822349548,
0.36416900157928467,
0.5031534433364868,
0.3118739426136017,
1.1334046125411987,
0.30657854676246643,
0.8443926572799683,
0.26100727915763855,
0.5602275729179382,
0.7008447647094727,
-0.9635100960731506,
0.5530250072479248,
0.14722739160060883,
-0.8278449773788452,
0.21942439675331116,
-0.36722099781036377,
0.337756872177124,
-0.21548037230968475,
-0.04020588845014572,
0.08914262056350708,
-0.7321234345436096,
0.07798600941896439,
0.5544105768203735,
-0.609686017036438,
0.36408424377441406,
0.7978706955909729,
-0.002715307753533125,
0.3178882896900177,
0.6338017582893372,
-0.31838059425354004,
-0.1315814107656479,
0.9284191131591797,
1.332723617553711,
0.3554553687572479,
-0.10668562352657318,
0.2928942143917084,
-0.815823495388031,
0.7096044421195984,
0.5407565236091614,
-0.3020995557308197,
1.0335603952407837,
-0.41494524478912354,
-0.23635046184062958,
0.6110764741897583,
0.042858369648456573,
-0.1833643764257431,
-0.6527103781700134,
-0.03746826574206352,
-0.2514210045337677,
-0.3556310534477234,
-0.47359615564346313,
1.6875437498092651,
0.5078528523445129,
-0.48597845435142517,
-0.5015420317649841,
0.24135953187942505,
-0.22634856402873993,
-0.1606668084859848,
-0.5198174118995667,
0.26395997405052185,
-0.15661956369876862,
-0.20024846494197845,
-0.07790806889533997,
-0.6589659452438354,
-0.8632087111473083,
-1.1621488332748413,
0.5317063927650452,
-0.9437821507453918,
0.6615447402000427,
-0.6331194639205933,
0.5915886759757996,
-0.059753332287073135,
-0.6260839104652405,
-0.12035771459341049,
0.0007558095385320485,
0.7880127429962158,
-0.10632286965847015,
0.14456167817115784,
0.9039393067359924,
0.2219313681125641,
-1.2540807723999023,
0.33218061923980713,
0.527377724647522,
-0.37095510959625244,
0.41879794001579285,
-0.09857571125030518,
0.04088738560676575,
0.44285836815834045,
0.17728908360004425,
0.5503879189491272,
-0.20154885947704315,
0.40383708477020264,
0.006046004593372345,
-0.1704264134168625,
-0.4659006893634796,
-1.1998238563537598,
-0.06774447113275528,
-0.33803483843803406,
-0.044227879494428635,
0.09449057281017303,
0.2713400423526764,
0.8859289884567261,
-0.5494743585586548,
4.225983619689941,
0.8315422534942627,
0.7375352382659912,
0.18501664698123932,
0.2465360164642334,
0.5951911211013794,
-0.3206460475921631,
-0.7963917255401611,
0.5450090169906616,
-0.3099178373813629,
-0.35357967019081116,
-0.00440884567797184,
0.19221651554107666,
-0.4477725923061371,
-0.012367636896669865,
0.1740160435438156,
-0.024283340200781822,
-0.3293198347091675,
-0.1660698503255844,
-0.9171021580696106,
-0.40339216589927673,
0.30746760964393616,
-0.31186750531196594,
0.18690705299377441,
0.32569417357444763,
0.048049140721559525,
0.18988355994224548,
0.1628435254096985,
-0.14306902885437012,
-0.6694396734237671,
-0.7275134325027466,
-0.9576500654220581,
0.03251964971423149,
0.3073776960372925,
-0.5059806704521179,
0.06516101956367493,
0.2441064566373825,
-0.8859586119651794,
0.46000775694847107,
-0.03202904015779495,
0.1237713098526001,
-0.6377384662628174,
0.08329413831233978,
-0.24309059977531433,
-0.17548570036888123,
0.6068991422653198,
0.5794387459754944,
0.19389930367469788,
-0.03895194083452225,
-0.5478048920631409,
0.3544568717479706,
-0.19126561284065247,
0.6416009068489075,
-0.44496604800224304,
-1.1249881982803345,
-0.07956227660179138,
-0.8382223844528198,
0.08359958976507187,
0.45634639263153076,
-0.01700684241950512,
0.31423085927963257,
-0.3999681770801544,
-0.2741798460483551,
0.01643451303243637,
-0.6840771436691284,
0.519704282283783,
-0.25190988183021545,
0.5497106909751892,
-0.3730153441429138,
0.16058923304080963,
0.029388517141342163,
-0.4711596667766571,
-0.28064802289009094,
-0.15066906809806824,
0.012793822214007378,
0.21891552209854126,
0.2523941397666931,
0.9532800912857056,
0.03245709091424942,
0.27336665987968445,
0.2325085550546646,
-0.05041692033410072,
-0.1422242969274521,
-0.13674752414226532,
0.19202926754951477,
0.8686193823814392,
-0.5295596718788147,
-0.018799591809511185,
-0.13499143719673157,
0.6276546716690063,
0.342553049325943,
0.9184319972991943,
0.38437458872795105,
-0.2357606589794159,
-0.9746012687683105
] |
Scaling and Asymptotic Scaling in the SU(2) Gauge Theory
|
We determine the critical couplings for the deconfinement phase transition in $SU(2)$ gauge theory on $N_\tau \times N_\sigma^3$ lattices with $N_\tau = 8$ and 16 and $N_\sigma$ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio $T_c / \sqrt{\sigma}$ in the entire coupling regime $\beta =2.30-2.75$, while the individual quantities still exhibit large scaling violations. We find $T_c / \sqrt{\sigma}=0.69(2)$. We also discuss in detail the extrapolation of $T_c / Lambda_{\rm{\bar{M} \bar{S}}}$ and $\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}}$ to the continuum limit. Our result, which is consistent with the above ratio, is $T_c / Lambda_{\rm{\bar{M}\bar{S}}} = 1.23(11)$ and $\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}} = 1.79(12)$. We also comment upon corresponding results for $SU(3)$ gauge theory and four flavour QCD.
|
J. Fingberg, U. M. Heller and F. Karsch
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208012
|
hep-lat/9208013
|
[
-0.0010890852427110076,
0.2623310685157776,
-0.04521903768181801,
0.16336441040039062,
0.19643062353134155,
-0.8309702277183533,
-0.5433593392372131,
-0.4662269651889801,
-0.7848681807518005,
1.2075347900390625,
0.5579518675804138,
0.2203838974237442,
0.3214865028858185,
-0.526721179485321,
0.5252740979194641,
0.8284466862678528,
-0.1884956955909729,
-0.9014847874641418,
-1.6641725301742554,
1.0671707391738892,
0.4428204596042633,
-0.39188066124916077,
-0.9834367036819458,
-1.079881191253662,
0.17488360404968262,
0.8297916054725647,
0.18391995131969452,
-0.3319881558418274,
1.366308569908142,
0.9015591740608215,
0.526874303817749,
-0.5029769539833069,
-0.6703345775604248,
0.04833849519491196,
-0.4102140963077545,
-0.35025355219841003,
-0.6489404439926147,
-0.14104756712913513,
0.7521430253982544,
-0.25121936202049255,
0.484078973531723,
-0.40622785687446594,
-0.06311298161745071,
-0.2240094244480133,
-1.0013543367385864,
0.36491867899894714,
0.34011271595954895,
0.3381385803222656,
0.3547428548336029,
-1.5025758743286133,
0.26353076100349426,
0.3413683772087097,
0.4842454791069031,
-0.22418656945228577,
-0.6807374954223633,
0.23215316236019135,
0.6855280995368958,
-0.4051560163497925,
-0.675379753112793,
-0.3827531933784485,
0.5045210123062134,
0.0019480049377307296,
0.37467727065086365,
-0.563820481300354,
0.3424040973186493,
0.8675804734230042,
-0.7628507018089294,
0.44962769746780396,
-0.16397421061992645,
-0.40980878472328186,
-0.09925263375043869,
-0.6670449376106262,
-0.27715611457824707,
0.24334941804409027,
-0.5110042095184326,
0.02318061888217926,
-0.34151363372802734,
-0.5370182394981384,
-0.560861349105835,
-0.5536773800849915,
-0.38716262578964233,
-0.0079075638204813,
-0.7255493402481079,
0.16846944391727448,
-0.7074005603790283,
-0.4361362159252167,
0.0705847442150116,
-0.5469160079956055,
0.19481876492500305,
0.13588568568229675,
0.1062406599521637,
0.634294867515564,
-0.29048311710357666,
-0.3099364638328552,
0.2708272933959961,
1.0043601989746094,
0.0527549609541893,
0.9219321012496948,
0.5719759464263916,
-0.06116124987602234,
0.013798017986118793,
0.5531378388404846,
-1.1373980045318604,
0.37889590859413147,
-0.9065964818000793,
0.4675377905368805,
-0.43002745509147644,
-0.5137640237808228,
-0.5366113781929016,
-0.47113415598869324,
0.15423370897769928,
0.06996242702007294,
0.5994307994842529,
0.5420752167701721,
0.19319379329681396,
0.5540767312049866,
-0.6370112299919128,
-0.30119311809539795,
-0.6734225153923035,
-0.4092251658439636,
0.882037341594696,
-0.016779383644461632,
0.32349610328674316,
0.40111565589904785,
-0.09142313152551651,
-0.5062103867530823,
0.7065297961235046,
0.9046927094459534,
-0.9700368642807007,
0.6973922252655029,
-0.18534576892852783,
-0.20587700605392456,
-0.3673573136329651,
0.49840855598449707,
-0.4252246022224426,
0.3820802867412567,
-0.7833362221717834,
-0.040059223771095276,
0.14410357177257538,
-0.6397687196731567,
0.892423689365387,
-0.5490815043449402,
0.19464200735092163,
0.7062419652938843,
0.6557797789573669,
0.15884536504745483,
0.3060060143470764,
0.4751235842704773,
-0.25447478890419006,
0.38357481360435486,
-0.6463449597358704,
-0.1037549152970314,
-0.00022273520880844444,
0.4485551118850708,
0.5188934803009033,
0.34210672974586487,
-1.049166202545166,
-0.002174138557165861,
-0.47934237122535706,
-0.25378888845443726,
0.2878144085407257,
-0.20714114606380463,
-0.6965925097465515,
0.6830298900604248,
-0.7394838929176331,
0.11513330787420273,
-0.5255622267723083,
-0.6722911596298218,
0.71973717212677,
-0.41759929060935974,
-0.22351869940757751,
0.12353117763996124,
-0.045887291431427,
0.9236947298049927,
0.5720707774162292,
0.2858681082725525,
0.3090517818927765,
-0.6663117408752441,
0.7401298880577087,
0.15028256177902222,
-0.10262852907180786,
-0.27657046914100647,
0.33304649591445923,
0.3115992546081543,
-0.3349684178829193,
-0.24495495855808258,
-0.06881260871887207,
-0.40085935592651367,
0.28625962138175964,
0.5614187121391296,
-0.09180213510990143,
0.09877727180719376,
-0.03768870607018471,
0.714462161064148,
-0.4307679831981659,
-0.11192578077316284,
-0.9303629398345947,
0.11797372996807098,
-0.9745364189147949,
-0.5157986879348755,
-0.12115829437971115,
0.25221195816993713,
-0.8479798436164856,
0.48273277282714844,
-1.723827600479126,
0.1483909636735916,
0.20909874141216278,
0.15922947227954865,
-0.1959124356508255,
-0.14763127267360687,
0.2839873135089874,
-0.038337547332048416,
0.49007827043533325,
-0.4214537739753723,
0.26218175888061523,
0.71723872423172,
0.26909294724464417,
0.3655301332473755,
0.3075592517852783,
0.026980295777320862,
0.674765408039093,
0.3896082639694214,
-0.14772488176822662,
0.32150813937187195,
-0.763966977596283,
-1.059609293937683,
0.35530900955200195,
0.7786752581596375,
0.25655651092529297,
0.03557799756526947,
0.40783780813217163,
0.3560175597667694,
-0.1454724818468094,
0.7698544859886169,
0.7347573041915894,
0.7497088313102722,
0.4759024977684021,
0.6286691427230835,
0.29188045859336853,
0.4685610234737396,
0.28320732712745667,
0.25815629959106445,
0.6068471670150757,
0.0029880048241466284,
-0.3384271562099457,
0.2538474202156067,
-0.5159735679626465,
0.2480817288160324,
-0.7207338809967041,
0.33656173944473267,
-0.6340128183364868,
0.544439971446991,
-0.5018206834793091,
0.5065647959709167,
-0.6124153137207031,
0.4077191948890686,
0.2577667236328125,
0.0022908293176442385,
-0.07745629549026489,
-0.10620086640119553,
-0.06246639043092728,
0.056610167026519775,
-0.07367578893899918,
-1.027598261833191,
-0.23772098124027252,
1.0755615234375,
-0.09821711480617523,
-0.08265668153762817,
0.2724817395210266,
-0.45955559611320496,
-1.2511111497879028,
-0.15693722665309906,
-0.6244848370552063,
0.21873649954795837,
-0.6746550798416138,
-0.49480727314949036,
0.669931173324585,
-0.9521876573562622,
0.6120705604553223,
0.05253829061985016,
-0.17724475264549255,
0.36551937460899353,
-0.353933185338974,
0.22372083365917206,
0.7122084498405457,
0.27363917231559753,
-1.0877765417099,
-0.04345472902059555,
-0.8280882239341736,
0.019948357716202736,
-0.23150433599948883,
-0.36098772287368774,
1.1880874633789062,
-0.01571515016257763,
1.0559366941452026,
0.003707688767462969,
-0.41913700103759766,
-0.41822442412376404,
-0.23775449395179749,
-0.8423781394958496,
0.38214462995529175,
0.49864888191223145,
-0.0952325314283371,
-0.08052615821361542,
-0.7703892588615417,
0.8596404194831848,
0.16837365925312042,
-0.379934698343277,
0.6170264482498169,
0.07985444366931915,
-0.5077902674674988,
0.47354617714881897,
0.04611736536026001,
-0.17989784479141235,
0.02451334148645401,
0.9774631261825562,
0.8971102833747864,
0.3709470331668854,
-0.4095383584499359,
-0.44948509335517883,
-0.4394349455833435,
0.7392389178276062,
0.04215790703892708,
-0.4505765438079834,
0.1064148023724556,
0.7520403861999512,
0.05003874748945236,
-0.6783498525619507,
0.472787469625473,
-0.7721096873283386,
-0.5118118524551392,
-0.17688630521297455,
-0.5545930862426758,
0.35092419385910034,
0.11515292525291443,
0.5530616641044617,
-0.8818812370300293,
-0.09869474917650223,
-0.07930216193199158,
0.031256891787052155,
-0.10778237134218216,
-0.15096619725227356,
0.7474825978279114,
0.13056640326976776,
0.5619012713432312,
0.022565796971321106,
-0.2004658579826355,
-0.48860615491867065,
-0.2868187427520752,
-0.02109341137111187,
-0.8736662268638611,
0.44375374913215637,
-0.016860855743288994,
0.31775733828544617,
0.17549288272857666,
0.21628084778785706,
-0.5484644174575806,
-0.8015685677528381,
-0.2710171341896057,
-0.11328904330730438,
0.4207793176174164,
0.6565621495246887,
-0.04659225046634674,
-0.5279185175895691,
-0.6879950165748596,
0.08992272615432739,
0.17199838161468506,
0.2755247950553894,
0.8699297308921814,
-0.7860753536224365,
0.5972362756729126,
0.5474618077278137,
-0.22708679735660553,
0.05690005049109459,
0.0868387222290039,
0.47304725646972656,
0.43814677000045776,
0.17066167294979095,
1.0151410102844238,
-0.4399886131286621,
-1.043472409248352,
-0.05122926086187363,
0.9717000722885132,
0.4719792306423187,
0.7279996275901794,
0.11108136177062988,
-0.22484037280082703,
-0.31927961111068726,
-0.8244689106941223,
-0.31977900862693787,
-0.2716667354106903,
-0.23030568659305573,
0.04178335890173912,
-0.14470508694648743,
0.2529347836971283,
-0.0643337145447731,
0.39823052287101746,
0.39816170930862427,
0.9369016885757446,
-0.3488423228263855,
0.28242379426956177,
0.3858974575996399,
0.52925705909729,
0.8966835141181946,
-0.19430264830589294,
-0.18752720952033997,
-0.6607643961906433,
0.15455874800682068,
0.6388515830039978,
0.34840869903564453,
0.2865833640098572,
-0.9133878946304321,
0.09556293487548828,
-0.6866081357002258,
0.8211097121238708,
0.12377876788377762,
-0.9543275237083435,
0.15114589035511017,
0.17199581861495972,
0.6428636312484741,
-0.1563248634338379,
-0.011418032459914684,
1.1323175430297852,
0.6010707020759583,
0.3973343074321747,
-0.7562938332557678,
0.3060013949871063,
-0.9616323709487915,
0.24522975087165833,
-0.017133381217718124,
-0.471375435590744,
-0.542396605014801,
-0.9829180836677551,
-0.24403847754001617,
-0.7833401560783386,
0.697601318359375,
1.1869029998779297,
0.19849567115306854,
-0.024069955572485924,
-0.7225980162620544,
-0.3244445323944092,
0.6643004417419434,
-0.33418309688568115,
-0.5461727380752563,
0.1722077578306198,
-0.027469221502542496,
-0.06856109946966171,
0.6382215619087219,
-0.11727189272642136,
-0.46244552731513977,
-0.04782893881201744,
-0.5650426149368286,
0.12799261510372162,
-0.6843538880348206,
-0.5559037327766418,
-0.4953424036502838,
-0.2736513912677765,
-0.08644118160009384,
0.4405114948749542,
0.301296204328537,
-0.1715621054172516,
0.0838007777929306,
0.3112817704677582,
-0.02195192314684391,
0.3357580602169037,
0.31854021549224854,
-0.08620395511388779,
0.5677829384803772,
0.9963229894638062,
0.5007386803627014,
-0.0008796801557764411,
0.1542106419801712,
0.48494693636894226,
0.2510562539100647,
0.23328819870948792,
0.10492580384016037,
-0.43093341588974,
-0.45987799763679504,
-0.20718030631542206,
-0.5921527147293091,
-0.805878221988678,
0.13320499658584595,
-0.5113347768783569,
0.6404383182525635,
-0.005847457330673933,
-0.6150214076042175,
-0.7772008776664734,
-1.1518728733062744,
-0.5246660113334656,
0.10246249288320541,
-0.14712858200073242,
-0.18245437741279602,
0.9742962718009949,
-0.9271449446678162,
0.05697057396173477,
-0.06747757643461227,
-0.2296302616596222,
-0.10785221308469772,
0.4942622780799866,
1.088788628578186,
0.14158888161182404,
0.5142472386360168,
-0.7971181869506836,
0.01867365837097168,
-0.7131366729736328,
0.3478091061115265,
-0.7887840867042542,
-0.8214519619941711,
0.03607405722141266,
-0.3359278738498688,
-0.09170175343751907,
-0.10914399474859238,
0.1324579417705536,
0.30939123034477234,
0.2652167081832886,
-0.4046301245689392,
-0.009570755995810032,
-0.72441565990448,
-0.20411477982997894,
0.7348566055297852,
0.019302884116768837,
-0.603009819984436,
-0.1318478137254715,
0.3261287212371826,
-0.029415085911750793,
-0.09929458051919937,
0.6246538162231445,
-0.2661724388599396,
-0.12739139795303345,
-0.4901876151561737,
0.961177408695221,
-1.051615595817566,
-0.6573120951652527,
-0.40941792726516724,
-0.9740319848060608,
0.7511852979660034,
0.8335176706314087,
0.14432425796985626,
-0.12129144370555878,
-0.3307453989982605,
-0.36854425072669983,
-0.1355571448802948,
-0.5180469155311584,
0.13232716917991638,
-0.9305582642555237,
-0.6568577289581299,
0.3610436022281647,
0.5109213590621948,
0.5042576789855957,
0.23762673139572144,
0.41016048192977905,
0.27369263768196106,
0.2811175286769867,
0.4153628647327423,
0.19191795587539673,
-0.40276023745536804,
-0.605856716632843,
-0.308647096157074,
-0.10910189151763916,
0.26686036586761475,
-0.16065479815006256,
0.5543491244316101,
-0.8762338161468506,
1.0841528177261353,
-0.9623466730117798,
0.2564256191253662,
-0.43886837363243103,
-0.08258426189422607,
0.6632202863693237,
-0.8992716670036316,
0.41144752502441406,
0.5914186239242554,
-0.34221112728118896,
-0.04302094504237175,
0.15993402898311615,
-0.05548116937279701,
-0.11376415193080902,
-0.7778221964836121,
-0.9870128035545349,
0.6811490654945374,
0.3195616900920868,
-0.43252354860305786,
-0.7113736271858215,
-0.8508681058883667,
0.7085422873497009,
0.16835777461528778,
0.5054065585136414,
0.8778173923492432,
0.038518887013196945,
0.30445438623428345,
0.6205998659133911,
0.16282491385936737,
-0.11079709231853485,
0.19807898998260498,
-0.13744302093982697,
-0.021161876618862152,
0.24859076738357544,
-0.11994273215532303,
-0.602754533290863,
-0.7451297640800476,
0.04462360963225365,
0.6644797325134277,
0.22966383397579193,
-0.526722252368927,
0.9232903718948364,
-0.4271817207336426,
-1.1019819974899292,
-0.5873976349830627,
-0.019370408728718758,
-0.3532656133174896,
0.12769977748394012,
0.5161404609680176,
0.1499699503183365,
0.5779041647911072,
-0.5203005075454712,
0.9059040546417236,
-0.6917303800582886,
-0.11062313616275787,
0.8773418068885803,
-0.9797677397727966,
-0.7720560431480408,
0.19965828955173492,
0.15783816576004028,
-0.7707624435424805,
-0.3185396194458008,
-0.8367911577224731,
0.7123167514801025,
-0.7722455859184265,
-0.16056939959526062,
0.030441131442785263,
-0.18899445235729218,
-0.13633406162261963,
0.6196115016937256,
0.6088452935218811,
-0.6964117288589478,
0.02893402986228466,
0.8321227431297302,
-0.5675772428512573,
0.3110993206501007,
0.40565845370292664,
0.7412313222885132,
0.1560666561126709,
-0.7538825273513794,
0.052486319094896317,
0.0893864557147026,
0.20478558540344238,
-0.17258505523204803,
0.25276440382003784,
0.15645918250083923,
0.5063501000404358,
0.23514242470264435,
0.6068497896194458,
-0.12197978049516678,
-0.20929019153118134,
0.6677844524383545,
-0.46108195185661316,
-0.4733641445636749,
-0.29799529910087585,
-0.6974071860313416,
-0.5805259943008423,
0.35147571563720703,
0.9206098914146423,
-0.21184547245502472,
0.3285059630870819,
0.3346380293369293,
-0.677829384803772,
-0.46805840730667114,
-0.983512818813324,
-0.1869015097618103,
-1.5450518131256104,
0.4798906743526459,
-0.6450585722923279,
-0.4871377944946289,
-0.048516858369112015,
0.5699396729469299,
0.017484543845057487,
-0.4084412753582001,
-0.25864362716674805,
-0.4628537595272064,
0.5500090718269348,
-0.08571469783782959,
-0.36111578345298767,
-0.5156996250152588,
-0.08640988171100616,
-0.47072872519493103,
-0.20478110015392303,
-0.15735496580600739,
-0.06592150777578354,
-0.26941439509391785,
0.08109311759471893,
0.7304115295410156,
0.11574192345142365,
0.9787805080413818,
-0.707097053527832,
-0.7737594842910767,
-0.023037347942590714,
0.3130497932434082,
-0.5993142127990723,
0.15635915100574493,
-0.13735148310661316,
1.1282463073730469,
0.3474027216434479,
0.5070224404335022,
-0.6998500823974609,
0.1927141696214676,
-1.5204368829727173,
-0.3678266108036041,
0.24014322459697723,
0.10536498576402664,
-0.395388662815094,
-0.7750920057296753,
0.18558910489082336,
0.29557478427886963,
-1.1895997524261475,
0.2602512538433075,
-0.8103958964347839,
-0.06654053181409836,
-0.9260903000831604,
0.7713872194290161,
0.42633453011512756,
0.35579073429107666,
-0.1424332559108734,
0.6944433450698853,
-0.17639915645122528,
0.02641078270971775,
0.31050392985343933,
0.6472703814506531,
-0.6892290115356445,
0.09373214095830917,
-0.2376355081796646,
-0.4520336985588074,
-0.07443903386592865,
0.0350777730345726,
-0.27854248881340027,
-0.08394747972488403,
0.3002914488315582,
-0.5210109353065491,
-0.27403220534324646,
0.01809774525463581,
-0.32509845495224,
0.4979251027107239,
0.2203129231929779,
-0.965806782245636,
-0.14321383833885193,
-0.37318551540374756,
-0.7243919968605042,
-0.28916534781455994,
-0.6298216581344604,
0.08398642390966415,
0.041085079312324524,
-0.18024508655071259,
0.057177986949682236,
0.5764257907867432,
-0.014652733691036701,
0.4911082983016968,
0.06078089028596878,
0.5576699376106262,
-0.09521487355232239,
-0.04816824197769165,
-0.7436649799346924,
0.23553015291690826,
-0.841362714767456,
-0.33478814363479614,
-0.19411738216876984,
0.36314481496810913,
-0.9132484793663025,
-0.8068576455116272,
-0.03100953809916973,
0.5629381537437439,
-0.05276218429207802,
0.6175608038902283,
-0.05429268628358841,
-0.5173362493515015,
-0.11774072796106339,
0.2262050062417984,
-0.3505525588989258,
-0.13005509972572327,
-0.9442922472953796,
0.43055611848831177,
0.435454398393631,
-0.657733142375946,
0.27122288942337036,
0.6499655246734619,
0.12153232097625732,
-0.13881289958953857,
-0.011978380382061005,
0.9708185195922852,
0.06233086809515953,
-0.6899158954620361,
0.6881312727928162,
0.18664239346981049,
0.5359928607940674,
-0.2912482023239136,
-0.4704068601131439,
0.5536458492279053,
0.5150390267372131,
0.2218567430973053,
0.6730190515518188,
0.7511316537857056,
0.43703681230545044,
0.35615789890289307,
0.2883061468601227,
-0.22589930891990662,
0.3456585705280304,
-0.10130586475133896,
0.7755275964736938,
0.49914419651031494,
-0.04178115725517273,
-0.34940198063850403,
-0.5812950134277344,
-0.05404076352715492,
-0.004348705057054758,
-0.020489761605858803,
-0.5487220287322998,
-0.26070746779441833,
0.3622514009475708,
0.2749572694301605,
-0.5312104821205139,
-0.4564465880393982,
-0.3571437895298004,
-0.27295035123825073,
0.904211163520813,
-0.17517246305942535,
-0.07646431773900986,
0.1912757009267807,
0.5162295699119568,
-0.019189374521374702,
-0.23157064616680145,
0.8852773308753967,
0.18608136475086212,
0.9129391312599182,
0.8119432330131531,
0.7030114531517029,
0.4899808466434479,
0.31870418787002563,
0.2576442360877991,
-1.2023179531097412,
0.16721956431865692,
0.30638694763183594,
-1.1280598640441895,
-0.287548691034317,
-0.9075996279716492,
0.15062707662582397,
-0.5979555249214172,
-0.2710924446582794,
0.9305378198623657,
0.40982183814048767,
0.3687478303909302,
0.37204504013061523,
-0.16367632150650024,
-0.004256660584360361,
0.989173412322998,
0.18214313685894012,
0.0880703404545784,
0.5660231709480286,
-0.10714276880025864,
0.2388790249824524,
1.10004460811615,
1.360180139541626,
0.29782167077064514,
0.7127476334571838,
0.37877345085144043,
-0.5378177762031555,
0.33774957060813904,
0.5737087726593018,
-0.28069326281547546,
0.1694393903017044,
-0.3380500376224518,
-0.583222508430481,
0.37587833404541016,
0.15475815534591675,
-0.3092547655105591,
-0.2817496657371521,
0.4567191004753113,
0.4606541097164154,
-0.8209207057952881,
-0.5142796039581299,
1.5571328401565552,
0.6778233647346497,
-0.5784330368041992,
-0.2792489528656006,
0.28183624148368835,
-0.4341467618942261,
0.4360924959182739,
-1.6333868503570557,
0.3276931047439575,
-0.41002926230430603,
-0.19739246368408203,
-0.10855533927679062,
-0.5121999979019165,
-0.2703220844268799,
-1.3215893507003784,
0.2875968813896179,
-0.339704304933548,
0.60173100233078,
0.2673754394054413,
-0.2198556363582611,
0.4743037521839142,
-0.4531623423099518,
-0.1303902566432953,
-0.1290576457977295,
0.9831219911575317,
0.32587507367134094,
0.3592768609523773,
1.0073963403701782,
0.42600780725479126,
-0.974358081817627,
-0.20833444595336914,
0.8411081433296204,
-0.8367676138877869,
1.0486873388290405,
-0.29351529479026794,
0.20307038724422455,
0.20202630758285522,
-0.2478116750717163,
-0.27241602540016174,
-0.6859523057937622,
0.595700740814209,
0.009226907975971699,
0.24177737534046173,
-0.3813854157924652,
-0.9931459426879883,
-0.20848345756530762,
-0.8251193761825562,
-0.25047075748443604,
0.33255597949028015,
0.35568952560424805,
0.0948442816734314,
-0.14360123872756958,
4.047340393066406,
0.6488218307495117,
0.7665503621101379,
0.4024006128311157,
1.0121691226959229,
1.2180578708648682,
-0.3969363272190094,
0.4155545234680176,
0.33093827962875366,
-0.8010909557342529,
-0.1025179922580719,
0.5598848462104797,
0.788811206817627,
-0.25231465697288513,
-0.0019372591050341725,
1.0107485055923462,
-0.0392351895570755,
0.26276785135269165,
-0.11791018396615982,
-1.0484551191329956,
-0.899501621723175,
0.15717670321464539,
-0.013335160911083221,
0.5811916589736938,
-0.16869215667247772,
0.29621830582618713,
0.22480712831020355,
-0.7266473770141602,
-0.5075433850288391,
-0.4216920733451843,
-0.4242928624153137,
-0.92039954662323,
-0.033000919967889786,
-0.1511239856481552,
-0.5966122150421143,
0.48527705669403076,
0.38151124119758606,
-0.10018419474363327,
0.19169096648693085,
0.024660736322402954,
-0.018854817375540733,
-0.24507242441177368,
0.2506856918334961,
-0.13455694913864136,
-0.059073738753795624,
0.7359442710876465,
0.10866247862577438,
0.4537099003791809,
0.08558300137519836,
-0.49776244163513184,
0.2050037533044815,
-0.2074183225631714,
1.1092724800109863,
-0.41293391585350037,
-0.8941358327865601,
-0.5523167252540588,
-0.6114529371261597,
-0.14226773381233215,
0.6346635818481445,
0.39909443259239197,
0.669796884059906,
-0.40669161081314087,
0.1240350604057312,
0.08177446573972702,
-0.32104113698005676,
0.49347445368766785,
-0.1595471203327179,
-0.17770637571811676,
-0.3680151104927063,
0.15520340204238892,
-0.16618534922599792,
-0.2592364549636841,
-0.34643855690956116,
0.43098562955856323,
0.10848835110664368,
0.06908763945102692,
-0.15757334232330322,
0.8330028653144836,
0.1411028653383255,
-0.12590189278125763,
0.058811064809560776,
-0.4359072744846344,
-0.3671013414859772,
-0.11937018483877182,
0.032075706869363785,
0.5377345085144043,
-0.7002674341201782,
0.09573278576135635,
-0.18071560561656952,
0.40831878781318665,
0.07348036020994186,
1.3023273944854736,
0.296840637922287,
-0.18250758945941925,
-0.5470466017723083
] |
Gauge invariant extremization on the lattice
|
Recently, a method was proposed and tested to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize $\int(\dl S/\dl A_\mu)^2$. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we show how extremization can be formulated in a way that preserves gauge invariance on the lattice. The method applies to any gauge group and any lattice action. The procedure is worked out in detail for the standard plaquette action with gauge groups U(1) and SU(N).
|
A.J. van der Sijs
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208013
|
hep-lat/9208014
|
[
0.48531898856163025,
-0.1618310511112213,
-0.21771027147769928,
0.20954269170761108,
0.9540549516677856,
-0.2467048019170761,
-0.2213844209909439,
0.5571954846382141,
-0.4092563986778259,
1.4726479053497314,
1.0154874324798584,
-0.3435901999473572,
-0.34281790256500244,
-0.8877139091491699,
-0.12417400628328323,
0.6837131381034851,
-0.49637535214424133,
-0.6390950679779053,
-1.004591941833496,
-0.15269038081169128,
0.7535063028335571,
-0.0072151427157223225,
-1.6827512979507446,
-0.3083898723125458,
-0.47915321588516235,
0.8152797818183899,
0.7096428871154785,
-0.23872044682502747,
1.3982466459274292,
1.1537683010101318,
1.0006879568099976,
-0.4356316924095154,
-0.17141325771808624,
-0.22233271598815918,
-0.6710066199302673,
-0.36616602540016174,
-0.05952487140893936,
0.3816133141517639,
0.6108195185661316,
-0.3051493167877197,
0.4673320949077606,
-0.1522558331489563,
0.08470303565263748,
-0.3868560194969177,
-0.6613035798072815,
-0.5074967741966248,
0.46280622482299805,
0.34324243664741516,
0.5435264706611633,
-1.5392918586730957,
-0.17236220836639404,
-0.2611977756023407,
0.3625733256340027,
-1.022049069404602,
-0.590141773223877,
-0.05865683779120445,
0.8455104231834412,
0.09010309725999832,
-0.5219020247459412,
-0.06917774677276611,
0.42454490065574646,
0.4699324667453766,
-0.03490802273154259,
-1.0427871942520142,
0.30796200037002563,
0.6305394768714905,
-0.03465930372476578,
0.1915438175201416,
0.4199303090572357,
-0.8664582371711731,
-1.05216646194458,
-0.4048280715942383,
-0.6391239166259766,
-0.20189112424850464,
-0.10258568823337555,
0.46672970056533813,
0.145127072930336,
-0.19305558502674103,
-0.7881559729576111,
-0.15795421600341797,
-0.29359546303749084,
-0.01625695452094078,
-0.6619373559951782,
0.5611307621002197,
0.35595959424972534,
-0.4885336756706238,
0.4856431782245636,
0.6967524886131287,
0.37597620487213135,
0.026463685557246208,
-0.5264580845832825,
0.5013477802276611,
0.23445965349674225,
0.15612071752548218,
1.0170977115631104,
0.9111349582672119,
-0.4702952206134796,
0.6919999718666077,
0.2126084268093109,
-0.004981840029358864,
-0.010076608508825302,
1.367833137512207,
-0.24987418949604034,
0.7886843085289001,
-0.8196005821228027,
0.3748122453689575,
0.18448811769485474,
0.16578108072280884,
0.04344901442527771,
-0.4003434181213379,
0.3551119565963745,
0.3460270166397095,
0.41240012645721436,
0.5519614815711975,
-0.018338415771722794,
0.2254382222890854,
-0.38125908374786377,
-0.46538522839546204,
-0.6653489470481873,
-0.09655729681253433,
0.36406293511390686,
0.18669776618480682,
1.1647614240646362,
0.476222962141037,
0.16588975489139557,
-1.0622211694717407,
-0.3142082393169403,
0.39803946018218994,
-1.1174346208572388,
0.401255339384079,
-0.012346218340098858,
0.0006623972440138459,
-0.27496138215065,
0.025851590558886528,
-0.6580889225006104,
-0.5984806418418884,
-0.5717779397964478,
-0.2156171053647995,
-0.20118087530136108,
-0.1993434578180313,
0.7828248143196106,
-0.8517559170722961,
0.14244964718818665,
1.6552311182022095,
-0.22170443832874298,
0.9123908877372742,
0.30919501185417175,
0.15622490644454956,
-0.6963911652565002,
0.5978444218635559,
-0.17215947806835175,
-0.19384773075580597,
-0.2858356237411499,
0.35366082191467285,
0.07164942473173141,
-0.3575705587863922,
-0.6777304410934448,
-0.06159525364637375,
-0.7377510666847229,
-0.279110312461853,
0.36917662620544434,
-0.24537265300750732,
0.5279678702354431,
1.2318059206008911,
-0.5021896958351135,
0.7836266756057739,
-0.6486174464225769,
0.12487149238586426,
0.5578925609588623,
-0.37332582473754883,
-0.1648740917444229,
-0.3344269096851349,
-0.4225381016731262,
0.7882595658302307,
0.9816411733627319,
0.49756717681884766,
0.0617397278547287,
-0.18839219212532043,
0.7142226696014404,
0.514408528804779,
0.014525585807859898,
-0.9993966221809387,
1.1341865062713623,
0.6068257093429565,
-0.5345560312271118,
-0.09883374720811844,
0.3872663378715515,
-0.15296325087547302,
-0.06004428490996361,
-0.11906671524047852,
-0.6307628750801086,
0.40504947304725647,
-0.8686820864677429,
0.6593197584152222,
-0.9274552464485168,
0.23586392402648926,
-0.45923325419425964,
0.29812467098236084,
-0.6344617605209351,
-0.3532200753688812,
0.13465139269828796,
0.2733285129070282,
0.019669046625494957,
0.19574441015720367,
-0.9515619277954102,
0.45261839032173157,
-0.09180580824613571,
0.40669432282447815,
-0.46203377842903137,
-0.0013673182111233473,
0.4682042598724365,
-0.2525944113731384,
0.24295590817928314,
-0.30969029664993286,
0.0019272627541795373,
0.18593767285346985,
-0.2988507151603699,
0.5222452282905579,
0.5340187549591064,
-0.32046663761138916,
0.6980886459350586,
0.6179975271224976,
-0.31881842017173767,
0.5972591042518616,
-0.0665411502122879,
-0.12613219022750854,
0.3386620283126831,
1.1089601516723633,
-0.18691082298755646,
1.4023371934890747,
0.41869330406188965,
0.681825578212738,
0.11025447398424149,
0.1069130003452301,
0.46078360080718994,
0.18984730541706085,
0.5811040997505188,
0.9862650036811829,
0.13157492876052856,
-0.14041197299957275,
0.3079015612602234,
0.12062228471040726,
0.3808259069919586,
0.19746606051921844,
-0.3610731065273285,
0.6491502523422241,
0.26341718435287476,
0.6232573390007019,
-1.0149126052856445,
0.7382083535194397,
-0.7387051582336426,
1.2640656232833862,
-0.4053482711315155,
-0.1097700372338295,
-0.6554500460624695,
-0.25018739700317383,
-0.22306986153125763,
0.6387677192687988,
-0.26392167806625366,
-0.39691466093063354,
-0.339228093624115,
0.5088602900505066,
0.7271568775177002,
-0.9605448842048645,
-0.6410744786262512,
0.9061768651008606,
-0.047029465436935425,
-0.06783398985862732,
0.1719016283750534,
-0.5347571969032288,
-1.275888204574585,
-0.03003399819135666,
-0.7156413793563843,
-0.16713891923427582,
-0.2633488178253174,
-0.14958250522613525,
0.34678828716278076,
-0.07954216003417969,
0.11228401958942413,
-0.3187522292137146,
0.2653875946998596,
0.19845308363437653,
0.1244155764579773,
-0.388522207736969,
0.273291677236557,
0.013723233714699745,
-1.071908712387085,
0.3727559745311737,
-0.027344614267349243,
0.48447078466415405,
-0.48705336451530457,
-0.364457368850708,
0.4696734547615051,
-0.39026713371276855,
0.46699273586273193,
0.23422783613204956,
-0.27160513401031494,
-0.5934445858001709,
0.21636517345905304,
-0.7658629417419434,
-0.5303857326507568,
-0.18835724890232086,
0.5076660513877869,
0.21948441863059998,
-0.5464359521865845,
1.253001093864441,
0.26427313685417175,
-0.6256312727928162,
0.5661102533340454,
0.02713783085346222,
-0.5641032457351685,
0.03196020424365997,
0.11793576180934906,
0.07034950703382492,
-0.15632854402065277,
1.2020061016082764,
0.7384650707244873,
-0.1640229970216751,
0.33316585421562195,
-0.39126601815223694,
-0.5754308104515076,
-0.07895594835281372,
0.6744111776351929,
-0.609062135219574,
0.20979468524456024,
1.0980656147003174,
-0.09266548603773117,
-1.136160135269165,
0.4773404896259308,
-0.8877606391906738,
-0.5943779945373535,
-0.14367572963237762,
-0.6357575058937073,
0.4359724521636963,
0.28367820382118225,
0.10691295564174652,
-0.5924171805381775,
-0.07748594880104065,
0.033351730555295944,
0.8405252695083618,
0.11915796250104904,
-0.2907968759536743,
-0.0008276067092083395,
-0.0538480170071125,
0.5030328631401062,
-0.35064107179641724,
0.04289062321186066,
0.14253896474838257,
-0.09713611006736755,
0.8740545511245728,
-0.39633938670158386,
0.669788122177124,
0.048449937254190445,
0.0569031685590744,
0.3698887825012207,
-0.3779493570327759,
0.21227887272834778,
-0.6426729559898376,
-0.8111541271209717,
0.20859724283218384,
-0.4207569360733032,
0.23033498227596283,
-0.20318341255187988,
-0.40645477175712585,
-0.7502330541610718,
-0.6674150228500366,
0.25332745909690857,
0.1343795508146286,
1.0772736072540283,
-0.4006308615207672,
0.9905608296394348,
0.2569228708744049,
-0.2958708107471466,
-0.032739151269197464,
-0.48426592350006104,
-0.1822493076324463,
-0.14697015285491943,
0.15775594115257263,
0.39764848351478577,
-0.05166446045041084,
-1.3633756637573242,
0.2977108061313629,
0.7949057817459106,
0.38874542713165283,
0.7150071859359741,
0.11646037548780441,
0.316808819770813,
-0.4592307209968567,
-0.2526378035545349,
0.24237550795078278,
-0.4306333065032959,
-0.19968192279338837,
-0.7698662877082825,
-0.6957558989524841,
0.08887691050767899,
-0.37577226758003235,
0.44121941924095154,
0.9896081686019897,
0.577015221118927,
-0.14031459391117096,
0.038153160363435745,
0.20186764001846313,
0.3378552496433258,
1.1453646421432495,
-0.08362464606761932,
0.0313001349568367,
-1.2959986925125122,
0.8019801378250122,
0.5211793184280396,
-0.13894595205783844,
0.3617154359817505,
-0.29326915740966797,
0.27242323756217957,
0.2695612609386444,
0.6164372563362122,
0.16707241535186768,
-1.0727394819259644,
0.16409730911254883,
-0.2780842185020447,
-0.16604457795619965,
-0.5341119170188904,
-0.5592904686927795,
0.375660240650177,
0.40443897247314453,
0.15260790288448334,
-1.1678667068481445,
-0.22898197174072266,
-0.7252622842788696,
0.21324560046195984,
0.39936715364456177,
-0.8709594011306763,
-1.006742000579834,
0.05557308346033096,
-0.8152630925178528,
-0.23451869189739227,
0.4159228801727295,
0.8153942227363586,
0.004080168902873993,
-0.2299201786518097,
-0.7560802102088928,
-0.48221448063850403,
0.13403621315956116,
0.2057376205921173,
-0.6475059390068054,
0.4686245322227478,
-0.11414886265993118,
-0.09677736461162567,
0.5510836243629456,
0.23188480734825134,
-0.8758842945098877,
-0.6292725801467896,
-0.29108700156211853,
0.24815507233142853,
-0.42935696244239807,
-0.12503118813037872,
-0.4713279604911804,
0.5326223969459534,
-0.5623945593833923,
0.3728969395160675,
-0.2654830813407898,
0.23789741098880768,
-0.19847910106182098,
-0.005154023878276348,
-0.15524248778820038,
-0.007465210277587175,
0.035921450704336166,
0.2793768048286438,
0.6538981199264526,
0.6811602115631104,
0.49646151065826416,
0.11684587597846985,
0.39324450492858887,
0.21663407981395721,
0.14843203127384186,
0.5655342936515808,
-0.7294045686721802,
0.027406170964241028,
-0.5548911690711975,
-0.2632989287376404,
-0.2842916250228882,
-0.6158179044723511,
0.4544866979122162,
-0.46891161799430847,
-0.02903023548424244,
0.07825266569852829,
-0.32119104266166687,
-0.7515642046928406,
-0.5893645286560059,
-0.6992985606193542,
0.2476506531238556,
-0.08877482265233994,
0.12639322876930237,
0.5216584205627441,
-1.0233978033065796,
-0.3964672386646271,
-0.22590675950050354,
-0.18307416141033173,
0.4350014328956604,
0.17789563536643982,
0.8578597903251648,
0.2026372253894806,
1.047570824623108,
-0.9156284928321838,
-0.020869800820946693,
-0.5465207695960999,
-0.15517657995224,
-0.7559984922409058,
-1.032113790512085,
-0.39813676476478577,
0.4241214096546173,
-0.4824807047843933,
-0.9761472344398499,
0.30500248074531555,
0.13286727666854858,
0.23486177623271942,
0.27210482954978943,
-0.19181647896766663,
-0.22976097464561462,
-0.5660569071769714,
0.4308035969734192,
0.826828122138977,
-1.1481837034225464,
-0.3322417736053467,
0.28793787956237793,
-0.026714645326137543,
0.29558345675468445,
-0.003377707442268729,
-0.02269917167723179,
0.2770436406135559,
-0.9581457376480103,
0.227024108171463,
-1.1058752536773682,
-1.0989408493041992,
-0.0718841403722763,
-1.006127953529358,
0.4646185636520386,
-0.10391949862241745,
0.37820279598236084,
-0.7229481339454651,
-0.3466872572898865,
-0.4845065474510193,
0.13934652507305145,
-0.40270793437957764,
0.0903937965631485,
-1.0337867736816406,
-0.42752957344055176,
-0.5395498871803284,
0.8659999370574951,
0.04599582031369209,
-0.042976852506399155,
0.08467260748147964,
-0.003383976174518466,
0.11530247330665588,
0.5525981783866882,
0.3778992295265198,
-0.429831326007843,
-0.4805202782154083,
0.030212027952075005,
0.35900187492370605,
-0.2984437942504883,
-0.5089532732963562,
0.8037601113319397,
-0.5918338894844055,
0.672602117061615,
-0.4726721942424774,
0.23801618814468384,
0.02138614095747471,
-0.3413023054599762,
0.7773751020431519,
-0.5320582389831543,
-0.26118963956832886,
0.2891593873500824,
-0.1331203579902649,
0.47663605213165283,
-0.06828310340642929,
-0.5772655606269836,
-0.6527130007743835,
-0.37289759516716003,
-0.7366705536842346,
0.5582712292671204,
-0.16378441452980042,
-0.0420750230550766,
-0.7451316118240356,
-0.6487168669700623,
0.6891993284225464,
-0.5094308257102966,
0.37091144919395447,
0.5511948466300964,
0.8177182078361511,
0.45077741146087646,
-0.48552441596984863,
-0.943223237991333,
-0.6540517807006836,
-0.1199108138680458,
-0.15507031977176666,
-0.5590570569038391,
-0.3829096853733063,
0.6574411392211914,
-0.12199349701404572,
-1.0827488899230957,
-0.3226560354232788,
0.2682015299797058,
0.5720263123512268,
0.06041780859231949,
0.391666978597641,
0.12210381776094437,
-0.4367838203907013,
-0.8863271474838257,
-0.0591772235929966,
-0.36597779393196106,
0.07191167026758194,
0.033352479338645935,
0.4192701280117035,
-0.24505089223384857,
-0.27489134669303894,
0.24033749103546143,
-0.5726029276847839,
-0.28573063015937805,
0.3689241111278534,
-1.1232407093048096,
-0.6590699553489685,
-0.00048659031745046377,
0.08322411775588989,
-0.8510355353355408,
-0.48315784335136414,
-0.6018022298812866,
-0.8305243253707886,
0.24487709999084473,
-0.11524898558855057,
0.21357548236846924,
-0.13328610360622406,
0.2640259563922882,
-0.06905988603830338,
0.739364504814148,
-0.032964371144771576,
-0.2425026148557663,
0.3623909652233124,
0.04491470754146576,
-0.3478352427482605,
1.1111838817596436,
1.0736218690872192,
0.19971002638339996,
-1.0878788232803345,
-0.011463414877653122,
0.25857627391815186,
0.34689608216285706,
-0.5758097171783447,
0.4097655415534973,
-0.4222257137298584,
0.08165954798460007,
0.39531615376472473,
0.9156412482261658,
0.18168361485004425,
-0.10698552429676056,
-0.6404000520706177,
0.15901543200016022,
-0.4266822338104248,
-0.2702246308326721,
-0.249793142080307,
0.09683171659708023,
0.23749209940433502,
1.1886776685714722,
-0.3337177038192749,
0.21301662921905518,
0.4431408941745758,
0.2441573143005371,
-0.3397446274757385,
-1.797373652458191,
0.22260628640651703,
-1.4107539653778076,
-1.0762665271759033,
-1.0075231790542603,
-0.6302188634872437,
0.126165509223938,
-0.09588413685560226,
-0.2155427783727646,
0.19808831810951233,
-0.5102617740631104,
-0.22322870790958405,
-0.6070512533187866,
0.5193147659301758,
-0.8660033941268921,
-0.5836089253425598,
-0.5169225931167603,
0.09641265869140625,
0.14770464599132538,
-1.1830157041549683,
-0.6084526181221008,
0.005160152446478605,
0.04591787979006767,
0.5039268136024475,
-0.04077861085534096,
0.5976189970970154,
-0.5456873178482056,
-0.7439635396003723,
0.03311244025826454,
0.05866852030158043,
-0.37451741099357605,
0.7162824869155884,
-0.6479107141494751,
0.7977895736694336,
-0.24370278418064117,
0.46127405762672424,
-0.1076081320643425,
0.09400852769613266,
-0.374856173992157,
-0.6119215488433838,
0.16529397666454315,
0.3093109428882599,
-0.07657753676176071,
-0.8204455375671387,
0.5655504465103149,
-0.06713943928480148,
-0.6487523317337036,
0.4987080693244934,
0.07423598319292068,
0.2309366911649704,
-0.5892175436019897,
0.094037264585495,
0.638664186000824,
1.1527386903762817,
0.012807528488337994,
0.6746826767921448,
-0.5059924125671387,
0.27517589926719666,
-0.6570633053779602,
1.0015349388122559,
0.10848311334848404,
0.6810774207115173,
0.09576840698719025,
-0.42652931809425354,
0.5182486772537231,
-0.07091332972049713,
-0.08800843358039856,
0.20014196634292603,
-0.2071131318807602,
-0.3246767520904541,
-0.19526010751724243,
0.22145818173885345,
0.022073619067668915,
1.174277424812317,
0.5975114703178406,
-0.41322216391563416,
-0.23058293759822845,
-0.3030450642108917,
-0.9103158116340637,
-0.07792133837938309,
-1.1084082126617432,
-1.146941065788269,
0.07166139036417007,
-0.03892585262656212,
0.17874231934547424,
0.7304033637046814,
0.011514030396938324,
-0.2877376079559326,
0.37629711627960205,
1.5333606004714966,
0.6713522672653198,
0.0662417784333229,
-0.4047843813896179,
0.47485849261283875,
-0.9301348924636841,
-0.3457031846046448,
-0.08826012164354324,
0.44534361362457275,
-1.011319637298584,
-1.1379367113113403,
0.08403647691011429,
1.0298651456832886,
-0.105402871966362,
-0.2294466495513916,
-0.05178487300872803,
-0.562869131565094,
0.39083391427993774,
-0.33247461915016174,
-0.7914067506790161,
0.4307211935520172,
-1.2611421346664429,
0.4801807701587677,
-0.3975888788700104,
-0.540099024772644,
-0.026984544470906258,
-0.02856580726802349,
0.1032877266407013,
0.697116494178772,
-0.11287262290716171,
0.898202657699585,
-0.4232748746871948,
-0.5991198420524597,
1.216004490852356,
0.38599616289138794,
0.7447141408920288,
0.4634990394115448,
-0.11128111928701401,
1.1293392181396484,
0.4418180286884308,
-0.033808980137109756,
0.8607673048973083,
-0.0659918338060379,
0.23346289992332458,
-0.037214621901512146,
0.28786757588386536,
-0.2377098649740219,
0.19594305753707886,
0.23728489875793457,
1.5734233856201172,
0.4053013324737549,
0.04208512604236603,
0.06421791762113571,
-0.02811695821583271,
0.7918844819068909,
0.7763708233833313,
-0.08269093930721283,
-0.05629930645227432,
0.25732889771461487,
0.1533106565475464,
0.7662093043327332,
-0.2432311326265335,
-0.6245956420898438,
-0.4243207573890686,
0.2682654559612274,
0.14409680664539337,
-0.1513712853193283,
-0.5315820574760437,
-0.1448671519756317,
0.6691647171974182,
-0.22185173630714417,
0.3482166528701782,
0.3695804476737976,
0.9361171126365662,
0.5559831261634827,
0.4196324646472931,
0.18137522041797638,
0.06064232438802719,
0.9748764634132385,
-0.20430906116962433,
-0.7325220704078674,
-0.8821442127227783,
0.6588043570518494,
-1.0994771718978882,
0.07629845291376114,
-0.42535316944122314,
-0.4476373791694641,
-0.5465981960296631,
-1.0928633213043213,
0.1997491866350174,
0.13745421171188354,
0.4709616005420685,
0.3027205169200897,
-0.2864951193332672,
-0.418725848197937,
0.9495886564254761,
-0.08045900613069534,
0.7250309586524963,
0.8113501071929932,
0.3162814676761627,
0.1526021957397461,
1.3818740844726562,
1.3081190586090088,
0.5731618404388428,
0.7314353585243225,
-0.37966176867485046,
-0.004592861048877239,
1.0083129405975342,
-0.10390685498714447,
0.7132291793823242,
0.3146369755268097,
-1.0523489713668823,
-0.28816989064216614,
-0.49654605984687805,
0.16158899664878845,
-0.25892218947410583,
-0.23055990040302277,
-0.0262624379247427,
0.16981914639472961,
-0.1839945763349533,
0.28921815752983093,
1.9500232934951782,
-0.14930815994739532,
-0.28499314188957214,
-0.42011985182762146,
0.7839454412460327,
-1.440282940864563,
0.3562091290950775,
-1.2981380224227905,
0.5527136921882629,
0.20119774341583252,
0.015536206774413586,
-0.48702067136764526,
-0.6805134415626526,
-0.43309393525123596,
-0.8411986231803894,
-0.03358295559883118,
-0.7292551398277283,
0.09691169857978821,
0.49119243025779724,
-0.053747281432151794,
0.9879287481307983,
-1.2602741718292236,
-0.06683394312858582,
0.4694884121417999,
0.6147942543029785,
-0.15086664259433746,
0.9980837106704712,
1.1020755767822266,
0.17289073765277863,
-0.9856215119361877,
0.40425625443458557,
0.3931303918361664,
-0.8006115555763245,
0.6952271461486816,
-0.37505030632019043,
0.45586690306663513,
-0.1927025318145752,
-0.6211998462677002,
0.036554351449012756,
0.06429904699325562,
0.5773735642433167,
-0.583177924156189,
-0.12949378788471222,
-0.1607068032026291,
-0.7602062821388245,
0.26775941252708435,
-0.9312923550605774,
-0.1000296026468277,
-0.10396143049001694,
0.2059887945652008,
-0.6159033179283142,
-0.3632213771343231,
3.791931390762329,
1.0881900787353516,
0.805307924747467,
0.8666971921920776,
0.9841746091842651,
1.1432141065597534,
-0.07214120030403137,
0.30129021406173706,
0.007443554233759642,
-0.6850501894950867,
0.12826277315616608,
0.3042300343513489,
0.21705704927444458,
0.3311834931373596,
-0.06378962844610214,
0.37339380383491516,
-0.18380451202392578,
-0.002950231544673443,
-0.2149849683046341,
-0.9906017780303955,
-0.9352102279663086,
-0.14512276649475098,
0.4921243488788605,
0.3258129358291626,
0.346996545791626,
0.1974075585603714,
0.019697600975632668,
-0.8724012970924377,
-0.6633365154266357,
-0.6577227711677551,
0.2521246373653412,
-0.7101786136627197,
0.07964081317186356,
0.2620794475078583,
-0.7489494681358337,
0.04105221480131149,
0.02444775588810444,
-0.6919504404067993,
0.2812784016132355,
-0.11822882294654846,
0.37794336676597595,
0.44489237666130066,
0.018299922347068787,
-0.7540269494056702,
-0.2442818135023117,
1.0579777956008911,
-0.0861167162656784,
0.5956992506980896,
0.2668508291244507,
-0.792132556438446,
0.1113058477640152,
-0.17713534832000732,
0.9340440630912781,
-0.7160454392433167,
-1.1064897775650024,
-0.9871797561645508,
-0.333575040102005,
-0.4901810586452484,
0.4606073498725891,
0.7636510729789734,
0.21328306198120117,
0.07326023280620575,
-0.05846485495567322,
0.5174397230148315,
-0.0525670126080513,
-0.10330899804830551,
0.26568374037742615,
-0.4406236410140991,
-0.28985363245010376,
0.011288478039205074,
0.31091392040252686,
0.2199944108724594,
-0.47228676080703735,
-0.10043808817863464,
-0.32003918290138245,
0.3065919876098633,
-0.06564737111330032,
1.1017863750457764,
-0.08889777213335037,
0.11332588642835617,
-0.44266459345817566,
0.0156449805945158,
0.2624414563179016,
-0.06389766931533813,
0.7632359862327576,
0.6663113832473755,
0.08042585104703903,
0.07752986252307892,
-0.12434951961040497,
0.6590990424156189,
0.09028898924589157,
0.8290172815322876,
-0.18564672768115997,
0.1568303108215332,
-0.8760703206062317
] |
Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity
|
Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations one needs an algorithm which for any given $N$ and a given compact four-dimensional manifold $M$ constructs all possible triangulations of $M$ with $\leq N$ simplices. Our first result is that such algorithm does not exist. Then we discuss recursion-theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four-dimensional manifold.
|
A. Nabutovsky, R. Ben-Av
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208014
|
hep-lat/9208015
|
[
-0.020050903782248497,
0.24422316253185272,
0.3200933635234833,
0.36113888025283813,
-0.26296061277389526,
-0.3335554599761963,
0.04468575865030289,
-0.6275811195373535,
-1.295569658279419,
1.041939616203308,
1.0256321430206299,
0.06051022186875343,
0.565150797367096,
-1.0183930397033691,
0.013745349831879139,
0.4934791624546051,
-0.8489674925804138,
-0.5267550945281982,
-1.3046071529388428,
0.35240039229393005,
0.526426374912262,
0.1173820048570633,
-1.054458737373352,
-0.41379278898239136,
-0.24204084277153015,
0.688605010509491,
0.0435236357152462,
0.6329220533370972,
1.4121493101119995,
0.8825350999832153,
0.8411564826965332,
-0.32903853058815,
-0.08141795545816422,
-0.38401082158088684,
-0.5290685892105103,
-0.3533250093460083,
-0.24501794576644897,
-0.06945197284221649,
1.0251270532608032,
-0.002227548975497484,
1.2004486322402954,
0.038045838475227356,
0.6564275622367859,
0.04590165987610817,
-0.9637326598167419,
0.17240110039710999,
-0.026533503085374832,
-0.12259882688522339,
0.016980860382318497,
-1.3514429330825806,
0.586863100528717,
-0.05478429049253464,
0.9807107448577881,
-0.4560365676879883,
-0.5836195945739746,
-0.27122947573661804,
0.04461076483130455,
-0.18265075981616974,
-0.3308425545692444,
-0.38226285576820374,
0.3103765547275543,
-0.2602936029434204,
0.550529420375824,
-1.1788980960845947,
0.7264344096183777,
0.2614203989505768,
-0.20691697299480438,
0.4456325173377991,
0.4189775288105011,
-0.6431176662445068,
-0.9276950359344482,
-0.7745356559753418,
-0.3900344967842102,
-0.13818709552288055,
-0.31368374824523926,
0.7949210405349731,
-0.272521436214447,
-0.34624555706977844,
-1.2989957332611084,
-0.7578068971633911,
0.13193057477474213,
-0.09222424030303955,
-0.21671034395694733,
0.4533672332763672,
-0.261042058467865,
0.08876161277294159,
-0.11683095246553421,
-0.5579809546470642,
0.28407520055770874,
-0.07159098982810974,
-0.08392394334077835,
0.8925262093544006,
0.1966599076986313,
-0.04861290752887726,
0.4939013123512268,
1.0797971487045288,
0.14273540675640106,
0.8444346785545349,
0.06680154800415039,
0.029216187074780464,
0.38228097558021545,
0.5199435949325562,
-0.6671150922775269,
0.6555448174476624,
-0.21402998268604279,
0.41880813241004944,
-0.29434534907341003,
0.032557304948568344,
0.03579869866371155,
-0.4371091425418854,
0.503082811832428,
-0.07410822808742523,
0.8338022232055664,
0.9722394347190857,
0.07181072980165482,
-0.22856616973876953,
0.0813981294631958,
0.07547769695520401,
-0.8254864811897278,
0.0741327553987503,
-0.1883143186569214,
-0.2774573862552643,
0.3098883032798767,
1.0647571086883545,
-0.11703213304281235,
-0.3588760197162628,
0.21464456617832184,
0.6457783579826355,
-0.17219342291355133,
0.11559554189443588,
0.6125054955482483,
-0.05069706588983536,
0.29697152972221375,
0.41217851638793945,
-0.8578218817710876,
0.09831070899963379,
-0.747745156288147,
0.5348228812217712,
0.1369931399822235,
-0.25246462225914,
0.5609858632087708,
-0.6457863450050354,
0.2440679669380188,
0.6649731397628784,
0.6462912559509277,
0.2856941819190979,
0.36306795477867126,
-0.5291404724121094,
-0.13917869329452515,
0.3630465269088745,
-0.331497460603714,
-0.2797894775867462,
-0.15369021892547607,
0.3228214681148529,
0.20624181628227234,
0.6008678078651428,
-0.7082040309906006,
0.6240043044090271,
-0.5212886929512024,
-0.6717400550842285,
0.47937339544296265,
-0.4266177713871002,
-0.13355523347854614,
0.23264825344085693,
-0.23772487044334412,
0.2722431719303131,
-0.19375114142894745,
-0.152902752161026,
0.04852127283811569,
-0.28040212392807007,
0.25606870651245117,
-0.07122185081243515,
-0.19011084735393524,
0.8539242744445801,
0.028707005083560944,
-0.005399575922638178,
0.17559047043323517,
-0.2136329561471939,
0.4242503345012665,
0.702359676361084,
-0.4180530309677124,
-0.9025759100914001,
1.3842464685440063,
0.10191770642995834,
-0.24227476119995117,
0.14902962744235992,
-0.23240160942077637,
-0.045690495520830154,
0.39337536692619324,
0.10748238116502762,
-0.024975592270493507,
-0.36619454622268677,
-0.3801406919956207,
0.7228291034698486,
-0.34811675548553467,
0.11172133684158325,
-0.8633596897125244,
0.3826298415660858,
-1.0767101049423218,
-0.20892108976840973,
-0.22148263454437256,
0.22919800877571106,
-0.7267544269561768,
0.08149053156375885,
-1.4470043182373047,
-0.027586128562688828,
-0.08806583285331726,
0.41453123092651367,
-0.36645519733428955,
0.2879778742790222,
0.32257264852523804,
-0.0734856054186821,
0.5570532083511353,
-0.7648363709449768,
-0.27100542187690735,
0.6232303380966187,
-0.27492308616638184,
0.4420325458049774,
0.33867236971855164,
-0.17430159449577332,
0.9567700028419495,
0.2617329955101013,
-0.23718300461769104,
0.7340103387832642,
-0.4791697859764099,
-0.4884006977081299,
-0.001504989224486053,
0.5302562713623047,
0.526544988155365,
0.05437387526035309,
0.15370529890060425,
0.6561902165412903,
0.19182834029197693,
0.7753453254699707,
1.0362882614135742,
0.41088008880615234,
0.8002219796180725,
0.7903056144714355,
0.8946017622947693,
0.21170714497566223,
-0.14325834810733795,
-0.019414056092500687,
0.8159059882164001,
-0.054940540343523026,
0.1660182625055313,
0.19783098995685577,
-0.5048298835754395,
0.23169350624084473,
-0.6823500394821167,
0.25824445486068726,
-0.4647083878517151,
0.6063471436500549,
-0.4798394441604614,
0.5025691390037537,
-0.9003037810325623,
-0.20485834777355194,
0.29327014088630676,
0.015728440135717392,
-0.23743008077144623,
-0.19241012632846832,
-0.445925235748291,
-0.15615519881248474,
-0.0813610777258873,
-0.11878843605518341,
-0.6924915909767151,
0.6597632169723511,
-0.0954272449016571,
0.10565538704395294,
-0.26639682054519653,
-0.0960351899266243,
-1.477959156036377,
-0.5080478191375732,
-0.8249808549880981,
-0.033925414085388184,
-0.8843849301338196,
-0.06507661938667297,
1.071938395500183,
-0.7605143189430237,
0.7178819179534912,
0.11936841905117035,
-0.15053685009479523,
0.6574375629425049,
-0.1986456662416458,
0.7024275660514832,
1.0873091220855713,
0.20565982162952423,
-1.2115638256072998,
0.33933088183403015,
-0.4124239385128021,
-0.023492000997066498,
0.21902267634868622,
-0.10387736558914185,
1.2670787572860718,
-0.4365013539791107,
0.17287257313728333,
-0.3562615215778351,
-0.567779004573822,
-0.36026641726493835,
-0.456352561712265,
-0.44949808716773987,
-0.10370872914791107,
0.7311356067657471,
-0.38279619812965393,
0.3106282353401184,
-0.6861085891723633,
1.0984338521957397,
0.5063363313674927,
-0.2201429307460785,
0.7504639625549316,
0.584839940071106,
-0.6820299029350281,
0.4197325110435486,
0.09277080744504929,
-0.08860375732183456,
-0.01270237099379301,
0.6371637582778931,
0.6848942041397095,
0.47925490140914917,
0.1691657155752182,
-0.5653757452964783,
-0.6521646976470947,
0.724635660648346,
-0.06693629920482635,
-0.8461538553237915,
-0.06596720963716507,
0.4543752372264862,
0.019827982410788536,
-0.8787318468093872,
0.06283960491418839,
-1.3860087394714355,
-0.7045683860778809,
-0.05589425563812256,
-0.31648746132850647,
0.6586690545082092,
-0.047613393515348434,
0.31734707951545715,
-0.4730258584022522,
0.1975136548280716,
0.7669420838356018,
0.6468838453292847,
0.36532115936279297,
-0.18421998620033264,
1.1624959707260132,
0.1449037790298462,
0.6653721928596497,
-0.050632767379283905,
0.12056668847799301,
0.1279386430978775,
-0.1641005128622055,
0.338866263628006,
-0.5778893828392029,
-0.018742816522717476,
0.6548773050308228,
0.46425339579582214,
0.06335984170436859,
0.9440358877182007,
-0.41243523359298706,
-0.607600748538971,
-0.7187883257865906,
-0.03061906434595585,
0.7350992560386658,
0.8624637722969055,
-0.3307584524154663,
-0.1158495843410492,
-1.2233444452285767,
-0.7616873383522034,
0.23061886429786682,
0.5011487603187561,
0.818695068359375,
-0.6190796494483948,
0.663163423538208,
0.6267216801643372,
-0.48820701241493225,
0.4422461688518524,
-0.3720102608203888,
-0.1702696979045868,
0.5377533435821533,
0.5594781041145325,
0.5276136994361877,
-1.1736772060394287,
-0.21729430556297302,
0.10984478145837784,
1.312180995941162,
0.6997211575508118,
0.8464498519897461,
0.628900408744812,
-0.2728781998157501,
-0.08463875949382782,
-0.7829542756080627,
-0.7398250699043274,
-0.20064321160316467,
-0.42974138259887695,
-0.7161694765090942,
-0.476558119058609,
-0.21503327786922455,
-0.45218607783317566,
0.4948836863040924,
0.012327550910413265,
0.21266993880271912,
-0.06791983544826508,
0.18124902248382568,
1.1241530179977417,
0.23903754353523254,
1.3060462474822998,
-0.6257510781288147,
-0.4688670337200165,
-0.8801140189170837,
0.4854399561882019,
0.5817092061042786,
-0.20032210648059845,
-0.19039399921894073,
-0.26819491386413574,
-0.7617977857589722,
-0.6641033887863159,
1.0653530359268188,
0.537188708782196,
-0.4316076338291168,
0.5287072062492371,
-0.5220715999603271,
0.26409024000167847,
0.013054931536316872,
-0.27489224076271057,
0.29121747612953186,
0.049985941499471664,
0.4479077160358429,
-0.4730806052684784,
0.000726835336536169,
-0.3002234399318695,
0.7795133590698242,
0.28947412967681885,
-0.9550628066062927,
-0.8807355165481567,
-0.8618324995040894,
-0.14584369957447052,
-0.3191292881965637,
-0.4277423322200775,
0.5251172184944153,
0.1978982836008072,
0.0329904668033123,
-0.8997828364372253,
-0.3204599618911743,
0.22334791719913483,
-0.6511509418487549,
-0.5011178255081177,
-0.36760130524635315,
0.205373153090477,
-0.21117794513702393,
0.5734473466873169,
0.015391278080642223,
-0.5023179054260254,
-0.41958799958229065,
-0.36444592475891113,
-0.1435326784849167,
-0.37049296498298645,
-0.6327598690986633,
-0.8471294045448303,
-0.18035097420215607,
-0.5774275660514832,
0.5252352356910706,
-0.3822600245475769,
0.16065652668476105,
0.29823631048202515,
0.32950150966644287,
-0.28089821338653564,
0.28844013810157776,
0.4041416049003601,
0.39637506008148193,
0.9595445394515991,
0.8359588980674744,
0.6703312397003174,
-0.28771284222602844,
0.21241100132465363,
-0.04082084447145462,
0.30067795515060425,
0.515891432762146,
-0.5759504437446594,
-0.5410403609275818,
-0.16497376561164856,
-0.04292360693216324,
-0.5682465434074402,
-0.8792700171470642,
0.34527263045310974,
-0.7337526679039001,
0.7404861450195312,
0.19070735573768616,
-0.6600514650344849,
-0.31453564763069153,
-0.8358408212661743,
-1.1928343772888184,
0.001823985017836094,
-0.049105748534202576,
-0.6438075304031372,
0.28639811277389526,
-0.32342928647994995,
0.05023680254817009,
-0.22217510640621185,
-0.28193092346191406,
-0.07775858044624329,
0.008082978427410126,
0.45924991369247437,
0.20215818285942078,
0.739322304725647,
-0.33662331104278564,
0.18292367458343506,
-0.14214050769805908,
0.43028414249420166,
-0.3645789623260498,
-0.7576254606246948,
-0.4053804278373718,
-0.29071685671806335,
0.03946299105882645,
-0.5859687924385071,
-0.06539375334978104,
0.5539717078208923,
0.49559012055397034,
0.24707302451133728,
0.33959564566612244,
-0.49477341771125793,
-1.0076994895935059,
0.8556363582611084,
0.0021211723797023296,
-0.6581189632415771,
0.23185427486896515,
0.10511691123247147,
0.47434356808662415,
0.2053445726633072,
0.09503339231014252,
-0.13735824823379517,
-0.03053107112646103,
-0.24309326708316803,
0.3883058726787567,
-1.2576385736465454,
-0.19837667047977448,
-0.37507763504981995,
-0.1083109974861145,
0.375993937253952,
0.7868746519088745,
0.15886269509792328,
-0.13163943588733673,
-0.19461104273796082,
-0.11363392323255539,
0.09002289175987244,
-0.36102211475372314,
-0.2913133203983307,
-0.9102064967155457,
-0.4004128873348236,
-0.05040140822529793,
0.32514050602912903,
-0.09540221840143204,
0.22066257894039154,
0.4795597791671753,
-0.3824220597743988,
-0.025707315653562546,
0.5818673968315125,
0.24467149376869202,
0.2746410369873047,
-0.24699483811855316,
0.42293038964271545,
-0.04506070166826248,
-0.11684536933898926,
-0.7022595405578613,
0.37586334347724915,
-1.4107667207717896,
1.5317929983139038,
0.06942638009786606,
-0.01960095949470997,
-0.046213969588279724,
0.11580513417720795,
0.5473863482475281,
-0.4859897494316101,
-0.3962411880493164,
-0.406279593706131,
-0.09269752353429794,
0.8389171957969666,
0.09872781485319138,
-0.8720122575759888,
-0.8438921570777893,
-0.5577031970024109,
-1.3294883966445923,
0.6597515344619751,
-0.13603277504444122,
-0.1720813661813736,
-1.092366099357605,
-0.5330780148506165,
0.047933485358953476,
-0.079692043364048,
0.4192049503326416,
0.37732455134391785,
0.6890982985496521,
-0.10262564569711685,
0.13216380774974823,
-0.23728714883327484,
-0.5077530145645142,
-0.6035845875740051,
-0.16834639012813568,
-0.17312327027320862,
-0.17431890964508057,
0.23945511877536774,
-0.1632266640663147,
-1.1532845497131348,
-0.017774950712919235,
0.09336013346910477,
0.15166817605495453,
-0.4107992649078369,
0.48760050535202026,
-0.394391268491745,
-0.04542921110987663,
-0.15009745955467224,
-0.033044494688510895,
-0.3889525830745697,
0.10436568409204483,
0.6355535984039307,
0.13945633172988892,
-0.28330492973327637,
-0.3463706076145172,
0.8577049970626831,
-0.4081003665924072,
-0.03061092086136341,
0.37369048595428467,
0.06663446873426437,
-0.42169541120529175,
0.8002651333808899,
0.4006336033344269,
-0.6729341149330139,
-0.6193085312843323,
-0.40416550636291504,
-0.1400964856147766,
-0.11712055653333664,
-0.45186153054237366,
0.4140891432762146,
0.16062627732753754,
-0.4494406282901764,
0.30174314975738525,
0.6681736707687378,
0.17686477303504944,
0.20983774960041046,
0.2861500382423401,
-0.826812744140625,
-0.248053178191185,
0.3679187595844269,
1.025054693222046,
-0.5926001667976379,
-0.49513769149780273,
-0.3943588137626648,
0.058306511491537094,
-0.36536866426467896,
-0.045895032584667206,
0.469112366437912,
-0.39257505536079407,
0.6384257674217224,
0.014898763038218021,
0.8278095722198486,
0.14635847508907318,
-0.3215312659740448,
0.030166951939463615,
-0.33293163776397705,
-0.22674919664859772,
-0.6343319416046143,
-0.8450690507888794,
-0.3389104902744293,
-0.0073158470913767815,
0.46619322896003723,
-0.0735478326678276,
0.357289582490921,
0.45744186639785767,
-0.16634388267993927,
-0.3667241036891937,
-1.1750019788742065,
-0.005067835561931133,
-1.5608932971954346,
-0.15161274373531342,
-0.6092178225517273,
0.018289634957909584,
-0.15089306235313416,
0.2542757987976074,
0.007044278550893068,
0.015937816351652145,
-0.884743332862854,
-0.36857786774635315,
-0.4075450003147125,
0.3218006193637848,
0.10030965507030487,
-0.8679007291793823,
-0.9055988788604736,
-0.22908452153205872,
-0.05327583849430084,
-0.16630348563194275,
-0.31013932824134827,
-0.11487292498350143,
-0.09413307905197144,
0.28036990761756897,
-0.2943040728569031,
0.416862815618515,
-0.5764275193214417,
-0.27290448546409607,
-0.11979832500219345,
-0.2253057062625885,
-0.5679089426994324,
-0.04506249353289604,
-0.4399142563343048,
0.37243521213531494,
0.2891819477081299,
0.2576301097869873,
-0.20912441611289978,
0.18889380991458893,
-0.8885029554367065,
-0.6615709066390991,
-0.7687235474586487,
0.3369320333003998,
-0.38534778356552124,
-0.7475606203079224,
0.11029119789600372,
-0.35920676589012146,
-0.9138892292976379,
-0.050173569470644,
-0.1616085022687912,
-0.1589423567056656,
-0.2545742988586426,
-0.07851361483335495,
-0.03713332861661911,
0.04532213509082794,
-0.05513916537165642,
0.2312265932559967,
-0.37605947256088257,
-0.5092015266418457,
-0.29637986421585083,
0.2504724860191345,
-0.9777064323425293,
0.28175580501556396,
0.7315819263458252,
-0.19077223539352417,
0.07657112926244736,
0.4656028747558594,
-0.10220896452665329,
0.1424321085214615,
-0.4946243166923523,
-0.6759357452392578,
-0.3000102937221527,
-0.17303603887557983,
0.01964949630200863,
0.9931880831718445,
0.47278159856796265,
-0.7861974239349365,
-0.101200632750988,
-0.5649186372756958,
-0.5526669025421143,
0.12100385874509811,
-1.0662068128585815,
-0.10106556117534637,
-0.19736237823963165,
-0.5609710812568665,
0.03461587056517601,
-0.20998325943946838,
-0.6139217019081116,
0.6459724307060242,
0.41331011056900024,
0.787002682685852,
-0.05676307529211044,
-0.049483973532915115,
-0.05330002307891846,
-0.19410820305347443,
-0.6721258163452148,
-0.13292217254638672,
-0.10324646532535553,
0.25000858306884766,
-0.6089347004890442,
-0.5369624495506287,
-0.19853779673576355,
0.39041954278945923,
-0.19431033730506897,
0.18436557054519653,
-0.5608572363853455,
-0.15434017777442932,
0.47584620118141174,
-0.08341347426176071,
-0.1490984559059143,
0.3720759153366089,
-0.8215005397796631,
0.4069393575191498,
0.06075309216976166,
-0.4361162781715393,
0.2603739798069,
0.6417644619941711,
0.25085991621017456,
-0.2914588451385498,
0.0776430293917656,
0.4950040578842163,
0.18439966440200806,
-1.0145999193191528,
1.5004594326019287,
-0.056999508291482925,
0.767794668674469,
0.548085629940033,
-0.09592052549123764,
0.6492255330085754,
0.5764926671981812,
0.810512363910675,
0.8322300314903259,
0.8177886009216309,
-0.068439781665802,
0.43892985582351685,
1.10794198513031,
0.394010454416275,
-0.1558241993188858,
-0.02320278063416481,
0.6278496384620667,
0.5267715454101562,
-0.16038790345191956,
0.05439162999391556,
0.6617082953453064,
0.4307752251625061,
-0.034540582448244095,
0.018237639218568802,
-0.39869457483291626,
0.0847507044672966,
0.2799442708492279,
0.12619653344154358,
-0.4617482125759125,
-0.036771610379219055,
-0.04338563606142998,
0.31360292434692383,
0.22654655575752258,
0.24738368391990662,
-0.2734926640987396,
0.3808848261833191,
0.7426567673683167,
0.33818650245666504,
-0.06863231211900711,
0.3940298855304718,
0.455691933631897,
0.8275669813156128,
0.2635701596736908,
0.5382235050201416,
0.5050435662269592,
0.5924500823020935,
0.7409188747406006,
-0.9280886650085449,
-0.22631384432315826,
0.556740939617157,
-1.0920428037643433,
0.5202645659446716,
-0.224216490983963,
-0.26155394315719604,
-0.3351309299468994,
-0.38847917318344116,
0.7296077013015747,
-0.07908618450164795,
0.6765583157539368,
0.6977023482322693,
-0.297457218170166,
0.2476041465997696,
0.6360406875610352,
-0.03533342480659485,
0.6815009713172913,
0.803778350353241,
0.44749730825424194,
0.232686385512352,
0.7250955104827881,
1.2973499298095703,
0.33481577038764954,
0.5871889591217041,
-0.1315116137266159,
-0.3355037271976471,
0.48637276887893677,
0.5589025020599365,
0.007386608514934778,
0.48344752192497253,
-0.7102169394493103,
-0.4464203119277954,
0.4802527129650116,
0.3680438995361328,
-0.5263354182243347,
0.0901499092578888,
0.10767218470573425,
0.7157899737358093,
-0.4310121536254883,
-0.3689148426055908,
0.7879371643066406,
0.058345045894384384,
-0.7261639833450317,
-0.4516701102256775,
0.09130530059337616,
-0.9029670357704163,
0.21410450339317322,
-1.0568958520889282,
0.5209872722625732,
0.6469799876213074,
0.5496553778648376,
0.021133728325366974,
-0.43703019618988037,
-0.13563941419124603,
-1.0760672092437744,
0.20368151366710663,
-0.8737619519233704,
0.4460262358188629,
-0.06800591200590134,
0.250201016664505,
0.5844386219978333,
-0.514559268951416,
-0.2803761065006256,
-0.3498551845550537,
0.8778566718101501,
-0.1437734216451645,
0.5209607481956482,
0.593443751335144,
0.130057230591774,
-0.6035359501838684,
0.5477348566055298,
0.6658605933189392,
-0.4320147633552551,
0.9306634664535522,
-0.38067877292633057,
0.29229599237442017,
0.2519919276237488,
-0.3794124722480774,
0.7188965678215027,
-0.6566029787063599,
0.1498660147190094,
0.043293546885252,
0.0822821855545044,
-0.2008804976940155,
-1.1181080341339111,
0.05411585792899132,
-1.0559394359588623,
-0.22469031810760498,
-0.8534645438194275,
0.6290786266326904,
0.326138973236084,
-0.7539602518081665,
4.0664567947387695,
1.1500070095062256,
0.5606278777122498,
0.24385181069374084,
0.9574223160743713,
1.5561782121658325,
-0.23934924602508545,
0.036678656935691833,
0.34090110659599304,
-0.6651309132575989,
0.18729835748672485,
0.48811423778533936,
0.8823099732398987,
-0.7763466238975525,
-0.40376168489456177,
0.2900407314300537,
-0.5334470272064209,
0.19140350818634033,
-0.2384507954120636,
-0.960233747959137,
-0.5891284942626953,
0.062113914638757706,
0.2027527093887329,
-0.2681562602519989,
0.5667337775230408,
0.18092209100723267,
-0.1583901047706604,
-0.9416969418525696,
-0.5331999659538269,
-0.2697223126888275,
-0.22056134045124054,
-0.6875628232955933,
0.16973157227039337,
-0.35913288593292236,
-0.6841885447502136,
0.5278022289276123,
-0.1045142114162445,
-0.7506940960884094,
0.1657116413116455,
0.6979801654815674,
-0.395501047372818,
-0.43575751781463623,
0.13827916979789734,
0.36964914202690125,
-0.49682000279426575,
0.728779673576355,
-0.2050122320652008,
0.8097422122955322,
0.42608073353767395,
-0.43453553318977356,
0.05351421236991882,
-0.13044126331806183,
0.41911834478378296,
-0.5556287169456482,
-0.982845664024353,
0.03470791503787041,
-0.4695450961589813,
-0.03519756719470024,
0.782501757144928,
0.40185147523880005,
0.27828675508499146,
-0.16257813572883606,
-0.6275188326835632,
-0.35030514001846313,
-0.24911071360111237,
0.609143853187561,
0.4410898685455322,
-0.15485984086990356,
-0.3391360342502594,
0.14993034303188324,
-0.31652161478996277,
-0.4632021486759186,
-0.13548073172569275,
-0.30667242407798767,
0.013759930618107319,
-0.4702063202857971,
-0.4923267066478729,
1.0472856760025024,
0.36571556329727173,
-0.08186154067516327,
-0.5995266437530518,
-0.18929243087768555,
-0.2672133445739746,
-0.13373209536075592,
-0.4390592873096466,
0.8712728023529053,
0.15467867255210876,
-0.18478819727897644,
-0.40670663118362427,
0.3683345913887024,
0.030932512134313583,
0.7421239614486694,
0.3744833171367645,
-0.7039339542388916,
-0.919516921043396
] |
Duality in Long-Range Ising Ferromagnets
|
It is proved that for a system of spins $\sigma _i = \pm 1$ having an interaction energy $-\sum K_{ij} \sigma _i \sigma _j $ with all the $K_{ij}$ strictly positive,one can construct a dual formulation by associating a dual spin $S_{ijk} = \pm 1$ to each triplet of distinct sites $i,j$ and $k$. The dual interaction energy reads $-\sum _{(ij)} D_{ij} \prod _{k \neq i,j} S_{ijk}$ with $tanh(K_{ij})\ = \ exp(-2D_{ij})$, and it is invariant under local symmetries. We discuss the gauge-fixing procedure, identities relating averages of order and disorder variables and representations of various quantities as integrals over Grassmann variables. The relevance of these results for Polyakov's approach of the 3D Ising model is briefly discussed.
|
Yannick Meurice
|
hep-lat hep-th
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208015
|
hep-lat/9208016
|
[
0.12152472883462906,
0.251051664352417,
-0.0024392905179411173,
-0.510648250579834,
0.37298470735549927,
-0.3630483150482178,
-0.4736422896385193,
-0.3395232856273651,
-0.306679368019104,
1.3226045370101929,
1.3196371793746948,
0.4631011486053467,
0.1657809168100357,
-0.9452922940254211,
-0.4714233875274658,
0.12051207572221756,
-0.18265528976917267,
-0.6461367011070251,
-0.46961942315101624,
0.17227703332901,
0.4840070903301239,
0.07985452562570572,
-1.5891661643981934,
-0.5986203551292419,
-0.5608499050140381,
0.5328482985496521,
0.7661517858505249,
0.1471216082572937,
1.0343247652053833,
0.5855769515037537,
0.24937601387500763,
-0.4724922776222229,
0.5048452615737915,
-0.23150783777236938,
-0.3956757187843323,
-0.5359438061714172,
-0.0003078579611610621,
0.501897931098938,
0.5393591523170471,
-0.3248828947544098,
0.6608214974403381,
-0.07823352515697479,
0.006668554153293371,
-0.019289357587695122,
-0.5832446217536926,
0.060543838888406754,
0.5640509724617004,
0.3095833361148834,
0.3379043638706207,
-1.4301937818527222,
0.10401799529790878,
0.3116838037967682,
0.23073400557041168,
-0.17311762273311615,
-0.18585030734539032,
-0.39131543040275574,
0.056698236614465714,
-0.042036015540361404,
-0.4910210967063904,
-0.18687704205513,
0.598119854927063,
0.21203826367855072,
0.49981576204299927,
-1.1705228090286255,
0.3803945481777191,
0.470175176858902,
-0.3593668043613434,
0.5245131254196167,
0.09084491431713104,
-0.8125583529472351,
-0.5453268885612488,
-0.5615003705024719,
-0.422687828540802,
0.21303613483905792,
-0.7099872827529907,
0.4927610158920288,
0.24140283465385437,
-0.3098127543926239,
-1.7247140407562256,
-0.30946552753448486,
-0.13892193138599396,
-0.3948673903942108,
-0.7274600267410278,
0.673996090888977,
-0.3630875051021576,
-0.7657432556152344,
0.41769519448280334,
-0.213582381606102,
-0.25103917717933655,
-0.1849307268857956,
-0.2942638695240021,
0.7948411107063293,
0.3789505064487457,
-0.30195435881614685,
0.988922655582428,
0.4575279653072357,
-0.16686947643756866,
0.7473944425582886,
0.7154449820518494,
0.22185631096363068,
0.10652851313352585,
0.9788080453872681,
-0.30000483989715576,
1.0008270740509033,
-0.3763849139213562,
0.24048559367656708,
-0.1579308807849884,
-0.09736037254333496,
0.06416808813810349,
-0.6991993188858032,
0.07924766838550568,
-0.4045000970363617,
-0.4742959141731262,
1.1711320877075195,
0.3617125153541565,
0.7469345331192017,
-0.3779588043689728,
0.5258200764656067,
-0.802558183670044,
-0.42424583435058594,
0.7130951285362244,
0.06594382226467133,
0.5146148800849915,
0.7461374402046204,
0.4235124886035919,
-0.28279805183410645,
0.20327219367027283,
0.6498864889144897,
-0.1932675987482071,
0.32795006036758423,
0.49086594581604004,
0.06353198736906052,
-0.259973406791687,
0.2783364951610565,
-1.1594966650009155,
0.16995446383953094,
-0.20252472162246704,
0.32171431183815,
0.2281651794910431,
0.16353149712085724,
1.0618455410003662,
-0.13635849952697754,
0.2753736674785614,
1.192816972732544,
-0.3854823708534241,
0.638312816619873,
0.09343750774860382,
-0.3034939169883728,
-0.6573301553726196,
0.7741515040397644,
-0.18163254857063293,
-0.4194853901863098,
-0.49789056181907654,
0.9166185259819031,
-0.0009833674412220716,
0.8398958444595337,
-0.7663333415985107,
0.32113343477249146,
-0.6287195682525635,
-0.2011411488056183,
0.4555344879627228,
-0.13501180708408356,
-0.26320430636405945,
0.6257254481315613,
-0.3108188211917877,
0.41082751750946045,
-0.8137854337692261,
-0.12251383811235428,
-0.21193376183509827,
-0.36649397015571594,
-0.24820645153522491,
-0.16536857187747955,
-0.04859152063727379,
1.1115851402282715,
0.2934972941875458,
0.47457242012023926,
-0.3476337492465973,
-0.6221641302108765,
0.3788890540599823,
0.21995756030082703,
0.14066529273986816,
-0.541496753692627,
0.4897475242614746,
-0.07684208452701569,
0.24384132027626038,
0.1111760213971138,
-0.37436771392822266,
-0.38015732169151306,
-0.011353404261171818,
0.09414265304803848,
0.1477690488100052,
0.3728027641773224,
-0.5247844457626343,
0.8339725732803345,
-0.6761051416397095,
-0.0024582266341894865,
-0.656099796295166,
-0.3054434061050415,
-0.7372590899467468,
-0.2314130812883377,
-0.6981112957000732,
0.9747686982154846,
-0.8484084010124207,
0.030113041400909424,
-1.4122848510742188,
0.018884090706706047,
0.2321118861436844,
0.13431669771671295,
-0.46440738439559937,
0.02031742036342621,
0.25272634625434875,
0.34155911207199097,
0.47507861256599426,
-0.21283888816833496,
0.4206589162349701,
0.6472053527832031,
-0.007130996324121952,
0.2970221936702728,
0.36421364545822144,
-0.2489479035139084,
0.3787778913974762,
1.22707998752594,
-0.43746140599250793,
0.2599426805973053,
-0.3618791997432709,
-0.21736857295036316,
0.14420418441295624,
0.8841100931167603,
0.3174864649772644,
0.7982577085494995,
-0.14195063710212708,
0.4496155381202698,
-0.10688995569944382,
0.6654765605926514,
0.7166615128517151,
0.6296725273132324,
0.7091767191886902,
0.31933048367500305,
1.029769778251648,
0.44891175627708435,
0.10525720566511154,
0.0777425765991211,
0.49151185154914856,
0.35479164123535156,
0.5331780910491943,
0.4113690257072449,
-0.21259604394435883,
0.7878648638725281,
-0.6485830545425415,
0.6150422692298889,
-0.23585650324821472,
0.4409087896347046,
-0.5023792386054993,
0.19588124752044678,
-0.6038908958435059,
-0.11072599142789841,
-0.3368440270423889,
1.02110755443573,
0.010634098201990128,
-0.18770235776901245,
-0.32550400495529175,
-0.1608269065618515,
0.08781632781028748,
-0.6738591194152832,
-0.17399848997592926,
0.9603017568588257,
0.15971152484416962,
-0.03545345738530159,
-0.10599285364151001,
-0.3699571490287781,
-1.7309925556182861,
-0.5057929754257202,
-1.149201512336731,
-0.16004985570907593,
-0.5022957921028137,
-0.0608455128967762,
0.8062968254089355,
-0.7165853977203369,
0.41279926896095276,
0.08055508881807327,
-0.4488588273525238,
-0.2672843635082245,
0.028688255697488785,
0.6922615170478821,
0.9626302123069763,
0.07872675359249115,
-0.8689475655555725,
0.01213214360177517,
-0.45855188369750977,
-0.11821191757917404,
-0.7783077955245972,
0.2105187326669693,
0.6900081038475037,
-0.09636115282773972,
0.17923316359519958,
-0.0317562036216259,
-0.7188673615455627,
-0.05928830802440643,
-0.5918369293212891,
-0.6236612796783447,
0.1471104621887207,
0.864783763885498,
0.5473856925964355,
0.006304052658379078,
-0.6254878640174866,
0.5331027507781982,
0.20060153305530548,
-0.6540906429290771,
0.2501107454299927,
0.546153724193573,
-0.7556138038635254,
0.3398720622062683,
0.21666011214256287,
-0.14756208658218384,
0.035446107387542725,
0.7890192270278931,
1.1134033203125,
0.44945454597473145,
-0.3582364022731781,
-0.4570394456386566,
-0.5785897374153137,
0.4002731144428253,
-0.27664628624916077,
-0.5587950348854065,
-0.49796172976493835,
0.842978298664093,
0.30460330843925476,
-1.130336880683899,
0.14139926433563232,
-0.7662039995193481,
-0.874739944934845,
-0.4084450602531433,
-0.371989369392395,
0.6780952215194702,
0.271930068731308,
0.2584960162639618,
-0.5822369456291199,
0.6932159066200256,
0.037896331399679184,
-0.07379487156867981,
-0.20051302015781403,
-0.37685224413871765,
0.7981460094451904,
0.38510483503341675,
0.6621781587600708,
-0.32928285002708435,
-0.3776364028453827,
-0.06439178436994553,
-0.3218264579772949,
0.9182918071746826,
-0.6410298347473145,
0.03206908702850342,
-0.10780062526464462,
0.17867343127727509,
0.20565813779830933,
0.6441652178764343,
-0.651384174823761,
-0.037359680980443954,
-0.7995460629463196,
0.13898132741451263,
0.9371742606163025,
0.3437568247318268,
-0.32519248127937317,
-0.5363461971282959,
-0.4877726137638092,
-0.3097812533378601,
0.7122920155525208,
0.4285745918750763,
0.8819563388824463,
-0.5419903993606567,
0.7452719211578369,
0.2783917188644409,
-0.6276028752326965,
0.615552544593811,
-0.17663905024528503,
-0.6765943765640259,
-0.2829190492630005,
0.4648742079734802,
1.716435432434082,
-0.8406989574432373,
-0.8831702470779419,
0.33182504773139954,
1.221178412437439,
0.5768398642539978,
0.8220694065093994,
-0.02328609675168991,
-0.3473590314388275,
-0.23773927986621857,
-0.5877504348754883,
-0.004812023602426052,
-0.34121450781822205,
-0.16249512135982513,
-0.5167487859725952,
0.14864958822727203,
0.38476356863975525,
-0.4521036148071289,
0.6124243140220642,
0.6762036085128784,
0.763915479183197,
0.010911012068390846,
0.6046428680419922,
1.1692465543746948,
0.353990763425827,
0.7691160440444946,
0.12181717157363892,
0.15923605859279633,
-0.6168545484542847,
0.44135424494743347,
1.0954519510269165,
-0.3178248703479767,
-0.1592714935541153,
-0.5893688797950745,
0.365689218044281,
-0.3725115656852722,
0.7992826104164124,
0.3799881935119629,
-0.7570305466651917,
0.2085532546043396,
0.2542560398578644,
0.7323047518730164,
-0.8009853363037109,
0.39489999413490295,
0.37365585565567017,
0.2147921323776245,
0.015330000780522823,
-0.8624895215034485,
-0.34749630093574524,
-0.7180642485618591,
0.6949513554573059,
0.5335251688957214,
-0.37027883529663086,
-0.8507457375526428,
-0.771827757358551,
-0.7623884081840515,
-0.3815639317035675,
0.2689237594604492,
0.9951999187469482,
0.1333875060081482,
0.4505631625652313,
-0.6216883659362793,
-0.33628323674201965,
0.47028106451034546,
0.006877971347421408,
-0.37970274686813354,
0.6804803609848022,
0.17948363721370697,
-0.2554836571216583,
0.7260566353797913,
0.24115034937858582,
-1.0043288469314575,
-0.38668766617774963,
-0.30465441942214966,
-0.21776314079761505,
-0.32400375604629517,
-0.13681894540786743,
-0.5925809741020203,
-0.156769260764122,
0.055833764374256134,
0.8738116025924683,
-0.32154467701911926,
0.4458940923213959,
-0.6374942064285278,
-0.03136163577437401,
-0.3220943510532379,
-0.0890861377120018,
0.1364758312702179,
-0.0030361118260771036,
0.8561553955078125,
0.6007073521614075,
0.18612858653068542,
-0.07971435785293579,
0.005791377276182175,
0.4396657943725586,
-0.1431080400943756,
0.38933876156806946,
0.01739879511296749,
-0.6553733944892883,
-0.2880203127861023,
0.030934695154428482,
-0.061482157558202744,
-1.0314823389053345,
0.5552430152893066,
-0.45154720544815063,
0.22969788312911987,
0.5203145146369934,
-0.501055121421814,
-0.4258204400539398,
-0.14444500207901,
-1.0560963153839111,
0.5234711170196533,
-0.5478758811950684,
-0.6029555201530457,
0.5862592458724976,
-0.3385925889015198,
0.02259889617562294,
-0.08175239711999893,
-0.22675035893917084,
0.13838599622249603,
0.7067822217941284,
1.031296968460083,
0.6343396306037903,
0.7810971736907959,
-0.9560548067092896,
0.45064738392829895,
-0.2524735629558563,
0.7512065172195435,
-1.0106260776519775,
-0.10533065348863602,
-0.40426647663116455,
-0.2588420510292053,
-0.21763771772384644,
-0.6412614583969116,
-0.023575598374009132,
-0.22076213359832764,
0.23617787659168243,
0.22180713713169098,
-0.40013885498046875,
-0.3111301362514496,
-0.9056404829025269,
0.6500344276428223,
0.4853847026824951,
-1.3184021711349487,
-0.4033801257610321,
0.21157994866371155,
-0.19746193289756775,
0.20693494379520416,
0.4261957108974457,
-0.3502087891101837,
-0.08815134316682816,
-0.25878599286079407,
0.597451388835907,
-0.7985180020332336,
-0.25978726148605347,
-0.509274959564209,
-0.8922670483589172,
0.28449538350105286,
0.9003795385360718,
0.4430517554283142,
-0.17916348576545715,
-0.4235754907131195,
-0.6800851225852966,
-0.14305627346038818,
-0.7224348783493042,
-0.4543292224407196,
-0.8422440886497498,
-0.06440054625272751,
-0.3520399034023285,
0.369284987449646,
-0.14943724870681763,
-0.41834768652915955,
0.3048200309276581,
0.5847510695457458,
-0.13424377143383026,
0.12995967268943787,
-0.07260642945766449,
-0.3909149169921875,
-0.343172162771225,
0.47994256019592285,
-0.14053352177143097,
0.569141149520874,
-0.8729491829872131,
0.9675517082214355,
-0.9519204497337341,
1.1473305225372314,
-0.8259710073471069,
0.6078539490699768,
-0.24139085412025452,
-0.0925983265042305,
0.9539361596107483,
-0.4603714942932129,
-0.24590349197387695,
0.3111319839954376,
-0.21870385110378265,
0.48784807324409485,
-0.23001721501350403,
-0.9494396448135376,
-0.5103393793106079,
-0.4036095440387726,
-1.3262559175491333,
0.44039976596832275,
0.0283811092376709,
0.03745010122656822,
-0.7649192214012146,
-0.610834002494812,
0.3794041574001312,
-0.13111017644405365,
0.07835433632135391,
0.3425747752189636,
0.055803991854190826,
0.10715576261281967,
-0.05147146061062813,
-0.4388289451599121,
-0.6829052567481995,
-0.23713593184947968,
0.43176090717315674,
-0.5336931347846985,
-0.12780557572841644,
-0.1430290788412094,
-0.19070416688919067,
-1.4070230722427368,
-0.028715139254927635,
0.25469231605529785,
0.0827009379863739,
-0.6619358062744141,
0.3561476171016693,
-0.40228432416915894,
-0.22693833708763123,
-0.3701883554458618,
-0.35275205969810486,
-0.4875621795654297,
-0.13208958506584167,
0.8048507571220398,
0.3375259339809418,
0.5399041771888733,
-0.3257216513156891,
0.38126951456069946,
-0.9964503645896912,
0.29848524928092957,
0.5101395845413208,
-0.16095657646656036,
-0.81125807762146,
-0.2638499140739441,
0.25835537910461426,
-0.8411760926246643,
-0.2918716073036194,
-0.07635869830846786,
0.4045228958129883,
-0.1805446743965149,
-0.24815352261066437,
0.19945237040519714,
-0.18693144619464874,
-0.04492659121751785,
0.34478452801704407,
0.4362587034702301,
-0.3603079617023468,
0.04997196048498154,
0.23313991725444794,
-0.08880139142274857,
-0.7581839561462402,
0.5403537750244141,
1.3041337728500366,
0.23095650970935822,
-0.841192901134491,
-0.10629665106534958,
-0.1817290037870407,
0.05768492445349693,
-0.16783353686332703,
0.06088116765022278,
-0.2517615258693695,
0.12810949981212616,
0.19169674813747406,
0.7209839820861816,
0.44375836849212646,
-0.2978880703449249,
0.06326654553413391,
-0.35197708010673523,
-0.05357147380709648,
-0.8984444737434387,
-0.6505592465400696,
-0.348883718252182,
-0.027602029964327812,
0.616762101650238,
0.01154129859060049,
0.49045330286026,
0.9875316023826599,
-0.1891196072101593,
-0.07686562091112137,
-0.9984139204025269,
0.20130646228790283,
-1.253151297569275,
-0.7554824352264404,
-1.1717169284820557,
-0.41803932189941406,
0.2757435441017151,
-0.4781430661678314,
0.18236401677131653,
-0.6038727760314941,
-0.4119853377342224,
-0.5297121405601501,
-0.5749139189720154,
-0.05646718293428421,
-0.23896673321723938,
-1.0451172590255737,
-0.4327787756919861,
-0.47872212529182434,
-0.31502819061279297,
-0.33626604080200195,
-0.24449600279331207,
-0.11869405955076218,
0.03528400510549545,
0.3279823064804077,
-0.4749690592288971,
0.8193923234939575,
-0.6362131237983704,
-0.4150032699108124,
-0.4037719964981079,
-0.2181359827518463,
-0.9779521822929382,
0.06254497170448303,
-0.2853589653968811,
0.42991068959236145,
0.1642187535762787,
0.5212680697441101,
-0.44399526715278625,
-0.026319902390241623,
-0.41252169013023376,
-0.6113843321800232,
0.2389853447675705,
0.1325272023677826,
0.035334181040525436,
-0.5745270848274231,
0.06956082582473755,
0.012916378676891327,
-1.376315712928772,
0.3684496283531189,
-0.12595094740390778,
-0.16800656914710999,
-0.6309619545936584,
0.291360467672348,
0.7578263282775879,
0.7010306119918823,
-0.6410653591156006,
0.9599266648292542,
-0.052805960178375244,
-0.02300197258591652,
-0.6465678215026855,
0.12489482015371323,
-0.36885640025138855,
0.582129180431366,
0.1503034383058548,
-0.7484620213508606,
-0.5723116993904114,
0.12363631278276443,
-0.6972403526306152,
-0.29404065012931824,
-0.272450715303421,
-0.143747940659523,
-0.38075128197669983,
-0.31978273391723633,
-0.105226069688797,
0.4981438219547272,
0.32906514406204224,
-0.6619086861610413,
-0.24110054969787598,
-0.06105665862560272,
-0.3854372501373291,
0.012726166285574436,
-1.6924935579299927,
-0.543643057346344,
0.39017248153686523,
-0.768171489238739,
0.3531539738178253,
0.13050027191638947,
-0.2027926743030548,
0.2930818796157837,
0.15351276099681854,
1.0926483869552612,
-0.09311725944280624,
0.012290776707231998,
-0.4900192618370056,
0.21221736073493958,
-0.4358491003513336,
-0.12828439474105835,
-0.5340855717658997,
0.3054952919483185,
-0.6872448325157166,
-0.7965974807739258,
-0.20352432131767273,
0.9354720115661621,
0.12056227028369904,
0.18406791985034943,
-0.4721814692020416,
0.15272577106952667,
0.06236628443002701,
-0.2106073945760727,
-0.89429771900177,
0.018581844866275787,
-0.873245120048523,
0.23405326902866364,
-0.5561758279800415,
-0.6517364382743835,
0.2965010702610016,
1.212182879447937,
0.4429750442504883,
0.2492155283689499,
0.06986767053604126,
0.4977722465991974,
-0.37992143630981445,
-0.6252078413963318,
0.7843531370162964,
0.4249585270881653,
0.944393515586853,
0.49230021238327026,
-0.30997925996780396,
0.6843976974487305,
0.09180456399917603,
0.2222619205713272,
1.0230448246002197,
0.03947431966662407,
0.47669506072998047,
0.22998841106891632,
0.8038226366043091,
-0.007984559051692486,
0.07650478184223175,
0.2546144723892212,
0.346087247133255,
0.4414740800857544,
-0.487760066986084,
0.2666923701763153,
0.17185142636299133,
0.3834800124168396,
0.17334608733654022,
0.13389496505260468,
-0.24036039412021637,
0.04705838859081268,
-0.17493802309036255,
-0.049587544053792953,
-0.3379893898963928,
-0.49068689346313477,
-0.7351212501525879,
0.43763893842697144,
-0.114345483481884,
-0.04819586127996445,
-0.08209950476884842,
0.1904345452785492,
0.7704463005065918,
0.18788491189479828,
0.013729124329984188,
0.7064602971076965,
0.3464645743370056,
0.4549376368522644,
0.3502674996852875,
0.8251901268959045,
0.2239619344472885,
0.6840959191322327,
0.11562839895486832,
-1.2962040901184082,
0.22701162099838257,
0.4978788197040558,
-1.1755262613296509,
-0.7383759617805481,
-0.6218075752258301,
0.05896077677607536,
-0.17899374663829803,
-0.441093385219574,
0.45064210891723633,
-0.43498358130455017,
0.1698678880929947,
0.7141846418380737,
0.4638477861881256,
0.10024061053991318,
0.9026723504066467,
-0.5663243532180786,
0.4809485971927643,
1.3897079229354858,
-0.2486467808485031,
0.1757640689611435,
1.4270707368850708,
0.7635102868080139,
-0.40921592712402344,
0.5425804853439331,
0.30048179626464844,
-0.34497225284576416,
0.19320780038833618,
-0.10520550608634949,
-0.7881671786308289,
0.5670056939125061,
-0.8199397921562195,
-1.0980879068374634,
0.15264476835727692,
0.7826043963432312,
-0.34708884358406067,
-0.05566395819187164,
0.6658574342727661,
0.8384076952934265,
-0.6041260957717896,
0.34052327275276184,
1.6420960426330566,
0.3945060074329376,
-0.2453393042087555,
0.21660089492797852,
0.35732173919677734,
-0.5152338743209839,
0.4010241627693176,
-1.7820979356765747,
0.14259976148605347,
-0.5236969590187073,
0.37421372532844543,
-0.33539989590644836,
-0.6842725872993469,
-0.36082661151885986,
-0.7257905602455139,
-0.14865534007549286,
-0.6204295754432678,
0.7880739569664001,
0.3808886706829071,
0.25756144523620605,
0.39487889409065247,
-0.3594757914543152,
-0.2744410037994385,
0.17155006527900696,
1.3696255683898926,
-0.3119966387748718,
1.0677490234375,
0.971919059753418,
0.9182018041610718,
0.04521257057785988,
0.37529727816581726,
0.7074099779129028,
-1.1404764652252197,
1.0809246301651,
-0.010350184515118599,
-0.11513159424066544,
0.22393420338630676,
-0.6313223838806152,
-0.07706844061613083,
-0.12768206000328064,
0.6156085133552551,
-0.9959848523139954,
-0.4380311965942383,
-0.5100506544113159,
-0.8172046542167664,
-0.026142099872231483,
-1.103205680847168,
0.1595730483531952,
-0.7467952370643616,
-0.4195999503135681,
-0.20351089537143707,
0.2408532053232193,
3.862668514251709,
1.3379111289978027,
0.9745480418205261,
0.48661789298057556,
0.9384997487068176,
1.0990861654281616,
-0.5518231391906738,
0.13802313804626465,
0.10602708160877228,
-0.6684286594390869,
-0.032773327082395554,
0.17200736701488495,
0.9384137988090515,
0.1436033993959427,
-0.760619044303894,
0.9236922264099121,
-0.05759327858686447,
0.6585690379142761,
0.23033499717712402,
-1.262580394744873,
-1.0968708992004395,
0.40278178453445435,
-0.12538157403469086,
-0.32937124371528625,
-0.35065269470214844,
0.5612512826919556,
-0.03860434517264366,
-0.5497468709945679,
-0.3242136538028717,
-0.17780090868473053,
-0.4790298640727997,
-0.5849637985229492,
0.34342721104621887,
-0.21130800247192383,
-0.7053685188293457,
0.11159469932317734,
0.33475908637046814,
-0.6832528114318848,
-0.37207192182540894,
0.37172672152519226,
-0.039944350719451904,
0.005898219998925924,
-0.12073829770088196,
-0.32399898767471313,
-0.5766360759735107,
1.1438767910003662,
-0.1668207198381424,
0.46070724725723267,
0.3333514332771301,
-0.5309005975723267,
0.611962080001831,
-0.11568388342857361,
0.9441633224487305,
-0.563423216342926,
-1.1351054906845093,
-0.14511924982070923,
-0.7210537791252136,
0.0485430583357811,
0.8239798545837402,
0.28820687532424927,
0.15280184149742126,
0.43049100041389465,
-0.46964338421821594,
-0.18702079355716705,
-0.8099858164787292,
0.32631367444992065,
0.4302380681037903,
-0.16702774167060852,
-0.8513618111610413,
0.6541749835014343,
0.41310423612594604,
-0.0517779104411602,
-0.1461741179227829,
0.6412445902824402,
-0.13818995654582977,
0.6064692139625549,
-0.45524874329566956,
0.9407373666763306,
-0.6578768491744995,
0.12292324006557465,
0.12646304070949554,
-0.17655833065509796,
-0.05121510103344917,
0.027038628235459328,
0.05224401131272316,
0.7138140797615051,
-0.05270889028906822,
0.028520632535219193,
-0.7025851607322693,
0.8709413409233093,
0.30316290259361267,
0.9642632007598877,
0.22871747612953186,
-0.10838916897773743,
-0.42917221784591675
] |
Embedding Z(3) in SU(3)
|
We consider the design of a non-local MonteCarlo algorithm for $SU(3)$ lattice systems according to the idea of {\em embedding} the degrees of freedom corresponding to the center of the group $Z(3)$. As a crucial ingredient to reach this goal, we present a practical implementation of a cluster algorithm for $Z(3)$ systems with general random pair interaction.
|
Enrico Onofri
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208016
|
hep-lat/9208017
|
[
0.2973954379558563,
-0.2026018649339676,
-0.3816637694835663,
0.5569491386413574,
-0.41558006405830383,
0.18599814176559448,
-0.035689592361450195,
-0.5207071304321289,
-0.7140240669250488,
1.0086884498596191,
0.6308237314224243,
-0.08846025913953781,
0.15223239362239838,
-0.5153880715370178,
-0.19633997976779938,
0.3985162377357483,
0.08174382895231247,
-0.598682701587677,
-1.2560142278671265,
0.6520317792892456,
0.15950332581996918,
-0.4377139210700989,
-1.0620049238204956,
-0.4679926037788391,
-0.35088279843330383,
0.7002177238464355,
0.07160431891679764,
-0.18822184205055237,
0.6826373338699341,
0.6615419983863831,
0.41378581523895264,
-0.6676429510116577,
-0.22591663897037506,
-0.08017407357692719,
-0.569276750087738,
-0.7058073878288269,
-0.45673471689224243,
-0.14465263485908508,
1.0802801847457886,
-0.0540960319340229,
0.7747553586959839,
-0.48091331124305725,
0.08896461129188538,
-0.31266874074935913,
-0.5980291366577148,
-0.201088085770607,
-0.2106662392616272,
-0.15307581424713135,
0.27338406443595886,
-1.1858450174331665,
0.10129650682210922,
0.473702996969223,
0.270324170589447,
-0.48814690113067627,
-0.05441635102033615,
-0.038799915462732315,
0.02764902636408806,
-0.07983280718326569,
-0.9814112782478333,
-0.5938796401023865,
0.6064055562019348,
0.06156620755791664,
0.6766729950904846,
-1.0181241035461426,
0.02038876712322235,
1.0469439029693604,
-0.11070207506418228,
0.40086910128593445,
-0.08656042069196701,
-0.4214598834514618,
0.2887044847011566,
-0.31486672163009644,
-0.8717122673988342,
-0.0071835569106042385,
-0.9743276238441467,
0.07610099762678146,
0.30880025029182434,
-0.36436545848846436,
-0.5128604173660278,
-0.07433132082223892,
0.0352911651134491,
-0.05761678144335747,
-0.7738773822784424,
0.2886927127838135,
-0.5559224486351013,
-0.4356977939605713,
-0.10012082755565643,
-0.3282160758972168,
-0.21254393458366394,
0.44063323736190796,
-0.07811389118432999,
0.7023599743843079,
-0.6181965470314026,
0.5315195918083191,
0.47903159260749817,
0.6295175552368164,
-0.05365724116563797,
0.3266729414463043,
0.20946814119815826,
-0.024213261902332306,
-0.16167306900024414,
0.41107210516929626,
-1.286426305770874,
-0.1429990828037262,
-0.5371643900871277,
0.3811292052268982,
-0.5726888179779053,
0.17727188766002655,
-0.2141261100769043,
-0.6420559883117676,
0.9193912148475647,
-0.04349309206008911,
-0.05492410808801651,
0.27371281385421753,
0.10538140684366226,
0.40951675176620483,
-0.4725067913532257,
0.5148864984512329,
-0.27897220849990845,
-0.21453163027763367,
-0.09718617796897888,
0.2878281772136688,
0.0714738667011261,
0.5209022760391235,
0.21274089813232422,
-0.009581593796610832,
0.4275866150856018,
0.306179016828537,
-0.7050334811210632,
0.04103318229317665,
0.017258968204259872,
-0.07827502489089966,
-0.4575826823711395,
1.156722068786621,
-0.1155640259385109,
-0.009382912889122963,
-0.1858956217765808,
0.679753303527832,
0.5476816892623901,
-0.1235194057226181,
0.51422518491745,
-0.9643144607543945,
-0.07365761697292328,
1.0307170152664185,
-0.11271022260189056,
0.0016969578573480248,
-0.2121732085943222,
0.3213544189929962,
-0.32968229055404663,
0.11275777965784073,
-0.38149988651275635,
-0.11276187747716904,
-0.27001550793647766,
0.2895505130290985,
-0.22841055691242218,
0.2703247368335724,
-0.6930124759674072,
-0.4342716336250305,
-0.2407160848379135,
-0.42839500308036804,
0.1202993392944336,
-0.029821833595633507,
-0.5803979635238647,
0.037088487297296524,
-0.5211359858512878,
0.028138544410467148,
-0.4682282507419586,
0.09744331240653992,
0.3396725058555603,
-0.5701605081558228,
-0.30882498621940613,
0.8905518054962158,
-0.44931063055992126,
0.6841527819633484,
0.24676978588104248,
0.090027816593647,
0.5394808053970337,
-0.8396719694137573,
0.13304650783538818,
0.23439763486385345,
-0.11135517805814743,
0.29107123613357544,
0.07845519483089447,
-0.04217042773962021,
-0.040148988366127014,
-0.3923830986022949,
0.269706130027771,
-0.039501529186964035,
0.5190519094467163,
-0.03288228437304497,
-0.2927437722682953,
0.16363927721977234,
-0.5447437763214111,
0.8680246472358704,
-0.24767115712165833,
-0.15407244861125946,
-1.1594184637069702,
-0.06957988440990448,
-0.3244623839855194,
-0.38606134057044983,
-0.008241440169513226,
0.371177613735199,
-0.5676283836364746,
0.52781081199646,
-1.0981754064559937,
-0.11956722289323807,
0.7497522830963135,
-0.030470652505755424,
-0.5478324294090271,
-0.07623207569122314,
0.37970423698425293,
-0.3179752230644226,
0.47318851947784424,
-0.418771892786026,
0.12449309974908829,
0.24418972432613373,
0.1402275115251541,
0.06188443675637245,
0.34157314896583557,
0.6964824795722961,
0.28564563393592834,
0.15788771212100983,
-0.010670403018593788,
0.7803870439529419,
-0.09678421914577484,
-0.1920260637998581,
0.48232534527778625,
0.10388734191656113,
-0.2350672483444214,
-0.2949804365634918,
0.0003570276312530041,
0.012798604555428028,
-0.24842345714569092,
0.2756442725658417,
0.22553329169750214,
-0.19423525035381317,
0.33550944924354553,
0.37681081891059875,
0.06115233898162842,
0.7169913649559021,
0.20115867257118225,
-0.12143523246049881,
0.052062083035707474,
-0.36490970849990845,
-0.5952505469322205,
0.11206571757793427,
0.05688682571053505,
0.21930624544620514,
-0.44897782802581787,
0.4234359562397003,
0.11798234283924103,
0.12301775813102722,
0.2662671208381653,
0.5411952137947083,
-1.0697828531265259,
0.026940422132611275,
-0.5036492347717285,
-0.13684558868408203,
-0.39317262172698975,
-0.23764188587665558,
0.5082602500915527,
0.05018526315689087,
-0.2203199565410614,
-0.5197693109512329,
-0.06872466206550598,
0.7134008407592773,
-0.4001789689064026,
0.2429303377866745,
0.8812242746353149,
-0.12309237569570541,
-0.7679685354232788,
0.29274168610572815,
-1.0022517442703247,
0.36050349473953247,
-0.6990211606025696,
-0.09846308082342148,
0.36331692337989807,
-0.7482224106788635,
0.43834638595581055,
0.23884953558444977,
-0.596808671951294,
0.5555768609046936,
-0.0715952217578888,
0.22791247069835663,
0.03603644669055939,
0.5158762335777283,
-0.40475162863731384,
0.3623957931995392,
-0.9704558253288269,
-0.14948560297489166,
0.15569506585597992,
0.11447067558765411,
0.5483371019363403,
0.017354585230350494,
0.4602898359298706,
0.5454515218734741,
-0.4939199686050415,
-0.004911381751298904,
0.38282379508018494,
-0.6153502464294434,
0.23010049760341644,
-0.1395585536956787,
0.41233229637145996,
0.333373099565506,
-1.0412005186080933,
0.06344103813171387,
-0.003516098950058222,
-0.2766086757183075,
0.2950630784034729,
0.34807923436164856,
-0.4607318639755249,
0.5882654786109924,
-0.17155519127845764,
0.2420368492603302,
-0.15828196704387665,
1.2547521591186523,
0.5021725296974182,
-0.00455193966627121,
0.023372512310743332,
-0.35434722900390625,
-0.2009846568107605,
0.23070968687534332,
-0.3711259961128235,
-0.47253119945526123,
-0.09453825652599335,
0.5295949578285217,
-0.11525614559650421,
-0.2908390760421753,
0.27912893891334534,
-0.5873786807060242,
-0.3691079318523407,
0.6366757154464722,
-0.530028760433197,
0.6994795203208923,
-0.5060399770736694,
0.2533475160598755,
-0.4576781094074249,
-0.004164178390055895,
-0.24878066778182983,
0.11492098122835159,
0.40686947107315063,
-0.26737892627716064,
0.6258800029754639,
0.2452840954065323,
0.03171410411596298,
-0.3230283260345459,
-0.03596598282456398,
-0.4085400104522705,
-0.5050104260444641,
0.6643163561820984,
-0.12434350699186325,
0.5186207890510559,
-0.06643263250589371,
0.6697927117347717,
-0.2093232274055481,
0.27076300978660583,
-0.09974982589483261,
-0.4685065448284149,
-0.5857003927230835,
-0.4705108106136322,
0.4495450556278229,
0.62516188621521,
-0.21865345537662506,
-0.5137857794761658,
-0.5640864372253418,
-0.36568304896354675,
0.46250852942466736,
-0.3772258162498474,
0.35716938972473145,
-0.11739960312843323,
0.035032257437705994,
-0.16944333910942078,
-0.6762291193008423,
0.2375609427690506,
0.3010416030883789,
0.3814508616924286,
0.8455883860588074,
0.4412569999694824,
0.6967728137969971,
-0.1860477775335312,
0.032405149191617966,
0.45770004391670227,
0.691340982913971,
0.3378324508666992,
0.9358741641044617,
0.5341124534606934,
-0.18866734206676483,
0.28536105155944824,
-0.39661288261413574,
-0.024577446281909943,
-0.5778955221176147,
-0.32713115215301514,
0.6523811221122742,
-0.19353964924812317,
0.5390743017196655,
0.02014211378991604,
0.41280800104141235,
0.5045355558395386,
0.27268752455711365,
0.10497288405895233,
0.2623121440410614,
-0.2625829577445984,
0.32330140471458435,
0.22572959959506989,
0.3623034656047821,
0.8825188279151917,
-1.1742736101150513,
0.15625087916851044,
0.013510802760720253,
0.5029430389404297,
-0.2533063590526581,
-0.49339723587036133,
0.04710252210497856,
-0.8525059223175049,
0.5614697933197021,
0.07229915261268616,
-0.5130777955055237,
0.182430699467659,
0.46186622977256775,
0.9237288236618042,
-0.24948734045028687,
0.491497278213501,
0.5117552280426025,
0.10653230547904968,
0.1775224655866623,
-0.8964545130729675,
0.07191503793001175,
-0.6480185985565186,
0.25773340463638306,
0.6103253364562988,
-0.659583330154419,
-0.5223928689956665,
-0.8944159746170044,
0.15302063524723053,
-0.4088915288448334,
0.286533385515213,
1.1073377132415771,
0.3017115592956543,
0.20990878343582153,
-0.9762272834777832,
-0.6535295844078064,
0.288516104221344,
-0.20115280151367188,
-0.5470283627510071,
0.7184531092643738,
0.08496419340372086,
0.013871247880160809,
0.57037752866745,
-0.10991523414850235,
-0.6149003505706787,
0.2594945728778839,
-0.6410651803016663,
0.4335324466228485,
-0.5916233062744141,
-0.44296225905418396,
0.051736101508140564,
-0.4246717691421509,
-0.6554535031318665,
0.7360492944717407,
0.05493225157260895,
-0.4429364800453186,
-0.36267024278640747,
-0.1770758479833603,
-0.32901352643966675,
0.23432126641273499,
0.38532987236976624,
-0.4910726547241211,
0.9440199732780457,
0.922177791595459,
0.5593169927597046,
0.19297905266284943,
0.34106510877609253,
0.5388156771659851,
-0.27925577759742737,
0.28947263956069946,
0.28435760736465454,
-0.34499821066856384,
-0.29322195053100586,
-0.2148139327764511,
-0.7999981045722961,
-0.669909656047821,
-0.16482357680797577,
0.4969477653503418,
1.2903083562850952,
-0.15653440356254578,
-0.47317689657211304,
-0.4383639693260193,
-0.16346536576747894,
-0.6612100005149841,
0.8481224775314331,
0.34004104137420654,
0.11097604036331177,
0.6864661574363708,
-0.4641270339488983,
0.3414895236492157,
-0.5956435203552246,
-0.3172430992126465,
-0.20441442728042603,
0.6258906722068787,
1.024662971496582,
0.8676000237464905,
0.23609869182109833,
-1.0007632970809937,
0.5369064807891846,
-0.4114399254322052,
-0.22298656404018402,
0.10570427775382996,
-0.47369980812072754,
-0.049207840114831924,
0.08960410207509995,
0.5018532276153564,
-0.0586148276925087,
-0.03481641039252281,
-0.033336881548166275,
-0.3271375894546509,
-0.7187986373901367,
0.4675375521183014,
-0.07401914894580841,
0.05059988796710968,
0.7522925138473511,
0.22400188446044922,
-0.632438063621521,
-0.15480953454971313,
0.23574765026569366,
-0.1797141283750534,
-0.3122798204421997,
0.06103852763772011,
-0.7813575863838196,
-0.09967289119958878,
-0.6399456858634949,
0.45496493577957153,
-0.3502300977706909,
-0.7082998156547546,
-0.29996246099472046,
-0.6140202879905701,
0.40681660175323486,
0.4969238340854645,
0.8195163011550903,
0.30879560112953186,
-0.6441388130187988,
-0.13654032349586487,
0.556142270565033,
-0.5783861875534058,
-0.7012247443199158,
-0.8553372621536255,
-0.33319994807243347,
-0.2767338156700134,
1.04305100440979,
-0.6880268454551697,
-0.060863833874464035,
-0.32970136404037476,
-0.08767344057559967,
0.1714574247598648,
0.6978797316551208,
0.6909817457199097,
-0.14455242455005646,
-0.01614801026880741,
0.27274957299232483,
-0.08601941913366318,
0.6826370358467102,
-0.5085853338241577,
0.6324124336242676,
-0.30538469552993774,
1.0831133127212524,
-0.9992879629135132,
-0.3007264733314514,
-0.03728177770972252,
-0.5724636912345886,
0.5973615050315857,
-0.0056867441162467,
0.18706825375556946,
0.8954436779022217,
-0.5295853614807129,
0.07009631395339966,
0.08559924364089966,
-0.7187142968177795,
0.3808543086051941,
-0.34117400646209717,
-0.1053066998720169,
0.5296962261199951,
-0.12308944016695023,
-0.05846136063337326,
-0.7339585423469543,
-0.8537423014640808,
0.0677027702331543,
-0.10645661503076553,
0.011332149617373943,
0.49280592799186707,
-0.08672904968261719,
0.007316975854337215,
0.23771026730537415,
-0.13459406793117523,
-0.9198423027992249,
0.3107745945453644,
-0.031465958803892136,
0.12640130519866943,
0.5817100405693054,
-0.27942878007888794,
-0.6691916584968567,
-0.8142699599266052,
0.09931919723749161,
0.2399444431066513,
0.09128197282552719,
-0.3700796663761139,
0.7124261856079102,
-0.6218693256378174,
-0.6257296204566956,
-0.4397388696670532,
0.862713634967804,
0.10355045646429062,
0.26510873436927795,
0.29456663131713867,
0.2575886845588684,
-0.2576404809951782,
-0.10149060189723969,
0.014978606253862381,
-0.12477671355009079,
-0.07716426998376846,
0.42621472477912903,
-0.8457430005073547,
-0.02191285789012909,
0.591656506061554,
0.5939441323280334,
-0.595467209815979,
0.17482280731201172,
-0.9929317235946655,
-0.031144963577389717,
-0.317989319562912,
0.230098158121109,
-0.6782424449920654,
-0.31172487139701843,
-0.2859896123409271,
0.6665980815887451,
0.6183197498321533,
0.28018972277641296,
-0.22360070049762726,
-0.43372324109077454,
0.4028557538986206,
-0.5756134390830994,
0.18031273782253265,
1.143355131149292,
-0.29082760214805603,
-1.0463390350341797,
0.3995985686779022,
0.346646249294281,
0.10697871446609497,
-0.4150504767894745,
0.6855829954147339,
-0.41413700580596924,
0.12513789534568787,
0.5513517260551453,
0.0048096259124577045,
0.149590402841568,
0.1628762036561966,
0.3299309313297272,
0.671808660030365,
-0.10319811850786209,
-0.4114021360874176,
-0.24710866808891296,
-0.22484979033470154,
0.0830770954489708,
0.5963649153709412,
0.32510143518447876,
0.1843152642250061,
0.3154112994670868,
-0.28403282165527344,
0.1431959718465805,
-0.035523928701877594,
-0.03666365146636963,
-0.9142804741859436,
0.18087942898273468,
-0.6831297278404236,
0.12049388885498047,
0.4584956467151642,
0.5408093333244324,
-0.06110125780105591,
-0.2767309844493866,
-0.21758076548576355,
0.513454020023346,
-0.3790779709815979,
-0.09967095404863358,
0.11826370656490326,
-0.970250129699707,
0.3121456205844879,
-0.5242084264755249,
-0.25253212451934814,
-0.6222168803215027,
0.08361397683620453,
-0.3117152154445648,
-0.5456045269966125,
0.7080784440040588,
-0.3918227255344391,
0.45601803064346313,
-0.9634777307510376,
-0.5828796625137329,
-0.19608765840530396,
0.031206654384732246,
-0.6333058476448059,
0.49012574553489685,
-0.0007383915362879634,
0.6995146870613098,
0.1415441930294037,
-0.13490469753742218,
-0.5303363800048828,
0.39106664061546326,
-0.7930218577384949,
-0.019041158258914948,
-0.1310684233903885,
0.24452859163284302,
-0.2279645800590515,
-1.3190879821777344,
-0.15615016222000122,
0.4564121663570404,
-0.9244797229766846,
0.08057650178670883,
-0.500097393989563,
0.2837306559085846,
-0.6192525029182434,
0.14044156670570374,
0.2697093188762665,
0.5276610851287842,
0.10776658356189728,
1.0151187181472778,
-0.15071919560432434,
0.009324552491307259,
0.3798696994781494,
0.2557930052280426,
-0.03430759906768799,
0.14310508966445923,
-0.22184669971466064,
-0.5343215465545654,
-0.1929149031639099,
0.8057681918144226,
0.05974699929356575,
-0.3650491237640381,
0.06735076755285263,
-0.11842229962348938,
0.3871021866798401,
0.12714244425296783,
-0.6444324851036072,
0.23394671082496643,
0.7068396806716919,
-0.667215883731842,
-0.4308713376522064,
-0.7960821986198425,
-0.7925452589988708,
0.5263232588768005,
-0.6273812055587769,
-0.5533245801925659,
-0.028453825041651726,
0.14699938893318176,
0.15149883925914764,
0.5431966781616211,
-0.23737043142318726,
0.349901407957077,
0.36144837737083435,
-0.33505895733833313,
0.6160212159156799,
-0.08782955259084702,
-0.4084150791168213,
0.13508273661136627,
-0.8272220492362976,
-0.5467882752418518,
-0.5697972774505615,
0.7154988646507263,
-1.073194146156311,
-1.2867616415023804,
-0.6114583611488342,
0.5559221506118774,
0.116167813539505,
0.21275758743286133,
-0.652045488357544,
-0.5662056803703308,
0.014861267991364002,
-0.21883387863636017,
-1.1333110332489014,
-0.4625086784362793,
-0.6874016523361206,
0.33983922004699707,
-0.2734864056110382,
-0.8934643864631653,
0.4634619355201721,
-0.31879115104675293,
0.0950390100479126,
0.10559289157390594,
0.0055115376599133015,
1.1601521968841553,
0.8354023694992065,
-0.05416133627295494,
0.7359816431999207,
0.48555970191955566,
0.26712700724601746,
0.18148058652877808,
-0.7665885090827942,
0.4436015486717224,
0.3922899067401886,
-0.22905060648918152,
0.4740278720855713,
0.7160183787345886,
-0.07328766584396362,
0.21894428133964539,
-0.2026704102754593,
0.4464012086391449,
0.05946367606520653,
-0.0007525226101279259,
-0.15960994362831116,
0.08609354496002197,
-0.16564755141735077,
0.08749967813491821,
-0.2772080898284912,
-0.09079243987798691,
0.38501280546188354,
-0.4445704519748688,
-0.2689420282840729,
-0.05483805388212204,
0.47637003660202026,
-0.10041390359401703,
-0.9375717043876648,
-0.15035565197467804,
-0.29910042881965637,
0.11196103692054749,
0.8041322827339172,
0.062350351363420486,
-0.2593296468257904,
0.8992695808410645,
0.6222104430198669,
-0.15386730432510376,
-0.19314217567443848,
0.38747045397758484,
0.06177213415503502,
1.3088098764419556,
0.8456951379776001,
0.5207473039627075,
0.29045575857162476,
0.1568859964609146,
0.01693328097462654,
-1.0667587518692017,
0.7657166123390198,
0.7847182154655457,
-0.8060528039932251,
0.3078446388244629,
-0.49446454644203186,
-0.024409478530287743,
-0.9080418348312378,
-0.4784190356731415,
0.31984320282936096,
-0.776404082775116,
0.00009598972974345088,
0.5095685124397278,
-0.40958040952682495,
0.6036946177482605,
0.47668740153312683,
0.3848769962787628,
0.3848237693309784,
0.3803834021091461,
-0.10261835157871246,
-0.04045744985342026,
0.8073116540908813,
1.3482216596603394,
0.37921813130378723,
0.01707775518298149,
0.138504758477211,
-0.8451643586158752,
0.47541460394859314,
0.6715453863143921,
-0.35806792974472046,
0.29825228452682495,
0.01613520458340645,
-0.8004361987113953,
0.69054114818573,
-0.25467050075531006,
-0.0005625584162771702,
-0.5212494134902954,
0.5795006155967712,
0.25547489523887634,
-0.0694500058889389,
-1.1578035354614258,
1.5000611543655396,
0.4038832187652588,
-0.4919637143611908,
-0.35918548703193665,
0.7096459269523621,
-0.12262296676635742,
-0.2947070598602295,
-1.1373010873794556,
0.47799456119537354,
0.013017823919653893,
-0.13455000519752502,
-0.030903128907084465,
-0.5106402039527893,
-0.4573335647583008,
-0.6028479337692261,
0.35298147797584534,
-0.47559359669685364,
0.058853257447481155,
0.1295633614063263,
0.11282050609588623,
0.5058788657188416,
-0.099380724132061,
0.25359290838241577,
0.10334306210279465,
0.4834654629230499,
-0.13323017954826355,
0.13561169803142548,
0.1478729546070099,
0.563010573387146,
-0.7849480509757996,
0.6971016526222229,
0.7357873916625977,
-1.1272377967834473,
0.6334476470947266,
-0.5231292247772217,
0.7292758822441101,
0.359892874956131,
0.2548758387565613,
0.5356417298316956,
0.25440514087677,
0.2930222749710083,
-0.34032148122787476,
-0.12826049327850342,
-0.41988804936408997,
-0.7498552799224854,
0.2720987796783447,
-0.37859150767326355,
0.15303261578083038,
0.024830477312207222,
0.023073360323905945,
0.433921217918396,
-1.0780853033065796,
4.403778553009033,
0.39404863119125366,
0.4962606132030487,
0.3510706424713135,
0.501552164554596,
0.5247312188148499,
-0.6859065294265747,
-0.09609273821115494,
0.2230370044708252,
-0.33011582493782043,
-0.3650859594345093,
0.18297874927520752,
0.08468949794769287,
-0.05296116694808006,
0.03709888830780983,
0.7019162178039551,
-0.5878729820251465,
-0.4027349352836609,
0.004313953220844269,
-1.1728447675704956,
-0.6238170266151428,
-0.2167595475912094,
0.15895546972751617,
-0.1486828774213791,
0.2672679126262665,
-0.03671424835920334,
-0.050694335252046585,
-0.544042706489563,
-0.05523015558719635,
-0.4225977063179016,
0.13207541406154633,
-1.104283332824707,
0.2967127859592438,
-0.13486699759960175,
-1.1357238292694092,
0.7019548416137695,
0.2735537588596344,
0.036695901304483414,
0.09340118616819382,
-0.4505203068256378,
-0.35290566086769104,
-0.42990347743034363,
0.2065832018852234,
0.011581897735595703,
-0.284719318151474,
0.7740992903709412,
-0.37739017605781555,
0.5309147834777832,
0.05863615497946739,
-1.029831886291504,
0.6768249273300171,
0.3768889605998993,
1.1939425468444824,
-0.2775781452655792,
-1.0333157777786255,
-0.2767837941646576,
-0.4510364830493927,
-0.2021823674440384,
0.26593518257141113,
-0.16087757050991058,
-0.10828303545713425,
-0.5570687651634216,
-0.34385156631469727,
0.4827450215816498,
0.07716145366430283,
-0.0918997973203659,
-0.1405036747455597,
0.6281667947769165,
-0.3015030324459076,
0.18103428184986115,
-0.05680641159415245,
-0.14079508185386658,
0.11818414181470871,
0.7446713447570801,
-0.09643598645925522,
0.003629365935921669,
-0.2991521954536438,
0.3959740102291107,
0.11160200089216232,
0.2514929473400116,
0.3270195722579956,
-0.11221417784690857,
-0.4909721612930298,
0.28251543641090393,
0.2432372272014618,
0.8038003444671631,
-0.7364404797554016,
0.24080881476402283,
-0.2634906768798828,
0.05916137620806694,
0.0009102770127356052,
0.7812369465827942,
0.3781358301639557,
0.51520836353302,
-0.5349642038345337
] |
The triviality bound on the Higgs mass; its value and what it means
|
Older lattice work exploring the Higgs mass triviality bound is briefly reviewed. It indicates that a strongly interacting scalar sector in the minimal standard model cannot exist; on the other hand low energy QCD phenomenology might be interpreted as an indication that it could. We attack this puzzle using the $1/N$ expansion and discover a simple criterion for selecting a lattice action that is more likely to produce a heavy Higgs particle. Depending on the precise form of the limitation put on the cutoff effects, our large $N$ calculations, when combined with old numerical data, suggest that the Higgs mass bound might be around 750 $GeV$, which is higher than the $\sim 650~GeV$ previously obtained. Preliminary numerical work indicates that an increase of at least 19\% takes place at $N=4$ on the $F_4$ lattice when the old simple action is replaced with a new action (still containing only nearest neighbor interactions) if one uses the lattice spacing as the physical cutoff for both actions. It appears that, while a QCD like theory could produce $M_H / F ~ \sim 6$, a meaningful ``minimal elementary Higgs'' theory cannot have $M_H/ F~ \gtapprox 3$. Still, even at 750 $GeV$, the Higgs particle is so wide ($\sim 290~$GeV), that one cannot argue any more that the scalar sector is weakly coupled.
|
H. Neuberger, U. M. Heller, M. Klomfass, P. Vranas
|
hep-lat hep-ph
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208017
|
hep-lat/9208018
|
[
0.35448065400123596,
-0.2731475830078125,
0.16918449103832245,
0.18525373935699463,
-0.44859662652015686,
-0.2213646024465561,
0.47713422775268555,
-0.6481426954269409,
-0.40598925948143005,
1.0565437078475952,
0.4820767045021057,
0.4678163230419159,
0.2549230456352234,
-0.9145836234092712,
0.08667803555727005,
0.11552821844816208,
0.5236119627952576,
-0.642058789730072,
-0.909141480922699,
0.3878539502620697,
0.8259963393211365,
-0.5631643533706665,
-0.8013613224029541,
-0.3336901068687439,
-0.26905539631843567,
0.2646805942058563,
0.24468477070331573,
-0.05741246044635773,
1.0248225927352905,
0.9032236337661743,
0.08290375024080276,
-1.0751484632492065,
-0.11178635060787201,
-0.2681668698787689,
-0.5654409527778625,
-0.22823841869831085,
-0.21682313084602356,
0.47593235969543457,
1.0829029083251953,
-0.491433709859848,
0.44178736209869385,
0.010077170096337795,
-0.009960523806512356,
-0.2785167098045349,
0.04860921576619148,
-0.2575533986091614,
-0.7905449271202087,
-0.4459449350833893,
0.2985397279262543,
-1.1614913940429688,
-0.01942117139697075,
0.19793005287647247,
1.063032627105713,
-0.3406727612018585,
-0.49310532212257385,
-0.6906753182411194,
0.18235278129577637,
0.1645498424768448,
-0.4980510175228119,
-0.24290449917316437,
0.5536236763000488,
-0.009059648960828781,
0.09634979814291,
-0.7063631415367126,
0.24239851534366608,
0.6673117280006409,
-0.8666198253631592,
0.6404644846916199,
-0.6766437888145447,
-0.5708032846450806,
0.42523765563964844,
-0.1328858882188797,
-0.9588456153869629,
0.16324248909950256,
-1.0220218896865845,
0.10536941885948181,
0.25415974855422974,
-0.3314635753631592,
-1.6844292879104614,
-0.5086244940757751,
-0.6260693073272705,
-0.09468492865562439,
0.04688020050525665,
0.02066439762711525,
0.17258843779563904,
-0.7142837643623352,
-0.14017827808856964,
-0.33868423104286194,
-0.02722518891096115,
-0.00431072385981679,
-0.0006408392800949514,
0.9801424145698547,
-0.28005704283714294,
-0.14982828497886658,
0.3008469343185425,
0.35968348383903503,
-0.13470463454723358,
0.09114479273557663,
0.13140402734279633,
0.4631999731063843,
0.18110992014408112,
-0.18754686415195465,
-0.5542313456535339,
0.5182368755340576,
-0.7276610732078552,
0.3240630030632019,
-0.4579314887523651,
-0.3979725241661072,
0.2513214647769928,
-0.7000011205673218,
0.23794902861118317,
-0.30805325508117676,
0.38406428694725037,
0.6558291912078857,
0.23435136675834656,
0.13151581585407257,
-0.28513962030410767,
0.4063599407672882,
-0.39872169494628906,
-0.2398303747177124,
0.39035192131996155,
-0.2533416152000427,
0.28796324133872986,
0.007093105930835009,
0.4416294991970062,
-0.01886461302638054,
0.3728090226650238,
0.37511155009269714,
-0.7150404453277588,
-0.33209747076034546,
0.04229199141263962,
-0.21988925337791443,
-0.4525669813156128,
0.24409155547618866,
-0.31395119428634644,
0.14377199113368988,
-0.170667365193367,
0.10762769728899002,
0.033824510872364044,
-0.47405722737312317,
0.5309210419654846,
-0.6268499493598938,
0.9565027952194214,
0.7671306729316711,
0.050658393651247025,
0.15531045198440552,
0.017599066719412804,
0.2531719505786896,
-0.22336332499980927,
0.053034208714962006,
-0.48298946022987366,
-0.11152758449316025,
-0.463649183511734,
0.7697669863700867,
-0.2453569918870926,
0.0002072208299068734,
-0.8397486209869385,
0.18684571981430054,
-1.0478116273880005,
0.3127574324607849,
0.15212997794151306,
0.0669771060347557,
-0.10540693253278732,
0.20245710015296936,
-0.6197634339332581,
0.01064364705234766,
-0.9785468578338623,
-0.9550377726554871,
0.3968749940395355,
-0.40189671516418457,
-0.272688627243042,
0.5433132648468018,
-0.2450781762599945,
0.6196552515029907,
-0.30076444149017334,
0.7443299293518066,
0.46655431389808655,
-0.04090898856520653,
0.05189034715294838,
0.5858238339424133,
-0.7188918590545654,
-0.42501455545425415,
0.6427417993545532,
0.16240063309669495,
-0.2694369852542877,
-0.00522496085613966,
-0.18577878177165985,
-0.1341528445482254,
-0.3152219355106354,
0.4816140830516815,
0.05736931040883064,
-0.21290694177150726,
-0.2601756751537323,
0.3271294832229614,
-0.5607917308807373,
-0.5054813027381897,
-0.7652822136878967,
0.363995224237442,
-0.10668306797742844,
-0.8097197413444519,
-0.06567247956991196,
0.3851754367351532,
-0.3025536835193634,
0.3483413755893707,
-1.48914635181427,
-0.23193447291851044,
1.18123459815979,
0.437995582818985,
-0.1599772572517395,
0.1849920004606247,
0.05997050553560257,
0.007077025715261698,
0.11454383283853531,
-0.045583777129650116,
0.1468411237001419,
0.4412061274051666,
0.6598862409591675,
0.47269731760025024,
0.7396053671836853,
0.48471659421920776,
-0.20204070210456848,
0.5019860863685608,
-0.15738005936145782,
0.5696987509727478,
-0.6168631315231323,
-0.7016592025756836,
0.01687067747116089,
0.7137143015861511,
0.5349557995796204,
-0.709553599357605,
-0.28965067863464355,
0.038117192685604095,
0.2831360399723053,
0.703688383102417,
0.6151038408279419,
0.2412109375,
-0.32270413637161255,
0.3715228736400604,
0.5046776533126831,
0.4306870102882385,
-0.16362832486629486,
-0.30664753913879395,
0.1250515580177307,
0.20348785817623138,
-0.13096940517425537,
0.225521981716156,
-0.3181859254837036,
0.31667736172676086,
0.09335092455148697,
0.8347106575965881,
-0.6397740840911865,
0.41285499930381775,
0.19476459920406342,
0.6521949172019958,
-0.7840741872787476,
-0.3267397880554199,
0.5436839461326599,
0.31540027260780334,
-0.3412553668022156,
-0.17751823365688324,
-0.013994318433105946,
0.4464704990386963,
-0.0632137581706047,
-0.6125166416168213,
0.5026556253433228,
1.1375349760055542,
0.020577168092131615,
0.028170177713036537,
0.8578567504882812,
-0.023797962814569473,
-0.8262051343917847,
-0.31626009941101074,
-1.2818634510040283,
0.28490111231803894,
-0.636608362197876,
0.18681681156158447,
0.52668696641922,
-0.8901928663253784,
0.5910577178001404,
-0.540510356426239,
0.03149978071451187,
0.4259563684463501,
-0.34397435188293457,
0.49958738684654236,
0.5382956266403198,
0.2063601166009903,
-0.16796813905239105,
0.609496533870697,
-0.8438919186592102,
-0.1368999481201172,
-0.7538366913795471,
0.46333223581314087,
0.8194540143013,
-0.3727080225944519,
0.4825548231601715,
-0.27769482135772705,
-0.5550582408905029,
-0.489469051361084,
0.36577293276786804,
-0.4337295889854431,
0.03693027421832085,
0.29141002893447876,
-0.21557752788066864,
-0.15761469304561615,
-0.855989933013916,
0.641526460647583,
-0.34524035453796387,
-0.454853892326355,
0.4490112364292145,
0.1427108496427536,
-0.58499675989151,
0.9030165076255798,
0.09133637696504593,
-0.6410740613937378,
-0.1137290671467781,
0.7811233997344971,
0.6453877687454224,
-0.2350810319185257,
0.16291971504688263,
-0.4982277452945709,
-0.5707031488418579,
0.3488183319568634,
-0.00869311299175024,
-0.08113139867782593,
-0.5410082340240479,
0.5016015768051147,
0.04902433976531029,
-0.15965639054775238,
0.05929533392190933,
-0.33858731389045715,
-0.38802504539489746,
0.36814039945602417,
-0.3075624108314514,
0.7354670166969299,
-0.8025491833686829,
0.15416336059570312,
-1.2554086446762085,
0.22583071887493134,
0.4817272126674652,
-0.03788251429796219,
0.6303004622459412,
-0.1831098347902298,
0.6884389519691467,
-0.1646377444267273,
0.7497344017028809,
-0.7779422402381897,
-0.35168683528900146,
0.11175376176834106,
-0.45303037762641907,
-0.20192959904670715,
-0.4861268103122711,
0.1573777049779892,
-0.038475412875413895,
0.39970773458480835,
0.5111729502677917,
0.8572628498077393,
0.03133684769272804,
-0.3299609422683716,
-0.5177263617515564,
-0.6548342704772949,
0.26263678073883057,
0.39017221331596375,
0.1856798380613327,
-0.3304287791252136,
-0.3892761170864105,
-0.21262411773204803,
0.19946777820587158,
-0.07864376902580261,
-0.10828780382871628,
-0.7040694952011108,
-0.09814414381980896,
0.22109538316726685,
-0.3140523433685303,
0.13649456202983856,
-0.15849575400352478,
0.7269917726516724,
0.104790098965168,
0.25829029083251953,
0.8899312615394592,
-0.27566710114479065,
0.4545957148075104,
0.4209960997104645,
0.9238705635070801,
0.6343668699264526,
0.3629806637763977,
0.41615813970565796,
-0.14584937691688538,
-0.1320343315601349,
-0.30175113677978516,
-1.104507565498352,
-0.4840841293334961,
-0.49408257007598877,
0.0949946865439415,
-0.12691672146320343,
0.017654981464147568,
0.22613798081874847,
0.9801108241081238,
-0.40729594230651855,
0.5147226452827454,
-0.2393578141927719,
0.7620489597320557,
0.36386528611183167,
0.6638196110725403,
0.22262154519557953,
0.010064242407679558,
0.4920903146266937,
-1.020858645439148,
0.049435656517744064,
0.3999035656452179,
0.749148964881897,
-0.2225727140903473,
-0.08355505019426346,
-0.17372213304042816,
-0.40764516592025757,
0.14779753983020782,
0.10959196090698242,
-0.7956311106681824,
0.33398815989494324,
0.1704397052526474,
1.2036265134811401,
0.3124931752681732,
-0.048813577741384506,
0.17696234583854675,
-0.24510113894939423,
0.7194849848747253,
-0.8242180943489075,
0.5719127058982849,
-0.6696583032608032,
0.4892275929450989,
0.6533574461936951,
-1.0221463441848755,
-0.15129642188549042,
-0.9520710706710815,
-0.43257176876068115,
-0.24907207489013672,
0.17365851998329163,
0.9384713172912598,
0.3864632248878479,
-0.39382031559944153,
-0.07406255602836609,
-0.315129816532135,
0.39939621090888977,
-0.5883968472480774,
-0.16561359167099,
0.5867332220077515,
-0.3655722141265869,
-0.12328635156154633,
0.3444753885269165,
0.2355116605758667,
-0.5923958420753479,
0.6734874844551086,
-0.5023224949836731,
0.2465624213218689,
-0.9847272634506226,
-0.5501134991645813,
-0.5592837333679199,
-0.5223583579063416,
-0.5678052306175232,
-0.00968987587839365,
0.16901813447475433,
0.016386836767196655,
-0.24741914868354797,
-0.11926412582397461,
-0.0008724437793716788,
-0.39182090759277344,
0.38725605607032776,
0.09705256670713425,
0.8891463875770569,
0.747546911239624,
0.13552795350551605,
0.48928260803222656,
0.5377017259597778,
-0.0676991418004036,
-0.12729285657405853,
0.3249990940093994,
0.5870245099067688,
0.028467414900660515,
-0.2388627976179123,
-0.32659316062927246,
-0.7010784149169922,
-0.8051643371582031,
0.22745518386363983,
-0.43735170364379883,
0.2639540433883667,
0.08525491505861282,
-0.7070907950401306,
0.058318980038166046,
-0.23832787573337555,
-0.5835579633712769,
0.3335159122943878,
0.08992210030555725,
-0.29446902871131897,
0.9166125655174255,
-0.14220929145812988,
-0.33987662196159363,
-0.429070383310318,
-0.6815283298492432,
-0.46795594692230225,
0.2843468189239502,
0.3639565110206604,
0.5031344890594482,
0.05121316388249397,
-0.5246469974517822,
0.5343716144561768,
-0.3929612338542938,
-0.1871737688779831,
-0.0065896110609173775,
-0.5609217286109924,
-0.08693267405033112,
0.3662331998348236,
-0.1781594604253769,
-0.011150689795613289,
-0.40434515476226807,
0.03304839879274368,
-0.34773170948028564,
-0.5055893659591675,
0.5459145903587341,
-0.3620537519454956,
-0.5569477677345276,
0.8695995211601257,
0.4551326334476471,
-0.496957391500473,
0.22643019258975983,
0.657492458820343,
0.0885232537984848,
0.16276152431964874,
0.2910730540752411,
-0.9622815847396851,
0.38689151406288147,
-0.3265380859375,
0.32582375407218933,
-0.7928087711334229,
-0.6032490134239197,
-0.41005611419677734,
-0.9671629071235657,
0.49400565028190613,
0.3777419328689575,
0.2051362246274948,
-0.2058558464050293,
-1.096228003501892,
0.01326662115752697,
-0.01703094318509102,
0.23755158483982086,
0.05673518776893616,
-1.2461899518966675,
-0.4963371753692627,
-0.46079903841018677,
0.20010092854499817,
-0.5513193607330322,
0.33241984248161316,
0.42309829592704773,
-0.07484441250562668,
-0.07647385448217392,
0.19908565282821655,
0.3432764410972595,
-0.1991712599992752,
0.07885099947452545,
0.47646376490592957,
-0.4730202555656433,
0.4086293578147888,
-0.6049597859382629,
0.17536869645118713,
-0.8778089880943298,
1.2110038995742798,
-0.3187418282032013,
-0.26032498478889465,
-0.2578701674938202,
0.24149030447006226,
0.2805715799331665,
-0.1676505208015442,
0.6914680004119873,
0.44648146629333496,
-0.0969313308596611,
0.22597546875476837,
0.5987644791603088,
-0.6038575172424316,
-0.007829356007277966,
-0.3811911642551422,
-0.5042917132377625,
0.46069809794425964,
-0.015439309179782867,
0.15765166282653809,
-0.387658953666687,
-0.3903595507144928,
-0.5047627687454224,
-0.17028029263019562,
0.4550682604312897,
0.6636300683021545,
0.10782137513160706,
0.4587043821811676,
-0.3171880543231964,
0.14641724526882172,
-0.48807263374328613,
0.24891936779022217,
-0.10513745993375778,
-0.587927520275116,
0.08515895158052444,
0.27223101258277893,
-0.36390039324760437,
-0.5792385935783386,
-0.2893471419811249,
0.5465141534805298,
-0.38445574045181274,
0.1573229730129242,
0.51116544008255,
-0.27087029814720154,
-0.5056856274604797,
-0.10948856174945831,
0.2319815456867218,
0.18680568039417267,
0.6845119595527649,
0.20454974472522736,
-0.2330317199230194,
0.44660383462905884,
-0.3329484164714813,
0.5736767053604126,
-0.45808330178260803,
-0.1298999786376953,
0.56704181432724,
-0.38536834716796875,
-0.3023563325405121,
0.6076459288597107,
-0.49924564361572266,
-0.43024224042892456,
-0.004894443787634373,
-0.4833623468875885,
0.11013105511665344,
-0.7140714526176453,
0.0680190920829773,
0.11185429245233536,
-0.44842225313186646,
-0.4452173113822937,
-0.0897739827632904,
0.11372944712638855,
-0.33199986815452576,
-0.5004846453666687,
-0.7008077502250671,
-0.35012286901474,
0.0268878024071455,
-0.8056252598762512,
0.8646175861358643,
-0.0069841681979596615,
-0.34022092819213867,
-0.40927794575691223,
-0.2199154794216156,
-0.07931091636419296,
0.15212276577949524,
0.06222546100616455,
-0.29252710938453674,
0.1340344250202179,
0.3497833013534546,
0.5283849239349365,
0.604628324508667,
0.6886060237884521,
-0.07532162964344025,
0.00893718097358942,
0.11955354362726212,
-0.5616230368614197,
-0.6269922852516174,
-0.6322811841964722,
0.5263503789901733,
0.6093758344650269,
0.015620915219187737,
0.09786971658468246,
0.2781244218349457,
-0.3793848156929016,
-0.09547289460897446,
-0.623872697353363,
0.22622312605381012,
-0.8542673587799072,
0.03366071730852127,
-0.11873162537813187,
0.1945675015449524,
0.19029156863689423,
1.2444536685943604,
-0.19009511172771454,
-0.061894144862890244,
-0.27306249737739563,
-0.1307789385318756,
0.35034608840942383,
-0.42225393652915955,
-0.24095426499843597,
-0.513543426990509,
0.11080697178840637,
-0.6402139067649841,
0.03404170274734497,
-0.21181078255176544,
-0.0004439474723767489,
-0.007213116157799959,
0.19708536565303802,
0.2980711758136749,
-0.06800287216901779,
0.7186282873153687,
-0.7359338998794556,
-0.9141073822975159,
-0.23253068327903748,
-0.3424973785877228,
-0.5313044786453247,
0.7545592188835144,
0.2119978666305542,
1.0519627332687378,
0.4332015812397003,
0.3806925415992737,
0.45840588212013245,
0.017637426033616066,
-0.5876583456993103,
0.0960434079170227,
0.26968005299568176,
-0.05246156454086304,
-0.2398616522550583,
-0.8755473494529724,
-0.2767890393733978,
-0.07979636639356613,
-0.8847442865371704,
0.011156155727803707,
-1.1904610395431519,
0.05103595182299614,
0.44691288471221924,
0.5015373229980469,
-0.2252359837293625,
0.7152059674263,
0.7383376359939575,
0.6033712029457092,
-0.17627651989459991,
-0.2572630047798157,
-0.1535741239786148,
0.13727392256259918,
-0.2462567836046219,
0.24121685326099396,
-1.1317046880722046,
0.16714662313461304,
-0.5539830327033997,
0.5068022608757019,
-0.0050993734039366245,
0.221598282456398,
-0.21045123040676117,
0.0036606984212994576,
0.17042627930641174,
-0.252548485994339,
-0.848296582698822,
0.2866193652153015,
1.0562824010849,
-1.126084804534912,
-0.36300480365753174,
-0.6168058514595032,
-0.5526543259620667,
0.4905520975589752,
-0.7010155916213989,
-0.2968185245990753,
-0.3128575086593628,
-0.4345009922981262,
0.43709656596183777,
0.16020284593105316,
-0.5875247716903687,
0.3288221061229706,
-0.24893099069595337,
0.19436080753803253,
0.33772000670433044,
-0.05023638904094696,
-0.5084730982780457,
0.19412587583065033,
-1.1217049360275269,
0.5000342130661011,
-1.0654747486114502,
-0.06806767731904984,
-1.1924331188201904,
-1.1724488735198975,
-0.6133644580841064,
0.6599013209342957,
0.48021355271339417,
0.1128116101026535,
-0.3075452744960785,
-0.19803214073181152,
0.2491268366575241,
-0.018965966999530792,
-0.46048715710639954,
-0.4035695493221283,
-0.7034265398979187,
0.1892707794904709,
0.01572372391819954,
-0.7650814652442932,
0.09291642159223557,
0.2002616673707962,
-0.07553981244564056,
0.1882418692111969,
-0.2873285114765167,
1.0113768577575684,
0.34705761075019836,
-0.3229934275150299,
1.3154898881912231,
0.7101889848709106,
0.15155453979969025,
-0.0710422545671463,
-0.3906964361667633,
0.41529399156570435,
0.36952412128448486,
0.015989895910024643,
1.0942012071609497,
0.5734192728996277,
-0.40231141448020935,
-0.16660207509994507,
-0.14280295372009277,
-0.2230580598115921,
-0.20883506536483765,
0.30795472860336304,
0.03762545436620712,
0.7837864756584167,
0.17219483852386475,
0.21332772076129913,
0.1266450732946396,
0.1364527940750122,
0.3564394414424896,
0.2396683394908905,
-0.5905617475509644,
0.007001624442636967,
0.17291240394115448,
-0.09175571799278259,
-0.5543371438980103,
-0.08916280418634415,
0.059369031339883804,
0.015223244205117226,
0.6220290064811707,
0.25554394721984863,
0.0765567496418953,
0.23559290170669556,
0.9141576886177063,
0.19473358988761902,
-0.019087297841906548,
0.6665758490562439,
0.13477373123168945,
0.8263428211212158,
0.3955713212490082,
1.42849862575531,
0.2845543324947357,
0.6791701912879944,
0.06205310672521591,
-0.7016450762748718,
-0.08741497993469238,
0.30171945691108704,
-0.8825323581695557,
-0.5908638834953308,
-0.5919541716575623,
0.21089725196361542,
-0.023588765412569046,
-0.09293989837169647,
0.7641015648841858,
-0.12322508543729782,
-0.013367938809096813,
0.5331344604492188,
-0.8649606704711914,
0.5266928672790527,
0.21719293296337128,
-0.3041594922542572,
0.11085706949234009,
0.17737647891044617,
0.412647008895874,
-0.09806741774082184,
0.6725643277168274,
0.9264568090438843,
0.2750508785247803,
0.10990332067012787,
-0.41998934745788574,
-0.39760398864746094,
0.06795469671487808,
0.36403852701187134,
-0.12053539603948593,
0.6100208163261414,
-0.01652483642101288,
-0.42429119348526,
0.16162903606891632,
0.16512548923492432,
-0.25339967012405396,
-0.2117854207754135,
0.6213188767433167,
-0.1299835592508316,
-0.8087602853775024,
-0.7844992876052856,
1.3675960302352905,
0.7741298079490662,
0.23138827085494995,
-0.9276690483093262,
-0.15309160947799683,
-0.7428335547447205,
-0.3640452027320862,
-0.8776320219039917,
0.3060031235218048,
0.014963335357606411,
-0.43461960554122925,
0.3484530746936798,
-0.053741976618766785,
-0.24402029812335968,
-0.6117691993713379,
-0.20319418609142303,
-0.4855597913265228,
0.5438835620880127,
-0.011263513937592506,
0.08528216928243637,
0.17867158353328705,
-0.3917350172996521,
-0.19673404097557068,
0.18357156217098236,
0.8745747208595276,
0.15606102347373962,
0.376107394695282,
0.9375388622283936,
0.34723231196403503,
-0.17152853310108185,
0.9685653448104858,
0.9213845729827881,
-1.2861006259918213,
0.5381538271903992,
-0.45334383845329285,
0.6426712870597839,
0.1101837009191513,
-0.0062703220173716545,
0.5833457112312317,
0.255598783493042,
-0.024563636630773544,
0.1518334597349167,
-0.5000513195991516,
-0.3178268373012543,
-0.9134339690208435,
-0.14313170313835144,
0.04809116572141647,
0.3658060133457184,
-0.09362111985683441,
0.26956167817115784,
0.055504102259874344,
-1.0638562440872192,
4.364166259765625,
0.47197380661964417,
0.6273295879364014,
0.7137207984924316,
0.3391501009464264,
1.0437101125717163,
-0.34386149048805237,
-0.4509015679359436,
-0.18657228350639343,
-0.5329745411872864,
0.011952489614486694,
0.15771736204624176,
0.4183468520641327,
-0.5279527306556702,
0.22866325080394745,
0.7600140571594238,
-0.5468471646308899,
-0.11165327578783035,
0.1410360485315323,
-0.7767581939697266,
-0.03986133635044098,
0.0008029830059967935,
0.09862135350704193,
-0.00047764828195795417,
0.18895195424556732,
0.21461237967014313,
0.03319732844829559,
-0.3778631091117859,
-0.011387881822884083,
-0.039305929094552994,
-0.4944320023059845,
-0.6743630766868591,
0.153458833694458,
-0.4706879258155823,
-0.727671205997467,
0.7310290932655334,
-0.23929733037948608,
-0.4024384021759033,
-0.13520006835460663,
-0.013481722213327885,
-0.027448046952486038,
0.06335415691137314,
-0.022929642349481583,
-0.10682372003793716,
-0.5863489508628845,
1.4574531316757202,
-0.19788990914821625,
0.6713294982910156,
0.6997972130775452,
-0.7725569009780884,
0.9323801398277283,
0.018379395827651024,
0.9846274852752686,
-0.41315752267837524,
-0.5263140797615051,
0.18009363114833832,
-0.4541360139846802,
0.09828522801399231,
0.8979315757751465,
0.00005689676618203521,
0.5918887853622437,
-0.4399062693119049,
-0.21733035147190094,
0.22883950173854828,
0.35452255606651306,
0.5444573163986206,
0.07676535099744797,
0.14640749990940094,
-0.334663987159729,
0.1927669793367386,
0.17034131288528442,
-0.6954637169837952,
-0.14360632002353668,
0.5346363186836243,
0.7917219996452332,
-0.1622113436460495,
-0.6965774297714233,
0.4361483156681061,
0.5033875703811646,
-0.15766163170337677,
0.5077848434448242,
-0.46525275707244873,
-0.8097211718559265,
0.13867509365081787,
-0.0333133228123188,
0.767568051815033,
0.20331613719463348,
0.16846796870231628,
-0.23172153532505035,
0.27020490169525146,
0.04133853688836098,
0.7679910659790039,
0.44289135932922363,
-0.49734464287757874,
-0.4334383010864258
] |
The Hyperfine Splitting in Charmonium: Lattice Computations Using the Wilson and Clover Fermion Actions
|
We compute the hyperfine splitting $m_{J/\psi}-m_{\eta_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a $24^3\times48$ lattice at $\beta = 6.2$, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83\err{13}{15} times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants $f_{\eta_c}$ and $f^{-1}_{J/\psi}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f^{-1}_{J/\psi}/f^{-1}_{\rho}$ we find 0.32\err{1}{2} with the Wilson action and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).
|
UKQCD Collaboration: C.R. Allton, C.T. Sachrajda, S.P. Booth, K.C. Bowler, D.S. Henty, R.D. Kenway, B.J. Pendleton, D.G. R...
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208018
|
hep-lat/9208019
|
[
-0.03903951123356819,
0.3723779022693634,
-0.09243162721395493,
-0.47007498145103455,
0.6549553275108337,
-0.3614175021648407,
0.12037546932697296,
-0.5269486308097839,
-0.8557426929473877,
1.582026720046997,
0.8632344603538513,
-0.5899209380149841,
0.7999688386917114,
-1.2102707624435425,
0.2565680742263794,
-0.1402675062417984,
-0.5345780253410339,
-1.1952619552612305,
-0.5162693858146667,
-0.6790720820426941,
0.4274088740348816,
-0.35956722497940063,
-1.813402533531189,
-0.12490884214639664,
-0.5932260751724243,
0.7158635258674622,
0.21679571270942688,
0.5314462780952454,
1.4404014348983765,
0.7154088616371155,
0.39268988370895386,
-0.1354741007089615,
-0.3636215627193451,
-0.9046403765678406,
-0.36635518074035645,
-0.4815170168876648,
0.3924855887889862,
-0.049875080585479736,
-0.09315638989210129,
-0.6032600998878479,
0.5429157018661499,
-0.06968782842159271,
0.8635643124580383,
-0.623991072177887,
-1.127049207687378,
-0.3115091323852539,
0.10745851695537567,
0.2420385181903839,
0.40316706895828247,
-1.1383626461029053,
0.45767974853515625,
0.16732996702194214,
0.21581491827964783,
-0.8690968155860901,
-0.46642667055130005,
-0.2948557436466217,
-0.2027837187051773,
0.30577918887138367,
-0.4553768038749695,
0.052838437259197235,
0.8133416175842285,
-0.02315220609307289,
1.3292211294174194,
-0.8600966930389404,
0.8625353574752808,
0.7750606536865234,
-0.14607331156730652,
0.38436055183410645,
0.02058534137904644,
-0.4288994371891022,
-1.0777310132980347,
-0.7542966604232788,
-0.16937299072742462,
-0.005769454408437014,
0.07727573812007904,
0.6650352478027344,
0.07786449790000916,
0.05851977318525314,
-2.171715021133423,
-0.9673758149147034,
-0.3410296142101288,
-0.434708833694458,
-0.41722753643989563,
1.1075478792190552,
0.15832698345184326,
-0.5202136635780334,
0.749815046787262,
-0.40062153339385986,
0.0532335564494133,
-0.44363534450531006,
0.19296908378601074,
0.5497198104858398,
0.40016940236091614,
0.09411193430423737,
0.096723772585392,
0.48625868558883667,
-0.17605386674404144,
0.5486516356468201,
0.12133236974477768,
0.5391450524330139,
-0.1551593393087387,
1.220763921737671,
-0.5063132643699646,
0.6878977417945862,
-0.35613057017326355,
-0.26295560598373413,
0.12097395211458206,
-0.11255353689193726,
-0.7273123264312744,
-0.313860148191452,
0.1431981921195984,
0.1568501740694046,
0.4258972406387329,
1.1427987813949585,
0.07985207438468933,
0.8446346521377563,
0.2329988330602646,
0.6045653223991394,
-0.5622386932373047,
0.4503844380378723,
0.2257489114999771,
0.055505551397800446,
-0.20727886259555817,
0.28173527121543884,
-0.3487437963485718,
-0.995917022228241,
0.08415047079324722,
1.1771540641784668,
-0.8821199536323547,
-0.4558887779712677,
-0.17808441817760468,
-0.1997092366218567,
-0.5651914477348328,
0.6429566144943237,
-0.29169371724128723,
0.20437856018543243,
0.0646277591586113,
0.33062174916267395,
0.2620604634284973,
-0.3673677146434784,
0.3269725739955902,
-0.9946860671043396,
0.39009132981300354,
1.3183075189590454,
-0.12949632108211517,
0.19763115048408508,
0.8352179527282715,
-0.5667365789413452,
0.12592540681362152,
0.5716056227684021,
-1.1429766416549683,
-0.2949655055999756,
-0.35432425141334534,
0.8272669315338135,
0.2571244537830353,
-0.22212304174900055,
-0.6920341849327087,
0.7048997282981873,
-1.0432958602905273,
-0.34788182377815247,
0.26879486441612244,
-0.25416281819343567,
-0.5481505990028381,
0.23615120351314545,
-0.5170031785964966,
0.4400598406791687,
0.03268575295805931,
-0.2866256833076477,
-0.1875246912240982,
-0.9115021228790283,
0.21823999285697937,
0.016154451295733452,
-0.06519391387701035,
0.47891753911972046,
-0.04575124755501747,
0.5168541669845581,
0.7926380038261414,
-0.0018455723766237497,
0.4070810377597809,
0.5180268883705139,
-0.4869576394557953,
-0.17043228447437286,
1.044187068939209,
0.2022232562303543,
-0.007595503237098455,
0.7846479415893555,
-0.3645712435245514,
-0.4982787072658539,
-0.39821815490722656,
0.5038439035415649,
0.15311141312122345,
0.7448368072509766,
-0.08539071679115295,
0.3404160439968109,
-0.4731096923351288,
-0.03992161154747009,
-0.4623936712741852,
-0.10979200899600983,
-0.1989678144454956,
-1.2613768577575684,
0.037539996206760406,
0.1705198734998703,
-0.31274649500846863,
0.30761638283729553,
-1.114861011505127,
0.7879918813705444,
0.024844776839017868,
0.1556469202041626,
-0.8854958415031433,
0.02672121860086918,
0.45048660039901733,
-0.6373257040977478,
-0.03383737429976463,
-0.4331434667110443,
0.09633456915616989,
0.2738603353500366,
-0.525078535079956,
-0.21276262402534485,
1.0679762363433838,
-0.7132600545883179,
0.6792625784873962,
-0.18568219244480133,
-0.030461739748716354,
0.2537297010421753,
-0.40566548705101013,
-0.202556312084198,
0.525989830493927,
0.677090048789978,
0.6864156723022461,
0.23150946199893951,
0.19540691375732422,
0.6139910221099854,
0.19388413429260254,
0.4514436423778534,
0.47260457277297974,
0.5963101387023926,
0.8192746639251709,
0.5754850506782532,
-0.10068359225988388,
0.546911895275116,
-0.4465729594230652,
-0.3947948217391968,
0.824299156665802,
0.4864340126514435,
0.1857806295156479,
-0.0527765117585659,
0.07765588909387589,
-0.27838215231895447,
-0.4623717665672302,
-0.04857802018523216,
-0.527466356754303,
1.0684008598327637,
-0.5692132115364075,
0.06401675194501877,
-0.37589773535728455,
-0.1492423117160797,
0.21935966610908508,
0.8050130605697632,
-0.6722745895385742,
-0.392428994178772,
-0.8270868062973022,
0.5880714654922485,
0.3120940923690796,
-0.1015673503279686,
-0.2729541063308716,
1.5057307481765747,
-0.01112950500100851,
0.02464895136654377,
-0.044892165809869766,
-0.2406138777732849,
-1.019881248474121,
-0.976664662361145,
-0.6386830806732178,
-0.0221897941082716,
-0.2994903326034546,
-0.416074275970459,
1.156913161277771,
-0.583916425704956,
0.6828189492225647,
-0.5628529191017151,
-0.20555782318115234,
0.9498056769371033,
-0.10093031078577042,
0.8245590925216675,
0.37305474281311035,
-0.8821988701820374,
-0.8075558543205261,
0.26955464482307434,
-0.14643342792987823,
0.6754043698310852,
0.04935550317168236,
0.4135911166667938,
0.3161167800426483,
-0.6810604333877563,
-0.009439102374017239,
-0.578464686870575,
-0.5483555197715759,
-0.08979444950819016,
0.24843056499958038,
-0.5312471985816956,
-0.016054783016443253,
0.4616110324859619,
-0.5098541378974915,
-0.6325361728668213,
-1.0397067070007324,
1.305206060409546,
0.6381727457046509,
-0.933975875377655,
0.7632063031196594,
0.8189772963523865,
-0.5356162190437317,
0.6172354221343994,
-0.6265204548835754,
0.0908861756324768,
-0.24359461665153503,
1.0791951417922974,
1.2217552661895752,
-0.08509122580289841,
0.25611943006515503,
-0.492436021566391,
-0.4256117045879364,
-0.003868203144520521,
-0.09503442794084549,
-0.26224952936172485,
-0.28447696566581726,
0.9546019434928894,
0.36743614077568054,
-0.8967675566673279,
0.7478471398353577,
-0.728874921798706,
-0.4990977942943573,
-0.039557237178087234,
-0.38650381565093994,
0.9818332195281982,
-0.15987896919250488,
0.1920166313648224,
-0.12174802273511887,
0.6063209772109985,
-0.26530200242996216,
0.7737517952919006,
0.31135663390159607,
-0.19125045835971832,
1.0349785089492798,
0.9415163993835449,
0.657744824886322,
-0.4711877703666687,
0.7611166834831238,
-0.03157024458050728,
0.25512945652008057,
0.5600531697273254,
-0.08054190129041672,
0.0781766027212143,
0.38751021027565,
0.09964146465063095,
0.2660349905490875,
0.54344642162323,
-0.35363826155662537,
0.2020494043827057,
-0.0671411007642746,
0.028806976974010468,
0.8430249691009521,
0.11465784162282944,
-0.09986989945173264,
0.8787705898284912,
-0.4554356038570404,
-0.4269728362560272,
0.15276707708835602,
-0.1351713389158249,
1.1479980945587158,
-0.812991738319397,
0.9493340849876404,
0.3225476145744324,
-0.1916220486164093,
-0.2640725076198578,
0.013094167225062847,
-0.3846052885055542,
0.35103845596313477,
0.6229813098907471,
1.415860891342163,
-1.238700270652771,
-0.597763180732727,
0.4903956949710846,
1.1710442304611206,
1.3218541145324707,
1.1556137800216675,
0.9457234144210815,
0.22321774065494537,
-0.20518559217453003,
-0.6619675159454346,
-0.35506749153137207,
-0.20563939213752747,
-0.33927494287490845,
-1.012384295463562,
-0.24378003180027008,
-0.5410079956054688,
-0.40274322032928467,
0.9405652284622192,
0.5507363677024841,
0.4579961597919464,
-0.13218915462493896,
1.1781928539276123,
-0.3091099262237549,
0.8015007972717285,
1.147401213645935,
0.26427677273750305,
-0.20745712518692017,
-1.5399320125579834,
0.49673616886138916,
0.4651646912097931,
0.3298451900482178,
-0.43334150314331055,
0.007439881097525358,
-0.50117027759552,
0.1814866065979004,
0.21319516003131866,
0.24457666277885437,
-0.2522009611129761,
0.2922866940498352,
-1.0251038074493408,
0.4453255236148834,
-0.2948637306690216,
-0.15007488429546356,
-0.002227806719020009,
0.7428252100944519,
-0.46855592727661133,
-1.114477515220642,
0.2813252806663513,
-0.6504274606704712,
0.7148306369781494,
0.5771762132644653,
-0.6439341902732849,
-1.1083470582962036,
-0.571597158908844,
-0.025002028793096542,
-0.7301833629608154,
-0.04698178172111511,
0.903650164604187,
-0.3047163486480713,
-0.05858578532934189,
-0.7259681224822998,
-0.4506783187389374,
0.21735599637031555,
0.20281817018985748,
-0.34590834379196167,
0.049449510872364044,
-0.12504620850086212,
-0.4690929651260376,
0.44061827659606934,
-0.08130915462970734,
-0.13813215494155884,
-0.058062560856342316,
-0.43215373158454895,
-0.0598876066505909,
-0.9741277098655701,
-0.5789348483085632,
-0.44375211000442505,
-0.3065869212150574,
-0.27966222167015076,
0.5209311246871948,
-0.3747038245201111,
0.537497341632843,
0.19672885537147522,
0.8198467493057251,
-1.0897399187088013,
-0.9730745553970337,
0.3645816147327423,
0.24473606050014496,
0.4652635157108307,
0.4640047252178192,
0.5407111048698425,
0.024524588137865067,
0.942313015460968,
-0.024091674014925957,
-0.01040571928024292,
1.0394158363342285,
-0.051039643585681915,
0.6902397274971008,
-0.28352150321006775,
0.2147543579339981,
-0.9427796602249146,
-0.4056040346622467,
0.4409480690956116,
-0.3121412396430969,
0.5032314658164978,
0.27269312739372253,
-0.5269564986228943,
-0.10936545580625534,
-0.6816760897636414,
-0.5961111187934875,
-0.3134409189224243,
0.19846884906291962,
-0.7737562656402588,
0.2579861581325531,
-0.34598812460899353,
-0.02052438072860241,
0.47909805178642273,
0.27379655838012695,
0.1040545403957367,
0.30754587054252625,
1.0287426710128784,
-0.6476612091064453,
0.3194027841091156,
-0.7656490206718445,
0.4362405836582184,
-0.43474477529525757,
0.4913424849510193,
-0.5062099695205688,
-0.2658957242965698,
-0.3802954852581024,
-0.09225205332040787,
-0.4656662046909332,
-0.8058652281761169,
0.0861588642001152,
-0.15660056471824646,
1.2668105363845825,
0.17588788270950317,
-0.6334074139595032,
-0.32592660188674927,
-1.1829149723052979,
0.29903632402420044,
-0.10812386125326157,
-0.8813639283180237,
-0.23033443093299866,
0.28398409485816956,
-0.3066442310810089,
0.06842003762722015,
0.3378556966781616,
-1.0194035768508911,
0.1585913747549057,
-0.07554750144481659,
0.23937131464481354,
-0.8775421977043152,
0.1915666162967682,
-0.43527963757514954,
-1.087597131729126,
-0.22734655439853668,
0.2521938383579254,
1.0072654485702515,
-0.4087945520877838,
-0.1455446481704712,
-1.0062309503555298,
0.2741893231868744,
-0.392966091632843,
0.17525938153266907,
-0.5702450275421143,
-0.24063420295715332,
-0.19942766427993774,
0.7882986664772034,
-0.07758203893899918,
-0.4897814989089966,
0.2966151833534241,
0.44352778792381287,
0.048376716673374176,
1.2051928043365479,
-0.19480225443840027,
-0.18079382181167603,
0.06451238691806793,
0.20797978341579437,
0.19603829085826874,
-0.05212215334177017,
-1.0152429342269897,
0.5911432504653931,
-1.30857515335083,
1.0259296894073486,
-0.3787367045879364,
0.04228226840496063,
-0.23874789476394653,
-0.24326853454113007,
0.8692150115966797,
-0.6103312373161316,
0.5215128660202026,
0.05857330933213234,
0.6929166913032532,
1.003341794013977,
0.5857641100883484,
-0.28937914967536926,
-0.28299757838249207,
-0.9331768155097961,
-1.3148037195205688,
1.0608434677124023,
-0.7381659746170044,
-0.565066933631897,
-1.5188952684402466,
-0.25039175152778625,
0.6824102997779846,
-0.3000715970993042,
1.3571950197219849,
0.23946230113506317,
0.48128870129585266,
-0.48310577869415283,
0.42061182856559753,
-0.761224091053009,
-0.3912455439567566,
-0.41901108622550964,
0.3336746394634247,
-0.501022458076477,
-1.2285821437835693,
-0.36370670795440674,
0.02740013599395752,
-1.4792386293411255,
-0.15346412360668182,
0.045014120638370514,
0.5793820023536682,
0.03325401619076729,
0.693899929523468,
-0.9010424017906189,
-0.21813079714775085,
-0.6909766793251038,
-0.21431715786457062,
-0.6178778409957886,
0.3538111448287964,
0.9786968231201172,
0.06618209928274155,
0.12700533866882324,
-0.35461437702178955,
0.49797025322914124,
-1.0447944402694702,
-0.20360462367534637,
0.6918908953666687,
-0.3532637655735016,
-0.22048883140087128,
0.6941521763801575,
0.5818681716918945,
-0.9706332683563232,
-1.0729386806488037,
-0.05961435288190842,
-0.20752200484275818,
0.05273130536079407,
-0.8897863626480103,
0.7077706456184387,
-0.44595202803611755,
-0.7146087288856506,
0.23002903163433075,
0.4319387376308441,
-0.32367777824401855,
-0.1023717001080513,
0.517200767993927,
-0.6246019601821899,
-0.7859680652618408,
0.26009947061538696,
0.9856202602386475,
-0.538305401802063,
0.14313547313213348,
-0.6788077354431152,
-0.4887792468070984,
0.03733829781413078,
-0.15342944860458374,
-0.15376949310302734,
-0.41786274313926697,
0.2743604779243469,
0.6021826863288879,
0.5832450985908508,
0.9036440849304199,
-0.1512908637523651,
0.6872398257255554,
-0.6933324337005615,
0.1159011498093605,
-0.9656633138656616,
-1.2697279453277588,
0.19786176085472107,
-0.16848629713058472,
0.7381485104560852,
-0.5138764381408691,
0.6625831723213196,
0.6147900819778442,
-0.8479717373847961,
-0.5009979009628296,
-1.4694950580596924,
0.5002695918083191,
-1.513946294784546,
-0.6741649508476257,
-0.19865620136260986,
-0.5999618768692017,
-0.5149986147880554,
0.2969619631767273,
0.50853431224823,
-0.07352060824632645,
-0.8830705285072327,
-0.032306089997291565,
0.09967535734176636,
-0.3253636062145233,
-0.0362296998500824,
-0.6561462879180908,
-1.09835946559906,
0.12342694401741028,
0.10447607189416885,
0.16588838398456573,
-0.3421066105365753,
0.5124331712722778,
0.00648524472489953,
0.5258520841598511,
-0.33831727504730225,
0.5079807639122009,
-0.3492937386035919,
-0.009457183070480824,
-0.35725510120391846,
0.07250873744487762,
-0.7323247194290161,
-0.28090375661849976,
-0.8399643898010254,
0.6713693737983704,
0.2360508292913437,
-0.15755578875541687,
-0.5205399990081787,
0.4989987015724182,
-0.034633781760931015,
-0.8340383768081665,
-0.4478721022605896,
0.6479145884513855,
0.15484364330768585,
-1.1394472122192383,
0.047843217849731445,
0.08918634057044983,
-1.059180736541748,
0.005438387393951416,
0.08973214030265808,
-0.17578749358654022,
-0.3306939899921417,
-0.08961427211761475,
0.07756498456001282,
0.9118820428848267,
0.2290298193693161,
0.6343404650688171,
-0.29640889167785645,
-0.5741243958473206,
-0.34221717715263367,
-0.5084343552589417,
-0.40564265847206116,
0.7212432026863098,
0.4864502251148224,
-0.8267262578010559,
0.8681129217147827,
0.23781336843967438,
-0.3632385730743408,
0.06313814222812653,
-0.6309085488319397,
-0.22575773298740387,
-0.4785063564777374,
0.32360750436782837,
0.2849504053592682,
1.0380115509033203,
0.36998721957206726,
-0.8944417834281921,
-0.7020761370658875,
-1.0219663381576538,
-0.5762197375297546,
-0.005091063678264618,
-1.078674077987671,
-0.3029361665248871,
-0.21321916580200195,
-0.5186068415641785,
0.5624443888664246,
-0.30169248580932617,
-0.06686422228813171,
0.5964232683181763,
0.18380025029182434,
0.19199824333190918,
-0.3038545548915863,
0.09226474165916443,
-0.05544818565249443,
0.08490008860826492,
-1.04562246799469,
-0.8390268087387085,
-0.7823249101638794,
-0.09901081025600433,
-1.0388166904449463,
-0.9090457558631897,
-0.411356121301651,
0.07749265432357788,
-0.04261202737689018,
-0.32805946469306946,
-0.7966616749763489,
0.5643754005432129,
0.147039994597435,
-0.1374184936285019,
-0.2427990436553955,
0.06730500608682632,
-0.15799415111541748,
0.7104652523994446,
0.10015078634023666,
-0.350221186876297,
0.15335029363632202,
0.769281268119812,
0.3166549801826477,
0.3140338063240051,
-0.7421169877052307,
0.8291836380958557,
0.17958378791809082,
-0.8413276672363281,
1.3758227825164795,
-0.13718219101428986,
1.317897081375122,
0.22184935212135315,
0.028928326442837715,
0.384277880191803,
0.4324929416179657,
0.6229237914085388,
0.7547245621681213,
0.5276145339012146,
0.1828552931547165,
-0.0006229932769201696,
-0.15658068656921387,
0.06488822400569916,
-0.006294203456491232,
0.6083247065544128,
-0.20219984650611877,
0.6089167594909668,
-0.3729408085346222,
0.261631041765213,
-0.3741161823272705,
0.5452138781547546,
0.11342790722846985,
-0.004556955303996801,
-0.34464943408966064,
-0.7597917318344116,
-0.10964644700288773,
0.6237363219261169,
0.22620098292827606,
-0.6066837310791016,
-0.17728500068187714,
0.20000869035720825,
-0.45775556564331055,
0.4786573648452759,
0.11643356084823608,
-0.5973660945892334,
0.7013583183288574,
0.620612382888794,
0.467682808637619,
0.42926958203315735,
0.3394460678100586,
0.24161659181118011,
0.3571551442146301,
1.235674500465393,
0.3960912823677063,
0.10958535224199295,
0.2812647521495819,
-0.7968210577964783,
-0.8532878756523132,
0.21974270045757294,
-1.1688672304153442,
-0.26696279644966125,
-0.2591213583946228,
-0.5250605344772339,
-0.043078966438770294,
-0.78018718957901,
0.8528005480766296,
-0.7307348847389221,
0.4868007004261017,
1.5517559051513672,
0.2814747989177704,
-0.10060206800699234,
0.15911181271076202,
-0.3198331594467163,
0.44422754645347595,
0.7994971871376038,
0.3745846450328827,
0.04665324091911316,
1.446423888206482,
1.3514776229858398,
-0.011437446810305119,
0.9199402332305908,
-0.4771359860897064,
-0.18317432701587677,
-0.08220603317022324,
0.2969563603401184,
-0.0702141746878624,
1.2464661598205566,
-0.34878531098365784,
-0.7201060056686401,
0.283096045255661,
0.4824633300304413,
-0.6760348677635193,
0.10972806066274643,
0.5587461590766907,
0.40460094809532166,
-0.13572277128696442,
-0.10083849728107452,
1.1701213121414185,
0.09774290025234222,
-0.16877099871635437,
-0.24132485687732697,
0.032317277044057846,
-0.11605846136808395,
0.2327020764350891,
-0.8808818459510803,
0.2873128652572632,
0.587136447429657,
0.6711260080337524,
-0.604189395904541,
-1.1361620426177979,
-0.6107947826385498,
-0.872083842754364,
-0.3250511586666107,
-0.3340529799461365,
0.5498723983764648,
0.19400976598262787,
0.7949782013893127,
0.32417163252830505,
-0.9667895436286926,
0.1451195478439331,
0.9206342697143555,
0.8377795219421387,
-0.5235574245452881,
0.6124826669692993,
0.8195762634277344,
0.8819657564163208,
-0.781502366065979,
0.8995957374572754,
0.5239778757095337,
-0.36638277769088745,
-0.019677268341183662,
-0.1436280906200409,
-0.22909098863601685,
-0.26359373331069946,
-0.41576194763183594,
0.11932221055030823,
0.6632164120674133,
0.1346297264099121,
-1.115219235420227,
-0.2533336281776428,
-0.264944463968277,
-0.9101807475090027,
0.0033018761314451694,
-0.9326922297477722,
0.7493122816085815,
0.27557697892189026,
0.7179206013679504,
-0.44450515508651733,
0.17675378918647766,
3.4099273681640625,
0.6903315186500549,
0.7462486028671265,
-0.08194471150636673,
0.7921807169914246,
0.8872559070587158,
0.6866313219070435,
0.032473914325237274,
0.6436992287635803,
-0.3830913305282593,
0.058489419519901276,
0.6681100726127625,
1.1078753471374512,
-0.2694336771965027,
-0.3542458117008209,
-0.037441980093717575,
-0.629780113697052,
0.20646774768829346,
0.13323737680912018,
-0.687645435333252,
-0.38167840242385864,
0.09214327484369278,
-0.1445620059967041,
-0.27746841311454773,
0.7515352964401245,
-0.6115853190422058,
0.08730631321668625,
-0.426766961812973,
-0.048029009252786636,
0.5767874717712402,
0.04207983613014221,
-0.9329928755760193,
0.19472068548202515,
-0.5946398973464966,
-0.5668893456459045,
0.6915627121925354,
0.3532746136188507,
-0.09611095488071442,
0.7525184154510498,
0.18098106980323792,
-0.2564663589000702,
-0.38705408573150635,
-0.5650491714477539,
0.5525509119033813,
-1.0102834701538086,
1.599143624305725,
0.07648976892232895,
1.2247148752212524,
0.720929741859436,
-0.6363588571548462,
-0.23849323391914368,
-0.10711915045976639,
0.4241417646408081,
-0.28202977776527405,
-1.1718485355377197,
0.05919447913765907,
-0.9278973340988159,
-1.1443061828613281,
0.12746457755565643,
0.4851743280887604,
0.979276716709137,
0.2359895408153534,
-0.2079116702079773,
0.936890184879303,
-0.03308369964361191,
0.14742298424243927,
0.4537617564201355,
-0.5301754474639893,
-0.8045077919960022,
-0.0690767765045166,
0.5618479251861572,
0.14006270468235016,
-0.3102557063102722,
-0.05130542442202568,
-0.19648320972919464,
-0.5288838148117065,
-0.5703616142272949,
0.8426026105880737,
0.10050199925899506,
-0.366000771522522,
-0.5820702314376831,
-0.7551574110984802,
-0.2219167798757553,
-0.16898153722286224,
-0.0677386075258255,
0.8778290748596191,
-0.13487321138381958,
0.14232876896858215,
-0.5076712965965271,
0.5272733569145203,
0.25594937801361084,
1.5337460041046143,
0.5829193592071533,
0.09765686839818954,
-0.7013078927993774
] |
Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model
|
An algoritm for the simulation of the 3--dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 Million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 Million spin updates per second on the same machine.
|
H. Rieger
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208019
|
hep-lat/9208020
|
[
-0.1938977688550949,
-0.14915737509727478,
0.5678834915161133,
0.44114068150520325,
-0.09959041327238083,
-0.4835137128829956,
-0.12071282416582108,
-0.7278366684913635,
-1.3451825380325317,
1.3915879726409912,
0.7189218997955322,
-0.11573536694049835,
0.4734475612640381,
-0.8859457969665527,
0.3497975468635559,
0.3373524248600006,
0.13842926919460297,
0.0695173442363739,
-1.6095716953277588,
0.37271854281425476,
-0.09871535748243332,
-0.15069414675235748,
-1.1056475639343262,
-0.7463884353637695,
-0.427204430103302,
1.0203752517700195,
-0.13378311693668365,
0.6419853568077087,
0.9070308208465576,
0.4127056300640106,
0.0921068862080574,
-0.059866465628147125,
-0.6789866089820862,
-0.36443331837654114,
0.023685351014137268,
0.0001872871653176844,
-0.19501076638698578,
-0.04901784658432007,
0.8265915513038635,
-0.22733598947525024,
0.5499975085258484,
-0.3259222209453583,
-0.02872198075056076,
-0.2197370082139969,
-0.23017244040966034,
0.5187780857086182,
0.0634465366601944,
0.26384979486465454,
-0.06910096853971481,
-1.2441664934158325,
0.14872212707996368,
0.43832144141197205,
0.7503969073295593,
-0.8174223303794861,
-0.26101425290107727,
0.032973505556583405,
-0.18808208405971527,
-0.4617128074169159,
-0.7388876676559448,
-0.13457800447940826,
0.3473754823207855,
-0.10266131162643433,
0.425576776266098,
-0.5127050876617432,
0.35233306884765625,
0.7296422123908997,
-0.46675893664360046,
0.7056865096092224,
-0.18856656551361084,
-0.32483208179473877,
-0.36044925451278687,
-0.028072509914636612,
-0.6396203637123108,
0.07040397077798843,
-0.7662312984466553,
-0.1216779425740242,
-0.17217032611370087,
0.09835010021924973,
-0.4894600212574005,
-0.5708645582199097,
0.20046496391296387,
0.39981505274772644,
-0.4640063941478729,
0.1910012662410736,
-0.15330290794372559,
-0.2288636863231659,
-0.3257730305194855,
-0.0834641307592392,
-0.5342671871185303,
0.4447014331817627,
-0.025158096104860306,
0.900955855846405,
-0.225290909409523,
-0.29291832447052,
0.33925870060920715,
0.6524233818054199,
0.26509398221969604,
0.6794827580451965,
0.20038209855556488,
-0.16074195504188538,
0.3364159166812897,
0.9152696132659912,
-0.9445350170135498,
0.31465357542037964,
-0.2612919211387634,
-0.014134206809103489,
-0.16811753809452057,
-0.004407085943967104,
-0.33863577246665955,
-0.26378971338272095,
0.2618352174758911,
-0.2180212438106537,
0.7113503813743591,
0.8909889459609985,
0.24755392968654633,
0.7241950631141663,
-0.11446841806173325,
-0.3098374605178833,
-0.8392913341522217,
-0.27804556488990784,
0.5091043710708618,
0.03319893777370453,
0.2710035741329193,
0.4399104714393616,
-0.5809909701347351,
-0.5111539959907532,
0.8550153970718384,
0.37290892004966736,
0.2513526678085327,
0.2809330224990845,
0.419260174036026,
-0.22808663547039032,
-0.2692733108997345,
0.815391480922699,
-0.4110620319843292,
0.49490368366241455,
-0.20338983833789825,
0.016913874074816704,
0.2990992069244385,
0.05820712819695473,
0.5409569144248962,
-0.2969503700733185,
0.43047773838043213,
0.8465250730514526,
0.3560127317905426,
0.37799686193466187,
0.7758228778839111,
0.2779650390148163,
0.17756417393684387,
-0.1746440976858139,
-1.2076776027679443,
0.1469920426607132,
0.03640008345246315,
-0.3372894823551178,
0.24573324620723724,
0.3655721843242645,
-0.7939574718475342,
0.8161527514457703,
-0.8877788782119751,
-1.0281825065612793,
0.4345768392086029,
0.18369634449481964,
-0.43386197090148926,
-0.06685518473386765,
-0.6088961362838745,
-0.18406707048416138,
0.012286513112485409,
-0.41658222675323486,
0.404769629240036,
-0.26300325989723206,
0.403982013463974,
0.4472905993461609,
-0.23289966583251953,
0.7087514400482178,
0.46260789036750793,
0.30810678005218506,
0.34693196415901184,
0.1040184423327446,
-0.19437019526958466,
0.4907709062099457,
0.16188976168632507,
-0.8365728855133057,
0.5417652726173401,
0.09157790243625641,
-0.5428874492645264,
0.1899980902671814,
-0.3631981909275055,
-0.6885242462158203,
-0.025217371061444283,
0.7682636976242065,
-0.02736530266702175,
0.015326160937547684,
-0.34082648158073425,
0.6273728013038635,
-0.6106395125389099,
0.08588316291570663,
-0.7783312797546387,
0.7462496757507324,
-0.20745527744293213,
-0.5171998143196106,
-0.3299415707588196,
0.506538450717926,
-1.5270367860794067,
0.2457124888896942,
-1.6603460311889648,
-0.31807202100753784,
1.1946243047714233,
-0.051166512072086334,
-0.7020947933197021,
-0.34511032700538635,
0.2827874422073364,
-0.36127138137817383,
0.37957802414894104,
-0.3280094563961029,
0.5872280597686768,
0.18604616820812225,
-0.2161472886800766,
0.15145017206668854,
0.7974042892456055,
0.19312065839767456,
0.8058198094367981,
0.27195438742637634,
-0.43925896286964417,
1.035317063331604,
-0.5485619306564331,
-0.4231744706630707,
0.24957628548145294,
0.30110964179039,
0.49821075797080994,
-0.09739499539136887,
0.5497207641601562,
0.7217379808425903,
0.06565628200769424,
0.5702670812606812,
1.1847169399261475,
0.5193670392036438,
0.5061703324317932,
0.849159836769104,
0.6090876460075378,
-0.07821239531040192,
-0.5515534281730652,
0.2925538122653961,
0.1386805921792984,
0.45703521370887756,
-0.23562151193618774,
-0.04381295293569565,
-0.7893027663230896,
0.1937703937292099,
-0.7923540472984314,
0.19143882393836975,
-0.3347046673297882,
0.556309163570404,
0.1577194184064865,
-0.000005595007678493857,
-1.6053826808929443,
-0.020093832165002823,
-0.08119601756334305,
0.09440937638282776,
-0.3254615366458893,
-0.22706077992916107,
-0.06873444467782974,
0.09041213244199753,
0.15020422637462616,
-0.7154658436775208,
-0.09705613553524017,
0.6922101974487305,
-0.14499607682228088,
0.06770636141300201,
0.2000405192375183,
-0.6014783382415771,
-1.1826683282852173,
0.35281118750572205,
-0.9098343849182129,
-0.09038751572370529,
-0.8259724974632263,
-0.08772742003202438,
0.8223091959953308,
-0.40415456891059875,
0.6188965439796448,
0.19497150182724,
-0.2106485217809677,
0.21468037366867065,
-0.7361307144165039,
0.5163715481758118,
0.9500176310539246,
-0.2619098424911499,
-0.5766953825950623,
0.08217799663543701,
-0.27321743965148926,
0.30292508006095886,
-0.43699491024017334,
0.16665266454219818,
0.873887836933136,
-0.46431198716163635,
0.13919024169445038,
-0.34238308668136597,
-0.5144686698913574,
0.09899254888296127,
0.19975045323371887,
-0.41879212856292725,
-0.058681420981884,
0.09878493845462799,
-0.5861268639564514,
-0.016085224226117134,
-0.4906613528728485,
0.9768880009651184,
0.1380060911178589,
-0.1756460815668106,
0.8497925996780396,
-0.10644116252660751,
-0.2364296168088913,
0.5360016226768494,
-0.07258514314889908,
-0.010774779133498669,
-0.06299427151679993,
0.9021037220954895,
1.0220403671264648,
-0.2836863398551941,
-0.2211833894252777,
-0.5894103050231934,
-0.4483819007873535,
0.5180401802062988,
0.14930953085422516,
-1.2401031255722046,
-0.26370206475257874,
0.388877809047699,
0.2929494082927704,
-0.25262314081192017,
0.5150683522224426,
-1.0297619104385376,
-0.5502607226371765,
-0.29747384786605835,
-0.7880269289016724,
0.3772110044956207,
0.02567652426660061,
-0.12801121175289154,
-0.9572435021400452,
-0.4114646315574646,
-0.3771103322505951,
-0.05654221028089523,
0.13531085848808289,
-0.528643012046814,
0.8854484558105469,
0.32432135939598083,
0.659654438495636,
-0.5080883502960205,
0.28460144996643066,
-0.4293311536312103,
0.09897669404745102,
0.27473801374435425,
-0.7426996231079102,
-0.09490631520748138,
0.03893028199672699,
0.2402825802564621,
-0.4180523455142975,
-0.07414267957210541,
-0.5344057083129883,
-0.9653419852256775,
-0.47943249344825745,
-0.4441555142402649,
0.4067267179489136,
0.5442209243774414,
-0.22199121117591858,
-0.10333220660686493,
-1.2881367206573486,
-0.49356284737586975,
-0.1726299226284027,
0.24949415028095245,
0.7641999125480652,
-0.6211850047111511,
0.053667906671762466,
0.47699540853500366,
-0.47917091846466064,
0.4185561537742615,
-0.018042396754026413,
0.8519879579544067,
0.8071709871292114,
0.45835456252098083,
0.8055394887924194,
-0.7818377017974854,
-0.8455424904823303,
-0.06068595498800278,
1.480189323425293,
1.078514814376831,
0.8387740254402161,
0.3165591061115265,
-0.07000739127397537,
-0.23231981694698334,
-0.6367623805999756,
-0.4970223307609558,
0.02681184560060501,
0.022203641012310982,
-0.26915645599365234,
-0.03963140770792961,
0.5535919666290283,
-0.26328355073928833,
0.289440780878067,
0.3633135259151459,
-0.005232485476881266,
0.5421853065490723,
0.5007872581481934,
0.4791976809501648,
0.6512339115142822,
0.7661899328231812,
-0.11509949713945389,
-0.33328375220298767,
-0.34500715136528015,
0.6962231993675232,
-0.3682589530944824,
0.22359585762023926,
-0.14474904537200928,
-1.0538944005966187,
-0.20773153007030487,
-0.8080213069915771,
0.9563454985618591,
0.5787007808685303,
-0.41628432273864746,
0.42140835523605347,
0.17413438856601715,
0.48047637939453125,
-0.4039625823497772,
-0.1703387349843979,
0.7612283825874329,
0.4755997657775879,
0.05270853266119957,
-0.6889030933380127,
0.46746698021888733,
-0.32465699315071106,
0.05801837146282196,
0.10460502654314041,
-0.9698097109794617,
-0.9416687488555908,
-0.3316442370414734,
0.6289452910423279,
-0.746963381767273,
0.1251542568206787,
0.876974880695343,
0.23996376991271973,
-0.23368977010250092,
-0.0821763426065445,
-0.3138856887817383,
0.6176019906997681,
-0.7325283885002136,
-0.1572662889957428,
0.025358643382787704,
-0.0955982655286789,
-0.021063530817627907,
0.7184336185455322,
0.0573279969394207,
-0.33461570739746094,
-0.32201141119003296,
-0.19227583706378937,
-0.24969178438186646,
-0.38875439763069153,
-0.3684092164039612,
-0.2841852903366089,
-0.5981602072715759,
-0.1602773517370224,
1.192284345626831,
0.27013182640075684,
-0.22257089614868164,
0.5905478596687317,
-0.28498271107673645,
-0.22224567830562592,
-0.3094221353530884,
-0.0027169319801032543,
0.4381565749645233,
0.8324182033538818,
0.5095548629760742,
0.7625727653503418,
0.15647506713867188,
0.5150150656700134,
0.36481237411499023,
0.06679036468267441,
0.05296795442700386,
0.0019919169135391712,
-0.29429084062576294,
-0.811556875705719,
0.08028805255889893,
-0.9457888007164001,
-0.9270972609519958,
0.48870280385017395,
-0.1716499775648117,
1.0735498666763306,
0.06164199486374855,
-0.22929693758487701,
-0.5560594797134399,
-0.5919645428657532,
-0.5830878615379333,
0.5888257026672363,
-0.38179126381874084,
-0.592905580997467,
0.8005680441856384,
-0.6232641339302063,
-0.1250888854265213,
-0.2905765473842621,
0.27133452892303467,
-0.6968865394592285,
0.2125057727098465,
0.5272554159164429,
-0.6084781885147095,
0.5590673685073853,
-0.5518059730529785,
0.7322176694869995,
-0.30010461807250977,
0.10166525840759277,
-0.5138579607009888,
-0.1529756486415863,
-0.2914889454841614,
-0.4565920829772949,
0.6152045130729675,
-0.1087053045630455,
-0.28080859780311584,
-0.08012041449546814,
0.4868229031562805,
0.34459516406059265,
-0.5375934839248657,
-0.24123790860176086,
-0.2786492109298706,
0.5380988717079163,
-0.2145795375108719,
-0.05884252116084099,
0.1719769686460495,
1.0041016340255737,
0.7609096169471741,
0.5818737745285034,
-0.28165701031684875,
-0.37534940242767334,
0.25102198123931885,
0.1691626012325287,
0.8311107158660889,
-0.4300750195980072,
-0.45620545744895935,
-0.11288988590240479,
-0.13749398291110992,
0.8164346218109131,
0.827568531036377,
-0.6053411960601807,
0.08805599063634872,
-0.31094595789909363,
-0.5923143625259399,
-0.007781824097037315,
-0.6376953125,
-0.07795774936676025,
-0.6725876927375793,
-0.6844058632850647,
-0.7176669836044312,
0.6281394958496094,
0.07666192203760147,
0.3766879737377167,
0.1701762080192566,
0.1646423190832138,
0.0436222180724144,
0.5583508014678955,
0.32184547185897827,
-0.12261559814214706,
0.059991881251335144,
0.1421508491039276,
-0.04694102704524994,
0.4444464147090912,
-0.6000601053237915,
0.37559080123901367,
-1.264477014541626,
1.1275248527526855,
-0.77704918384552,
0.026135258376598358,
0.31382283568382263,
0.41222792863845825,
0.3895075023174286,
-0.9068241715431213,
0.5036431550979614,
0.6765019297599792,
-0.07458370923995972,
0.7712897062301636,
0.5469101667404175,
-0.4929235577583313,
-0.6347084641456604,
-0.786762535572052,
-0.9195997714996338,
0.4211253225803375,
0.12104903161525726,
-0.40449902415275574,
-0.6490413546562195,
-0.7676336765289307,
-0.04927370697259903,
0.08198661357164383,
0.5242795348167419,
0.44230252504348755,
-0.4561308026313782,
0.02781437523663044,
0.24773170053958893,
-0.13821923732757568,
-0.2642524540424347,
-0.3421836495399475,
0.005431382916867733,
-0.05101577192544937,
0.16732193529605865,
0.004382351879030466,
-1.0502889156341553,
-0.6470261812210083,
-0.3815545439720154,
0.18125665187835693,
0.31027159094810486,
-0.6942222714424133,
1.085709571838379,
-0.022141985595226288,
-0.6754703521728516,
-0.610115647315979,
-0.4453776478767395,
0.055044181644916534,
0.41061723232269287,
0.5048820972442627,
0.1249367743730545,
0.010937395505607128,
0.020350387319922447,
0.3445467948913574,
-0.25571000576019287,
-0.4338657855987549,
0.4808969795703888,
-0.4842712879180908,
-0.44510728120803833,
0.13406389951705933,
0.06425602734088898,
-0.6270745992660522,
-1.0531433820724487,
-1.3497103452682495,
-0.02564486674964428,
-0.31889426708221436,
-0.6700193285942078,
0.058733679354190826,
-0.26294195652008057,
0.10922662913799286,
0.673547625541687,
1.0882734060287476,
0.37178298830986023,
-0.20518924295902252,
-0.03712661564350128,
-0.8631033301353455,
0.0326787494122982,
-0.2072158306837082,
1.5110491514205933,
0.19550278782844543,
-0.6665857434272766,
-0.3868251442909241,
-0.35763850808143616,
-0.6685109734535217,
0.5141953229904175,
0.6040045619010925,
-0.3535998463630676,
0.28335756063461304,
-0.24784311652183533,
-0.1753106564283371,
0.8774590492248535,
0.40110379457473755,
0.5600318908691406,
-0.20156307518482208,
0.15485318005084991,
-0.9410971403121948,
-0.03587288409471512,
-0.8097079396247864,
0.17370131611824036,
0.59571373462677,
-0.3990806043148041,
0.6354538798332214,
-0.484343022108078,
-0.6992680430412292,
-0.4810718297958374,
-0.6403619647026062,
-0.12655703723430634,
-1.4187461137771606,
0.054228007793426514,
-0.7197717428207397,
-0.4021914303302765,
0.1766212433576584,
0.2509877383708954,
-0.007370016071945429,
0.1678006798028946,
-0.7962042689323425,
0.07098425179719925,
0.5857774615287781,
0.31095826625823975,
-0.2914011478424072,
-0.6544974446296692,
-0.6481094360351562,
-0.5215944647789001,
-0.1833060085773468,
-0.01875442825257778,
-0.3710225224494934,
-0.1099248081445694,
-0.14487074315547943,
0.07530061900615692,
-0.11989302933216095,
0.494792103767395,
-0.8737949728965759,
-0.8307541608810425,
-0.006249799858778715,
-0.13553428649902344,
-0.775546133518219,
0.35227933526039124,
0.2808683514595032,
0.7181845307350159,
0.19996468722820282,
0.2948733866214752,
-0.5613676309585571,
0.3679923713207245,
-0.9137314558029175,
0.1971779316663742,
0.4321013391017914,
0.12767860293388367,
0.2045671045780182,
-0.39903759956359863,
0.35732099413871765,
-0.16542558372020721,
-0.753663182258606,
0.33983466029167175,
-0.6512122750282288,
-0.4458232522010803,
-0.3048606216907501,
0.37153908610343933,
0.7403715252876282,
0.3847575783729553,
-0.6826549172401428,
0.500971257686615,
-0.17364832758903503,
-0.3455958962440491,
0.6325287818908691,
-0.13659606873989105,
-0.5951074957847595,
-0.12115392833948135,
0.8182888627052307,
-0.44768786430358887,
0.13617831468582153,
0.9045432209968567,
-0.31541818380355835,
0.8583055734634399,
-0.2785404324531555,
-0.44164925813674927,
0.013392933644354343,
-0.073708176612854,
-0.686364471912384,
0.547868013381958,
0.14216382801532745,
-0.6873714327812195,
0.24066106975078583,
-0.6894974708557129,
-0.363971084356308,
0.36925849318504333,
-0.31146979331970215,
-0.40153422951698303,
-0.28287559747695923,
0.2855684757232666,
-0.7897047400474548,
-0.13404667377471924,
0.12805844843387604,
-0.0022367131896317005,
-0.45360907912254333,
0.4630875289440155,
-0.050251029431819916,
-0.19522370398044586,
-0.06163458153605461,
-0.08621847629547119,
-0.6675325632095337,
-0.17389260232448578,
-0.10480561852455139,
1.0045349597930908,
-0.37898966670036316,
-0.8918343186378479,
-0.3503219783306122,
0.2957558035850525,
0.300025999546051,
0.17351597547531128,
-0.540395975112915,
0.18150733411312103,
0.5894395112991333,
0.06992994248867035,
0.47789266705513,
0.013566384091973305,
-0.23814311623573303,
0.7909873127937317,
0.08211769908666611,
-0.8326831459999084,
0.5783248543739319,
-0.03350748494267464,
-0.03807000443339348,
-0.3370910584926605,
-0.18859699368476868,
1.1052066087722778,
-0.026956776157021523,
0.017202438786625862,
0.48290520906448364,
-0.3064892292022705,
0.2520565092563629,
0.19666405022144318,
-0.4992859661579132,
0.2322753369808197,
-0.17930571734905243,
0.47462180256843567,
0.8151209354400635,
-0.2541472315788269,
0.2789105474948883,
0.7092723846435547,
0.5030215382575989,
-0.006708908826112747,
0.12586691975593567,
0.2728455662727356,
0.08461063355207443,
0.8838669657707214,
-0.04770621657371521,
0.25559020042419434,
0.49608150124549866,
-0.0015115198912099004,
-0.0014087546151131392,
-0.2860780358314514,
-0.5635199546813965,
0.09939292073249817,
0.039455026388168335,
0.206672802567482,
-0.3531864881515503,
-0.21857509016990662,
-0.0694027841091156,
-0.23659847676753998,
0.44177016615867615,
0.02443491481244564,
-0.005233720876276493,
0.8074273467063904,
0.5600255131721497,
0.13710899651050568,
-0.03737438842654228,
0.3648616373538971,
0.1800188422203064,
0.42949140071868896,
0.1235014945268631,
0.854941189289093,
1.1098055839538574,
0.41836103796958923,
0.40297621488571167,
-0.8509954810142517,
0.25545746088027954,
0.47869622707366943,
-1.1252613067626953,
0.2580436170101166,
-0.7125051021575928,
-0.21841101348400116,
-0.5473148822784424,
-0.43624135851860046,
-0.1647622287273407,
-0.717444896697998,
-0.3537214398384094,
0.36046600341796875,
0.07637548446655273,
0.25510576367378235,
0.35738736391067505,
-0.19451843202114105,
0.18598148226737976,
0.41444119811058044,
-0.1781393587589264,
0.12286151200532913,
1.0083508491516113,
1.0535613298416138,
-0.29747000336647034,
0.09146811813116074,
0.27758219838142395,
-0.6188309192657471,
0.4397750198841095,
0.5182987451553345,
-0.264782190322876,
0.7877503633499146,
-0.6464754343032837,
-0.4311334788799286,
0.3051350712776184,
0.10194701701402664,
0.048695508390665054,
0.06423656642436981,
0.443418949842453,
-0.06681471318006516,
-0.6371248364448547,
-0.1583510935306549,
1.5081161260604858,
0.8747941255569458,
-0.34065911173820496,
-0.05901803448796272,
-0.06470649689435959,
-0.5435335636138916,
-0.13685184717178345,
-0.6682369112968445,
0.2557383179664612,
0.05640726909041405,
0.056926582008600235,
-0.4403113126754761,
-0.7862164974212646,
-0.6429010033607483,
-1.0577327013015747,
0.33022773265838623,
-1.0014077425003052,
0.7351991534233093,
0.3392811417579651,
0.5799134969711304,
-0.1198345422744751,
-0.48034006357192993,
-0.6569725275039673,
0.0395960733294487,
1.2084159851074219,
0.1234452947974205,
0.4255935847759247,
0.48130688071250916,
-0.443128377199173,
-0.6880924105644226,
0.549496591091156,
0.6086118221282959,
-0.9559847712516785,
0.36967599391937256,
-0.7961944937705994,
-0.030346069484949112,
-0.06280245631933212,
0.043536532670259476,
0.1904439777135849,
-0.13011246919631958,
0.3224662244319916,
-0.14118443429470062,
-0.15933597087860107,
-0.21387551724910736,
-0.7977064251899719,
0.19390979409217834,
-0.5232571959495544,
0.1657082885503769,
0.43999597430229187,
0.3777001202106476,
0.6936267614364624,
-0.34595900774002075,
4.170769214630127,
0.9119744896888733,
0.4710894525051117,
-0.3111269772052765,
0.6200942397117615,
0.37043797969818115,
-0.22324202954769135,
-0.4493982791900635,
0.28807204961776733,
-0.4664040803909302,
0.009711976163089275,
0.26233088970184326,
0.24792462587356567,
-0.40400445461273193,
-0.19393514096736908,
0.8343592882156372,
-0.0032024066895246506,
0.031147610396146774,
-0.14217065274715424,
-0.9722124338150024,
-0.6095736622810364,
0.560560941696167,
0.4660518765449524,
0.12328939139842987,
0.34619632363319397,
-0.14341843128204346,
0.352133572101593,
-0.5409340262413025,
-0.9286425709724426,
-0.7437551617622375,
-0.7613643407821655,
-0.7926872968673706,
-0.02116945944726467,
-0.601546049118042,
-0.7076566219329834,
0.2122185230255127,
0.5018701553344727,
-0.05801926553249359,
0.4421040117740631,
0.20226363837718964,
-0.4262178838253021,
0.06426091492176056,
-0.25324875116348267,
-0.10733333975076675,
-0.5084444284439087,
0.869722843170166,
-0.07780294865369797,
0.744596004486084,
0.118994802236557,
-0.4165568947792053,
0.22300267219543457,
-0.22298137843608856,
0.6052379012107849,
-0.442363440990448,
-0.7347094416618347,
-0.01580701395869255,
-0.9716655015945435,
0.0937243178486824,
0.6138010025024414,
-0.030635548755526543,
0.4891832172870636,
0.3107191026210785,
-0.32521939277648926,
0.2846120297908783,
0.08823073655366898,
0.4222106635570526,
0.4141501486301422,
0.23153924942016602,
0.3800864517688751,
-0.28933802247047424,
-0.08742145448923111,
-0.39090704917907715,
-0.4562399387359619,
0.2051192969083786,
0.1800716370344162,
0.35647010803222656,
0.3489125967025757,
0.5317500829696655,
0.18655692040920258,
0.12187346816062927,
-0.26394933462142944,
-0.3900333344936371,
-0.5954397916793823,
-0.0831507220864296,
-0.24028369784355164,
0.6646739840507507,
-0.3867250084877014,
-0.3080160617828369,
0.05857056751847267,
0.7299854755401611,
0.30905571579933167,
1.6061009168624878,
0.2908153831958771,
-0.42563027143478394,
-0.665807843208313
] |
The confined-deconfined Interface Tension and the Spectrum of the Transfer Matrix
|
The reduced tension $\sigma_{cd}$ of the interface between the confined and the deconfined phase of $SU(3)$ pure gauge theory is related to the finite size effects of the first transfer matrix eigenvalues. A lattice simulation of the transfer matrix spectrum at the critical temperature $T_c = 1/L_t$ yields $\sigma_{cd} = 0.139(4) T_c^2$ for $L_t = 2$. We found numerical evidence that the deconfined-deconfined domain walls are completely wet by the confined phase, and that the confined-deconfined interfaces are rough.
|
B. Grossmann, M.L. Laursen, T. Trappenberg and U.-J. Wiese
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208020
|
hep-lat/9208021
|
[
0.0848083347082138,
-0.7507108449935913,
-0.07195546478033066,
0.3944172263145447,
-0.19304342567920685,
-0.6101162433624268,
-0.6116037964820862,
-0.3720129728317261,
-0.7824754118919373,
1.2428656816482544,
0.10024778544902802,
-0.030907319858670235,
0.4609755873680115,
-0.8931570053100586,
-0.15184132754802704,
0.37562546133995056,
-0.07597209513187408,
-0.4590836465358734,
-1.2663805484771729,
0.4136349558830261,
-0.03430771455168724,
0.1107473224401474,
-1.3226003646850586,
-0.3487396240234375,
-0.2174854427576065,
1.239000678062439,
-0.24872702360153198,
0.29555007815361023,
1.1466422080993652,
0.30997663736343384,
0.4588618576526642,
-0.7475955486297607,
-0.6424692273139954,
-0.9587070941925049,
-0.5725895762443542,
-0.09578995406627655,
-0.001246937899850309,
-0.09241899102926254,
0.5087776780128479,
0.018037624657154083,
0.5091366171836853,
-0.767306387424469,
0.17101548612117767,
0.04360392689704895,
-0.5522246360778809,
0.3361360728740692,
-0.27459052205085754,
-0.1767580658197403,
0.38022613525390625,
-1.077918529510498,
0.14960305392742157,
0.29203397035598755,
0.5924413800239563,
-0.1850174367427826,
-0.17537519335746765,
-0.8521528244018555,
0.11916179955005646,
0.40335813164711,
-0.4338740110397339,
-0.4760715067386627,
0.4008735120296478,
0.44939523935317993,
0.6980018615722656,
-0.8515585064888,
0.12054944783449173,
0.8271468281745911,
-0.3560284674167633,
0.7343264222145081,
-0.11039138585329056,
-0.7317976355552673,
-0.37311285734176636,
-0.21322651207447052,
-1.0534138679504395,
0.22645050287246704,
-0.81182861328125,
-0.0876639112830162,
0.2751045823097229,
-1.004740834236145,
-0.7370828986167908,
-0.34199994802474976,
-0.2757934033870697,
-0.1319195181131363,
0.009080862626433372,
0.2295820266008377,
-0.3130871653556824,
-0.1331159472465515,
-0.06861574202775955,
-0.3144853711128235,
0.5063526034355164,
0.6442855000495911,
0.42520713806152344,
0.5559818148612976,
-0.5582050085067749,
0.04558875411748886,
0.5643647313117981,
0.667668342590332,
0.013911856338381767,
0.276926189661026,
0.12629319727420807,
0.1106538325548172,
0.09124859422445297,
0.6309884786605835,
-0.5800068378448486,
0.3798862397670746,
-0.6638964414596558,
0.5792256593704224,
-0.06858117133378983,
-0.2053031027317047,
0.06863012909889221,
-0.7443231344223022,
0.11331500113010406,
-0.0882088914513588,
0.3662343919277191,
0.7656044960021973,
0.5575379729270935,
0.9133673310279846,
-0.4986397325992584,
0.15334846079349518,
-0.7468149662017822,
-0.8212240934371948,
0.3697235882282257,
0.12323814630508423,
0.05675438046455383,
0.37482067942619324,
-0.10109254717826843,
-0.32517147064208984,
0.6110765933990479,
0.6660769581794739,
-0.7276440262794495,
0.6840956211090088,
0.2289738953113556,
-0.11739002913236618,
-0.2619308829307556,
0.5711488723754883,
-0.5594854950904846,
-0.32200369238853455,
-0.1579025685787201,
0.36927589774131775,
0.23691289126873016,
-0.08769301325082779,
0.5803058743476868,
-0.8298553824424744,
0.003461320186033845,
1.1615782976150513,
0.6213864684104919,
0.23446473479270935,
-0.34475356340408325,
-0.10395342856645584,
-0.13865484297275543,
0.38785454630851746,
-0.1268685907125473,
-0.24814876914024353,
-0.2141110748052597,
0.1958082765340805,
-0.05268298462033272,
1.0406652688980103,
-0.7763879895210266,
0.22907525300979614,
-0.5640298128128052,
-0.487854540348053,
0.3947037160396576,
-0.14346474409103394,
-1.1383717060089111,
0.19824576377868652,
-0.27299293875694275,
-0.22703389823436737,
-0.4077337980270386,
-0.31582650542259216,
0.4622028172016144,
-0.7822988629341125,
-0.07057126611471176,
0.3343545198440552,
-0.4297998547554016,
0.6588938236236572,
0.48501676321029663,
0.18092289566993713,
0.5056264996528625,
-0.36949583888053894,
-0.09877011179924011,
-0.02642730064690113,
-0.8666336536407471,
-0.41622665524482727,
0.25237908959388733,
0.011522769927978516,
-0.28257840871810913,
-0.35820743441581726,
-0.15088322758674622,
-0.580525815486908,
0.4944446086883545,
0.12879957258701324,
0.106728695333004,
0.3878326416015625,
-0.4292834401130676,
0.7884706258773804,
-0.44999322295188904,
-0.14807352423667908,
-1.1492542028427124,
0.5929692983627319,
-0.7451220750808716,
-0.5777142643928528,
0.004234870430082083,
0.13972482085227966,
-0.7564465999603271,
0.5456060171127319,
-1.3279355764389038,
0.10963977128267288,
0.6621415019035339,
-0.16250398755073547,
-0.6250041127204895,
-0.5093642473220825,
0.41710808873176575,
-0.2585804760456085,
0.18766304850578308,
-0.4678778648376465,
0.607633113861084,
0.1891200989484787,
0.25422385334968567,
0.38095271587371826,
0.4848593473434448,
0.18516913056373596,
0.45373958349227905,
-0.10747432708740234,
0.17886261641979218,
0.7026078701019287,
-0.5780531764030457,
-0.2829226553440094,
-0.1614268273115158,
0.2955962121486664,
0.40693771839141846,
-0.1645742505788803,
0.05412684753537178,
0.3980220556259155,
-0.11267518252134323,
0.2951853275299072,
0.8140621185302734,
0.726554274559021,
0.58560711145401,
0.5138577818870544,
0.047778502106666565,
0.11949527263641357,
0.3677491545677185,
0.11220626533031464,
0.16721229255199432,
-0.0043447124771773815,
-0.13817979395389557,
-0.09512392431497574,
-0.577021598815918,
0.3100013732910156,
-0.6515008211135864,
0.5092756748199463,
-0.44228246808052063,
0.50202476978302,
0.3344497084617615,
0.20049965381622314,
-1.2569694519042969,
-0.45013007521629333,
-0.3102736473083496,
0.5279417634010315,
-0.10878782719373703,
-0.17385053634643555,
0.22871838510036469,
0.2280491441488266,
-0.2759537100791931,
-0.551818311214447,
-0.5089748501777649,
1.2715705633163452,
-0.5336347818374634,
-0.040026433765888214,
0.7887019515037537,
-0.26932740211486816,
-0.9101043939590454,
0.4129084348678589,
-0.7000903487205505,
-0.21125651895999908,
-0.6505022644996643,
0.1051165834069252,
0.9419708251953125,
-0.710243821144104,
0.6653483510017395,
0.4139920473098755,
-0.21564480662345886,
0.6057643294334412,
-0.28649336099624634,
0.3769379258155823,
0.21441179513931274,
0.39453473687171936,
-0.5680632591247559,
0.0332036055624485,
-1.0050458908081055,
0.012716089375317097,
-0.4808914065361023,
0.36038175225257874,
0.6249713897705078,
-0.49016475677490234,
0.3008662462234497,
-0.1783066987991333,
-0.6978362798690796,
0.09511934965848923,
0.33753496408462524,
-0.8367648124694824,
0.22941479086875916,
0.6406607627868652,
-0.12074482440948486,
-0.511515736579895,
-0.9940288662910461,
0.5531644821166992,
0.10559418797492981,
-0.5232136845588684,
0.5853124856948853,
0.005708156619220972,
-0.07095248252153397,
0.33433330059051514,
-0.0028313894290477037,
-0.22258466482162476,
0.07924492657184601,
1.2338407039642334,
0.6987961530685425,
0.04978913813829422,
-0.08056066185235977,
-0.2604592442512512,
-0.10921702533960342,
0.13228565454483032,
0.16535510122776031,
-0.46499502658843994,
0.12215214967727661,
0.4022875428199768,
-0.013291723094880581,
-0.671590268611908,
0.44274505972862244,
-0.6390504837036133,
-0.8767682909965515,
0.38839516043663025,
-0.4008829593658447,
0.6235321760177612,
-0.09579706192016602,
0.05540880188345909,
-0.871010959148407,
-0.015514182858169079,
0.09806830435991287,
0.19191856682300568,
0.4275282323360443,
-0.058180924504995346,
0.3385891914367676,
0.23111703991889954,
0.38787490129470825,
-0.3058418929576874,
0.47200292348861694,
-0.4345703125,
-0.501111626625061,
0.39615148305892944,
-0.8132969737052917,
0.14521151781082153,
0.10486098378896713,
0.1620337814092636,
-0.2237226516008377,
0.07781879603862762,
-0.5461406111717224,
-0.6588395833969116,
-0.12613050639629364,
-0.7848815321922302,
0.19698074460029602,
0.578738808631897,
-0.6404566764831543,
-0.14053645730018616,
-0.41832080483436584,
-0.16606663167476654,
0.5054170489311218,
-0.07189857959747314,
0.7698923349380493,
-0.7901054620742798,
0.320380300283432,
0.01187886856496334,
-0.3054629862308502,
0.06127333268523216,
-0.4187853932380676,
0.3422858417034149,
0.25688326358795166,
-0.04190155491232872,
0.9396466612815857,
-0.4668806493282318,
-0.965839684009552,
-0.27061763405799866,
1.094361424446106,
0.7942622303962708,
0.6433062553405762,
0.2197805941104889,
-0.1616280972957611,
0.04963168501853943,
-0.5106232166290283,
-0.42461374402046204,
-0.3223247528076172,
-0.03486526757478714,
0.12237389385700226,
0.020900726318359375,
0.7862242460250854,
0.6997140049934387,
0.5812177062034607,
0.38292554020881653,
0.20570771396160126,
-0.020355969667434692,
0.7188712954521179,
0.06399823725223541,
0.6072410345077515,
0.5740050077438354,
-0.07370772212743759,
0.1321641355752945,
-0.6817455291748047,
0.14424677193164825,
0.26499855518341064,
0.12061607092618942,
-0.24460646510124207,
-0.35198768973350525,
-0.22553512454032898,
-0.7409387826919556,
0.6459486484527588,
0.3574342131614685,
-0.6590604782104492,
0.13876588642597198,
-0.15453524887561798,
0.35463085770606995,
0.026408305391669273,
0.2063726931810379,
0.9528818726539612,
0.19470998644828796,
0.4833720922470093,
-0.5840185284614563,
0.3207874000072479,
-0.11546585708856583,
0.005034423898905516,
0.5759471654891968,
-1.1668083667755127,
-0.48944374918937683,
-0.9976180195808411,
-0.10078155249357224,
-0.3535274863243103,
-0.3098144829273224,
1.011574149131775,
-0.1414458006620407,
-0.21876975893974304,
-0.37916621565818787,
-0.5322069525718689,
0.6808059811592102,
-0.4384046792984009,
-0.63590407371521,
0.5748803615570068,
-0.133436918258667,
0.13852210342884064,
0.8528900146484375,
0.123529814183712,
-0.36645978689193726,
-0.08842825144529343,
-0.49548691511154175,
0.4959087073802948,
-0.591457188129425,
-0.48866406083106995,
0.29026955366134644,
-0.6341496109962463,
-0.4887756407260895,
0.6866649389266968,
0.12673594057559967,
-0.2111809104681015,
0.11558114737272263,
-0.2246471494436264,
-0.19938255846500397,
0.2962328791618347,
0.06238968297839165,
0.191914901137352,
1.2200766801834106,
0.6141197085380554,
-0.10388656705617905,
0.4998680651187897,
0.8015654683113098,
-0.3330014944076538,
0.3114267885684967,
0.11468043923377991,
0.5763124823570251,
-0.48279204964637756,
-0.8996154069900513,
-0.06563560664653778,
-0.7779901027679443,
-0.036876510828733444,
-0.11662258207798004,
-0.21543638408184052,
0.656980574131012,
0.22354750335216522,
-0.7180590629577637,
-0.23381999135017395,
-0.20106855034828186,
-0.679764986038208,
0.479875385761261,
0.01598939299583435,
-0.07117033004760742,
0.8880271315574646,
-0.42086952924728394,
-0.06338000297546387,
-0.4287899136543274,
0.22632545232772827,
-0.8711634874343872,
0.18583287298679352,
0.7733467817306519,
0.12983882427215576,
0.2021821290254593,
-1.1827239990234375,
0.6741678714752197,
-0.48899585008621216,
0.36368897557258606,
-0.21390755474567413,
0.02669617347419262,
-0.14734064042568207,
-0.4099154472351074,
0.4607398211956024,
-0.23039761185646057,
-0.7778021097183228,
0.053902070969343185,
0.03579217940568924,
-0.29876768589019775,
-0.32063472270965576,
-0.35274285078048706,
-0.28830891847610474,
0.71829754114151,
0.07762257009744644,
-0.4976389408111572,
0.44073519110679626,
0.6592421531677246,
-0.08380229771137238,
0.5760418772697449,
-0.05234772339463234,
-0.9433517456054688,
0.23353679478168488,
-0.2818323075771332,
0.30718716979026794,
-0.6791541576385498,
-0.5588448643684387,
-0.10570251941680908,
-0.35172101855278015,
0.4357370138168335,
0.5658223628997803,
-0.0033392931800335646,
-0.27979379892349243,
-0.3057083189487457,
-0.15991488099098206,
0.4291027784347534,
-0.05193512141704559,
-0.2183111011981964,
-0.3998957574367523,
-0.2669777274131775,
-0.6398003101348877,
0.3796580731868744,
-0.08768777549266815,
0.4754456877708435,
0.5895315408706665,
-0.2664477229118347,
-0.05851871892809868,
0.7313098907470703,
0.21176806092262268,
-0.010869050398468971,
-0.08985844999551773,
0.7551116347312927,
-0.3666275143623352,
0.6826496720314026,
-0.795121967792511,
0.274508535861969,
-0.7053043246269226,
0.7716472148895264,
-0.2914891242980957,
-0.4358033537864685,
-0.6025781631469727,
0.10587229579687119,
1.0870155096054077,
-0.6620849370956421,
0.47797006368637085,
1.119509220123291,
-0.43285223841667175,
0.4385279417037964,
0.7259566783905029,
-0.7999805212020874,
-0.3343096673488617,
-0.6046000123023987,
-0.5957318544387817,
0.6592931151390076,
0.4263690412044525,
-0.30962321162223816,
-0.4429854452610016,
-0.8075792789459229,
0.08487062156200409,
-0.1798475831747055,
0.03742419183254242,
0.15893490612506866,
-0.4990440905094147,
0.22710829973220825,
0.10718616098165512,
-0.23990513384342194,
-0.7786388397216797,
0.1764070838689804,
0.08215901255607605,
-0.06033698841929436,
-0.09216023236513138,
0.008591622114181519,
-0.3628632128238678,
-0.9248517155647278,
-0.0788082703948021,
0.16223092377185822,
0.3903762102127075,
-0.04270269721746445,
0.6630095839500427,
-0.051197998225688934,
-0.572512149810791,
-0.7529836893081665,
0.0636657103896141,
-0.017328349873423576,
0.3374459743499756,
0.2669726312160492,
0.2187139242887497,
0.5066681504249573,
-0.005194368772208691,
0.41281354427337646,
0.041155606508255005,
0.19279834628105164,
0.2514985203742981,
-0.28513234853744507,
-0.3953729271888733,
0.5216264128684998,
0.1153937354683876,
-0.8445085287094116,
-0.5092863440513611,
-0.9803279042243958,
-0.34482645988464355,
-0.48664698004722595,
0.04677584022283554,
-0.7050598859786987,
0.17293216288089752,
-0.26572930812835693,
0.4979202151298523,
0.5710427761077881,
0.21771439909934998,
-0.4587610065937042,
-0.190736785531044,
-0.6109232902526855,
-0.5846011638641357,
-0.4481402039527893,
1.4298789501190186,
-0.5016670823097229,
-0.4832838475704193,
0.023419886827468872,
-0.23970144987106323,
-0.40355631709098816,
-0.12039676308631897,
0.34546834230422974,
-0.28251898288726807,
0.6041812896728516,
0.16195181012153625,
0.09672816097736359,
0.6489381194114685,
0.7388661503791809,
0.3941657543182373,
0.05489075556397438,
-0.30611899495124817,
-0.48276033997535706,
-0.22172261774539948,
-0.38692528009414673,
0.08710547536611557,
0.879237949848175,
-0.11176247149705887,
-0.11680375784635544,
-0.3861185312271118,
-0.7930130362510681,
-0.022867005318403244,
-0.8782780766487122,
-0.14127838611602783,
-1.0718759298324585,
-0.31988000869750977,
-0.723439633846283,
-0.7620325684547424,
-0.5277009606361389,
0.47222045063972473,
-0.2910684049129486,
0.047244593501091,
-0.8585380911827087,
0.07184445112943649,
0.5989328622817993,
0.26425814628601074,
-0.017285170033574104,
-1.1541208028793335,
-0.48851606249809265,
-0.09324926882982254,
0.060128968209028244,
-0.3500650227069855,
0.08474010974168777,
0.38321369886398315,
-0.26209357380867004,
0.0050710453651845455,
-0.12240530550479889,
0.9352201223373413,
-1.192799687385559,
-0.7062935829162598,
-0.23284418880939484,
-0.12281516939401627,
-0.7093186378479004,
0.4680083096027374,
0.3840293288230896,
0.5034862756729126,
0.4537386894226074,
-0.014994203113019466,
-0.26983189582824707,
0.3735416829586029,
-0.7562539577484131,
0.17056907713413239,
-0.13046644628047943,
0.08265634626150131,
-0.11787489056587219,
-1.08587646484375,
-0.0711652860045433,
0.7200706601142883,
-0.9914759993553162,
0.3505360782146454,
-0.64150470495224,
0.4764915406703949,
-0.2434021532535553,
0.08900569379329681,
0.04582930728793144,
0.20614930987358093,
0.22364039719104767,
1.2058950662612915,
-0.09861529618501663,
0.10855109989643097,
0.14038407802581787,
0.08200898766517639,
-0.34127384424209595,
-0.05809944123029709,
-0.029454324394464493,
-0.21601636707782745,
0.18942774832248688,
0.6818387508392334,
-0.10009099543094635,
0.28562119603157043,
0.24222935736179352,
-0.038535211235284805,
0.19155777990818024,
-0.46212485432624817,
-0.613844633102417,
0.38825738430023193,
0.4632681608200073,
-0.7304015159606934,
-0.25206458568573,
-0.42205455899238586,
-0.924200177192688,
0.4943065345287323,
0.0353165864944458,
-0.6725724935531616,
0.15600624680519104,
-0.16589775681495667,
0.2933386266231537,
0.18053480982780457,
0.29590120911598206,
0.17547450959682465,
0.1659119874238968,
0.25900644063949585,
0.17484328150749207,
0.3466331660747528,
-0.4819272458553314,
-0.015299685299396515,
-0.7690122723579407,
-0.04975114017724991,
-0.2840225398540497,
0.42596977949142456,
-0.557158887386322,
-0.73085618019104,
-0.31050217151641846,
0.3742246925830841,
0.41985735297203064,
0.16374970972537994,
-0.34286022186279297,
-0.33876141905784607,
0.11115023493766785,
0.14411693811416626,
-0.5143483281135559,
-0.2881963849067688,
-0.4468483626842499,
0.6569902300834656,
0.020737431943416595,
-0.537346363067627,
0.7717745304107666,
-0.23692204058170319,
0.0430794432759285,
-0.340699702501297,
-0.12247069180011749,
1.2283694744110107,
0.38799846172332764,
-0.49985480308532715,
0.25777602195739746,
-0.246892511844635,
-0.10253208130598068,
0.21184663474559784,
-0.7928647994995117,
0.0070633841678500175,
0.532929539680481,
0.18912354111671448,
0.9220119714736938,
0.7626762390136719,
0.6171741485595703,
0.22744783759117126,
0.48175787925720215,
0.45936131477355957,
-0.4625870883464813,
-0.03151664882898331,
0.46084871888160706,
0.12397601455450058,
-0.173069030046463,
0.21754993498325348,
0.08289740234613419,
0.09643273800611496,
0.21310719847679138,
-0.2868116796016693,
-0.2855704426765442,
-0.22958219051361084,
0.28406569361686707,
0.23968206346035004,
-0.8493654727935791,
-0.41359832882881165,
-0.30128929018974304,
0.47215306758880615,
0.6454315185546875,
-0.08599824458360672,
-0.10062223672866821,
0.4437449276447296,
0.28379544615745544,
-0.1895940750837326,
-0.2254197895526886,
0.6920179724693298,
0.3408871591091156,
0.6405995488166809,
0.7596039772033691,
0.657609760761261,
0.29941505193710327,
0.37524792551994324,
0.4664451777935028,
-0.6638266444206238,
0.37887001037597656,
0.5133465528488159,
-0.8458274602890015,
0.41251498460769653,
-0.3424345552921295,
-0.05621109530329704,
-0.16510958969593048,
-0.7367163300514221,
0.23062969744205475,
-0.7596789598464966,
0.36452510952949524,
0.8331615924835205,
-0.1422954797744751,
0.4261171221733093,
0.6557538509368896,
-0.08520261943340302,
-0.07040927559137344,
0.469268262386322,
-0.22084221243858337,
-0.3928201198577881,
1.1036871671676636,
1.4656747579574585,
-0.18042103946208954,
0.07743138074874878,
0.1283697932958603,
-0.8083519339561462,
0.6367939114570618,
0.3158624470233917,
-0.04246000573039055,
1.191552758216858,
-0.8622331619262695,
-0.22398225963115692,
0.3239717185497284,
0.202636256814003,
-0.22856484353542328,
-0.23220771551132202,
0.27256834506988525,
0.19560717046260834,
0.06073058024048805,
-0.7570450305938721,
1.3953447341918945,
0.7692584991455078,
-0.6439898610115051,
-0.5461403727531433,
0.2976668179035187,
0.048300497233867645,
-0.5862736701965332,
-0.38748684525489807,
0.5745385885238647,
-0.18529322743415833,
0.3864033818244934,
-0.1590173840522766,
-0.5028887987136841,
-0.5408625602722168,
-1.0030345916748047,
0.058362897485494614,
-0.6670641899108887,
0.5375679731369019,
-0.042901378124952316,
0.3549767732620239,
-0.0037100089248269796,
-0.6148425340652466,
-0.07796730101108551,
-0.11450547724962234,
0.6880702376365662,
-0.3591194748878479,
-0.3420034945011139,
0.8219348788261414,
0.7853044867515564,
-0.7956209182739258,
0.5047720670700073,
0.5513556599617004,
-0.40145400166511536,
0.7779597640037537,
-0.4813377857208252,
0.5129256248474121,
0.563530683517456,
-0.03619125485420227,
0.07901912182569504,
0.302161306142807,
0.541411280632019,
-0.016165392473340034,
-0.22398431599140167,
-0.030854977667331696,
-0.6486315131187439,
-0.2836662530899048,
-0.32568106055259705,
0.06870152801275253,
0.26683783531188965,
0.39899492263793945,
0.49519726634025574,
-0.4258575141429901,
4.372710227966309,
0.382995069026947,
0.515613853931427,
0.4117286503314972,
0.4317184090614319,
0.5856877565383911,
0.07488995790481567,
-0.6801941990852356,
0.2913169860839844,
-0.23045434057712555,
-0.46030890941619873,
0.179482564330101,
0.21695879101753235,
-0.5156331062316895,
-0.1734960824251175,
0.6595417261123657,
-0.2597726881504059,
-0.6073379516601562,
0.2850837707519531,
-0.937723696231842,
-0.43593645095825195,
0.011511807329952717,
0.46497905254364014,
-0.11108686774969101,
0.37618905305862427,
0.08285284787416458,
0.21911393105983734,
-0.4937669038772583,
-0.6130629181861877,
-0.42877721786499023,
-1.0077332258224487,
-0.84507817029953,
0.3472592830657959,
0.009074901230633259,
-0.598925769329071,
0.36828118562698364,
0.19822722673416138,
-0.32196182012557983,
0.31723520159721375,
0.07958101481199265,
-0.012415924109518528,
-0.3626563847064972,
0.1142091155052185,
-0.4320235550403595,
-0.5285943746566772,
0.9673863649368286,
0.1822403222322464,
0.7323782444000244,
0.5025545954704285,
-0.381845623254776,
0.20773263275623322,
0.07487408816814423,
0.5322803854942322,
-0.17915555834770203,
-1.2040956020355225,
0.3154292702674866,
-0.43618378043174744,
-0.47545939683914185,
0.4931374192237854,
-0.19704878330230713,
0.4814082086086273,
-0.5500921010971069,
-0.3272007405757904,
0.16832491755485535,
-0.34554848074913025,
0.6803719997406006,
0.2458612471818924,
0.5816041231155396,
-0.20831981301307678,
0.022828029468655586,
-0.05886480584740639,
-0.1187451109290123,
-0.42479026317596436,
0.5287439227104187,
0.12236469238996506,
0.2072264850139618,
0.4024466276168823,
0.2711339592933655,
0.1252664476633072,
0.05514189228415489,
0.3572832942008972,
-0.09985291957855225,
-0.4066942036151886,
0.41179415583610535,
0.1042460948228836,
0.604683518409729,
-0.10929542034864426,
0.17699772119522095,
-0.4767003655433655,
0.38128921389579773,
0.09475912898778915,
0.7428568601608276,
0.4033912718296051,
0.34091678261756897,
-0.9168115854263306
] |
Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors
|
Non-compact lattice QED with two flavors of light dynamical quarks is simulated on $16^4$ lattices, and the chiral condensate, monopole density and susceptibility and the meson masses are measured. Data from relatively high statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02 and 0.03 (lattice units) are presented. Three independent methods of data analysis indicate that the critical point occurs at $\beta =0.225(5)$ and that the monopole condensation and chiral symmetry breaking transitions are coincident. The monopole condensation data satisfies finite size scaling hypotheses with critical indices compatible with four dimensional percolation. The best chiral equation of state fit produces critical exponents ($\delta=2.31$, $\beta_{mag}=0.763$) which deviate significantly from mean field expectations. Data for the ratio of the sigma to pion masses produces an estimate of the critical index $\delta$ in good agreement with chiral condensate measurements. In the strong coupling phase the ratio of the meson masses are $M_\sigma^2/M_\rho^2\approx 0.35$, $M_{A_1}^2/M_\rho^2\approx 1.4$ and $M_\pi^2/M_\rho^2\approx 0.0$, while on the weak coupling side of the transition $M_\pi^2/M_\rho^2\approx 1.0$, $M_{A_1}^2/M_\rho^2\approx 1.0$, indicating the restoration of chiral symmetry.\footnote{$\,^{}$}{August 1992}
|
S.J. Hands, A. Kocic, J.B. Kogut, R.L. Renken, D.K. Sinclair and K.C. Wang
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208021
|
hep-lat/9208022
|
[
0.35384437441825867,
-0.06676780432462692,
0.4250496029853821,
0.25073423981666565,
0.02600046992301941,
-0.5771823525428772,
0.11480110883712769,
-0.6013699769973755,
-1.0838072299957275,
1.666993260383606,
0.7299090623855591,
-0.5259059071540833,
0.49624010920524597,
-0.600500762462616,
-0.2220318615436554,
0.5245853066444397,
-0.10722186416387558,
-0.8516157269477844,
-1.050453782081604,
0.5205287933349609,
0.2502465546131134,
-0.02327016554772854,
-1.008429765701294,
-0.30622199177742004,
-0.5235083699226379,
0.8370163440704346,
0.0946812555193901,
0.6559184789657593,
1.0815550088882446,
0.6241358518600464,
0.3028869926929474,
-0.9327796101570129,
0.21946854889392853,
-0.38424044847488403,
-0.7144328355789185,
0.01432878989726305,
-0.3412480056285858,
0.03674592077732086,
0.39428502321243286,
-0.11134848743677139,
1.3626182079315186,
-0.27244219183921814,
0.5310276746749878,
-0.3699539601802826,
-0.33314454555511475,
0.5010330677032471,
0.023874081671237946,
-0.16350401937961578,
-0.06781795620918274,
-1.2351956367492676,
0.3037411868572235,
0.5798520445823669,
0.016701774671673775,
-0.43975070118904114,
-0.317439466714859,
-0.5475572943687439,
0.3935101330280304,
0.15103548765182495,
-0.168397456407547,
-0.5544409155845642,
0.7720027565956116,
0.14078876376152039,
0.6976435780525208,
-0.5462415218353271,
-0.27365896105766296,
0.7845260500907898,
-0.13887551426887512,
0.8485913872718811,
-0.06532242149114609,
-0.0959773063659668,
-0.39504876732826233,
-0.5331599712371826,
-0.502665638923645,
0.0288426224142313,
-0.9872426986694336,
-0.12490515410900116,
0.11957339197397232,
-0.5848014950752258,
-0.7614957690238953,
-0.21288876235485077,
0.07057716697454453,
-0.027231542393565178,
-0.41789305210113525,
0.46451786160469055,
-0.3697631061077118,
-0.4292474687099457,
0.4214661121368408,
-0.13697269558906555,
0.24740734696388245,
0.4770747125148773,
0.3052437901496887,
0.6754873991012573,
-0.32030829787254333,
-0.11214637011289597,
0.748257577419281,
0.5806378722190857,
0.06480039656162262,
0.20746511220932007,
0.033750809729099274,
-0.27504393458366394,
0.10265252739191055,
0.6761523485183716,
-0.3404993414878845,
0.19263805449008942,
-0.9447683095932007,
1.0266307592391968,
0.25186657905578613,
-0.2086600810289383,
0.44409477710723877,
-1.2165954113006592,
0.27479833364486694,
0.3026210069656372,
0.3453023135662079,
0.8676100373268127,
0.26839229464530945,
0.9770132899284363,
-0.49199771881103516,
-0.0248457882553339,
-0.8261216282844543,
-0.23587745428085327,
0.08746105432510376,
0.2528032064437866,
0.46938851475715637,
0.5426896810531616,
-0.2112504094839096,
-0.08642446249723434,
0.40572699904441833,
0.9581187963485718,
-0.12328832596540451,
1.0362316370010376,
-0.1088552251458168,
-0.178376242518425,
-0.4056242108345032,
0.8045971989631653,
-0.7715708017349243,
-0.0037351269274950027,
-0.13955581188201904,
0.24752649664878845,
0.3483697772026062,
-0.1181645467877388,
0.8324264287948608,
-0.7295401096343994,
-0.20593266189098358,
0.8678876757621765,
0.15854822099208832,
0.058773867785930634,
0.09210854023694992,
-0.2412825971841812,
-0.060622960329055786,
0.30824846029281616,
-0.29889869689941406,
0.20635172724723816,
-0.12394176423549652,
0.1965055614709854,
-0.6963526606559753,
0.9750168323516846,
-0.5430482029914856,
0.08018334954977036,
-0.7108648419380188,
-0.5757681727409363,
0.9215846061706543,
-0.333297461271286,
-0.6508646607398987,
0.2648489475250244,
-0.8536030650138855,
0.16439634561538696,
-0.705668032169342,
-0.2332857996225357,
0.0064782872796058655,
-0.7953108549118042,
0.09604449570178986,
0.17422939836978912,
-0.4595286548137665,
0.9574607610702515,
0.3688001334667206,
0.3087332844734192,
0.4031519591808319,
-0.28047144412994385,
-0.49437716603279114,
0.16211703419685364,
-0.7168377041816711,
-0.326628714799881,
0.10047674924135208,
-0.14399535953998566,
-0.6946378946304321,
-0.19082890450954437,
0.22206345200538635,
-0.46087223291397095,
0.07782050222158432,
0.007976488210260868,
-0.3236386775970459,
0.2675819993019104,
-1.089357852935791,
0.5854442119598389,
-0.6455215811729431,
-0.23553691804409027,
-1.0562305450439453,
0.7280886173248291,
-0.5457019805908203,
-0.3240463137626648,
-0.3140709400177002,
0.09999877959489822,
-0.7225785851478577,
0.10076502710580826,
-1.6085809469223022,
0.044228170067071915,
0.15348057448863983,
-0.0005621016607619822,
-0.7253587245941162,
0.09520146250724792,
0.11711045354604721,
-0.5879051089286804,
0.09593486040830612,
-0.14903908967971802,
0.12027648836374283,
0.21108148992061615,
0.4181296229362488,
0.7093762159347534,
0.720962643623352,
0.3321823179721832,
0.8484628200531006,
-0.36243051290512085,
-0.0362635999917984,
0.873772919178009,
-0.1556173712015152,
-0.20983737707138062,
0.4165385067462921,
0.38759976625442505,
0.4524177610874176,
-0.7915950417518616,
-0.4131081700325012,
0.6287297606468201,
-0.2414461374282837,
0.11600225418806076,
0.8815747499465942,
0.3072516918182373,
0.8201048374176025,
0.8163564205169678,
0.1917225569486618,
0.30665716528892517,
0.34499964118003845,
-0.5605267286300659,
0.40278831124305725,
-0.26982539892196655,
0.1482720524072647,
0.4196898639202118,
-0.5076003670692444,
-0.2023312747478485,
-0.3936055898666382,
1.0534204244613647,
0.5341535806655884,
0.5871855616569519,
0.21860583126544952,
-0.29226675629615784,
-1.5825563669204712,
0.13343550264835358,
-0.14215391874313354,
0.4804331660270691,
-0.17608442902565002,
-0.0221409909427166,
-0.4019272029399872,
-0.2088213860988617,
-0.15298014879226685,
-0.5149544477462769,
-0.8473267555236816,
1.0080105066299438,
-0.4702313542366028,
0.648319661617279,
0.6716266870498657,
0.02176327258348465,
-1.1821495294570923,
-0.10958235710859299,
-0.7901801466941833,
-0.4298730790615082,
-0.2572341859340668,
0.7221311330795288,
1.0426920652389526,
-0.5308349132537842,
0.34428054094314575,
0.30390921235084534,
-0.2594764530658722,
0.2941558361053467,
-0.0531986840069294,
0.6567337512969971,
0.8709449172019958,
0.7448974847793579,
-0.8690269589424133,
0.29227155447006226,
-0.4531024098396301,
0.11039277911186218,
-0.02155853807926178,
-0.15175460278987885,
0.9351393580436707,
-0.16411465406417847,
0.5479094386100769,
-0.27800390124320984,
-0.7695234417915344,
0.1822504848241806,
0.13503094017505646,
-0.7798466682434082,
0.44753390550613403,
0.1247505247592926,
-0.33871978521347046,
-0.7232994437217712,
-0.6746847629547119,
0.553796648979187,
0.28214794397354126,
-0.4916236698627472,
0.38125550746917725,
0.005412449594587088,
-0.16067345440387726,
0.2247198224067688,
-0.15205039083957672,
0.1574491411447525,
0.27522286772727966,
0.38194069266319275,
0.5741952657699585,
0.11602423340082169,
-0.06455126404762268,
-0.4034055471420288,
-0.14096897840499878,
-0.2502865791320801,
0.5646619200706482,
-0.26329952478408813,
-0.388424813747406,
0.27839621901512146,
-0.23597624897956848,
-0.5389963388442993,
0.3408716022968292,
-0.8456127643585205,
-0.670073390007019,
0.21141983568668365,
-0.5174874663352966,
0.5367857217788696,
-0.0697707086801529,
0.16978886723518372,
-0.898817241191864,
-0.1857624053955078,
-0.009982272982597351,
0.7082099914550781,
0.613194465637207,
-0.20385827124118805,
0.2609325051307678,
0.2260037064552307,
0.5747383832931519,
-0.6408935189247131,
0.14995203912258148,
-0.1492176651954651,
-0.390156626701355,
0.6066232323646545,
-0.3740997016429901,
0.6316995024681091,
0.13531085848808289,
0.15241530537605286,
-0.28265631198883057,
0.3677498400211334,
-0.5524201393127441,
-0.4794086217880249,
-0.6092160940170288,
-0.929888129234314,
0.32749804854393005,
1.1044938564300537,
-0.8188559412956238,
0.06493986397981644,
-0.4511027932167053,
0.26515036821365356,
0.38534796237945557,
-0.08885721117258072,
0.41535067558288574,
-0.40297600626945496,
0.08238614350557327,
0.2732086181640625,
-0.43956583738327026,
0.3989456295967102,
-0.10130292177200317,
0.3737059235572815,
0.8309887051582336,
0.2357582151889801,
0.6661593317985535,
-0.15691880881786346,
-0.7464131712913513,
-0.18361806869506836,
0.8675757050514221,
0.47853538393974304,
0.755061149597168,
0.4855945110321045,
-0.20444102585315704,
0.0412459559738636,
-0.8922352194786072,
-0.33176979422569275,
-0.34577488899230957,
-0.15866893529891968,
0.11698092520236969,
-0.12314879149198532,
0.23426507413387299,
0.299752414226532,
0.38821759819984436,
0.8560969829559326,
0.13868123292922974,
-0.1651061326265335,
0.33624356985092163,
0.19544169306755066,
0.3023466467857361,
0.6343547701835632,
-0.23433175683021545,
-0.031709037721157074,
-0.874125063419342,
0.2382894605398178,
-0.005184782203286886,
0.45058104395866394,
0.20419208705425262,
-0.44887518882751465,
-0.03314545005559921,
-0.9940107464790344,
0.5063644647598267,
-0.0749560296535492,
-0.37062951922416687,
0.37224024534225464,
-0.19468608498573303,
-0.1451508104801178,
-0.4593454897403717,
0.1390478014945984,
0.34649258852005005,
0.24800215661525726,
0.31673169136047363,
-0.8028316497802734,
0.4197749197483063,
0.08819379657506943,
0.24169054627418518,
0.7931205630302429,
-0.8418017029762268,
-1.2505059242248535,
-0.5924311280250549,
-0.44309088587760925,
-0.0031570184510201216,
-0.2896121144294739,
0.8287431001663208,
0.1407201737165451,
-0.13055123388767242,
-0.34987571835517883,
-0.3598535656929016,
1.1881691217422485,
-0.8333911299705505,
-0.30202099680900574,
0.31782761216163635,
-0.38078606128692627,
-0.10704739391803741,
0.6426389217376709,
0.1231379583477974,
-0.7142130732536316,
-0.11100023239850998,
-0.39202436804771423,
0.20096851885318756,
-0.27522799372673035,
-0.8937761783599854,
-0.2915409207344055,
-0.4290916621685028,
-0.36389389634132385,
0.39962121844291687,
0.17031186819076538,
-0.346510112285614,
-0.45249879360198975,
-0.11178700625896454,
-0.3219359517097473,
-0.23743949830532074,
-0.01597173698246479,
0.6673241853713989,
0.8792438507080078,
0.9312170743942261,
0.6103798151016235,
0.44977253675460815,
0.47989243268966675,
-0.3232388198375702,
0.04322682321071625,
0.45265093445777893,
0.15604054927825928,
-0.48285606503486633,
-0.5403209924697876,
-0.07060792297124863,
-0.9356765747070312,
-0.2633337080478668,
-0.17952285706996918,
-0.4746915400028229,
0.8193832039833069,
0.056409116834402084,
-0.5266699194908142,
-0.2931886315345764,
-0.3163391947746277,
-0.6472378969192505,
0.49958139657974243,
-0.14286920428276062,
0.057455964386463165,
0.5263593792915344,
-0.026817556470632553,
-0.07003374397754669,
0.3543855547904968,
-0.3973156213760376,
-0.26518234610557556,
0.4316064715385437,
0.3689214289188385,
0.27719947695732117,
0.5982553362846375,
-0.8734169006347656,
0.8136225938796997,
-0.7802642583847046,
0.4337450861930847,
-0.1842447817325592,
-0.10842910408973694,
-0.7640973329544067,
-0.4656951427459717,
0.26588863134384155,
-0.3732908070087433,
-0.0602254681289196,
-0.12771040201187134,
-0.06153794378042221,
-0.3181036412715912,
-0.30787864327430725,
-0.31856009364128113,
-0.31519395112991333,
0.6719512343406677,
-0.01667298935353756,
-0.4497951865196228,
-0.007677566725760698,
0.7072892189025879,
0.2735941708087921,
0.5197121500968933,
-0.4343959391117096,
-0.09097427874803543,
0.22672055661678314,
-0.5442862510681152,
0.20767010748386383,
-0.9004968404769897,
-0.22644419968128204,
-0.019204039126634598,
-0.42790231108665466,
0.3017183244228363,
0.7935935258865356,
0.07638491690158844,
-0.17470909655094147,
-0.0003328819293528795,
-0.11729542165994644,
-0.3864787518978119,
-0.6027423739433289,
-0.6104806661605835,
-0.4234347641468048,
-0.14610782265663147,
-0.8152627944946289,
0.5291919708251953,
-0.3718622922897339,
0.35870373249053955,
0.11469964683055878,
-0.1453734040260315,
-0.25727009773254395,
0.3850763738155365,
0.47698190808296204,
0.3620338439941406,
-0.10866856575012207,
0.7427964210510254,
0.022628359496593475,
0.24978354573249817,
-0.6170527338981628,
0.39339479804039,
-0.6009281277656555,
1.2924330234527588,
-0.5707327723503113,
-0.6969701647758484,
-0.003603335004299879,
0.44343307614326477,
0.4715198576450348,
-0.9379104971885681,
0.3567151725292206,
0.4308568835258484,
-0.3653491735458374,
0.602250874042511,
0.6414011120796204,
-0.42879363894462585,
-0.17969639599323273,
-0.18780790269374847,
-0.6035622954368591,
0.47641438245773315,
-0.0997915118932724,
0.22693248093128204,
-0.55193692445755,
-0.7617473006248474,
0.10056386888027191,
0.19429339468479156,
-0.21351087093353271,
0.26015549898147583,
0.28490200638771057,
0.36142879724502563,
0.15846030414104462,
0.4251422882080078,
-0.6244724988937378,
0.35318177938461304,
-0.08798243850469589,
-0.2664240002632141,
-0.04537864774465561,
0.1142946109175682,
-0.4682994782924652,
-0.723829984664917,
-0.057837165892124176,
0.43654757738113403,
0.14885126054286957,
-0.0903957262635231,
0.6494033336639404,
-0.5161487460136414,
-0.4179105758666992,
-0.5012833476066589,
-0.20008134841918945,
0.1525789052248001,
-0.14746376872062683,
0.5803351402282715,
0.19655361771583557,
0.16475869715213776,
0.2328711897134781,
0.3285028040409088,
-0.18533551692962646,
0.05111080780625343,
0.6357038617134094,
-0.013428953476250172,
-0.31063443422317505,
0.5899101495742798,
-0.17948544025421143,
-0.7608547210693359,
-0.18871359527111053,
-0.9982618093490601,
-0.01370758656412363,
-0.1719180941581726,
-0.16884207725524902,
-0.30316171050071716,
0.1167488694190979,
-0.05465291440486908,
0.5500299334526062,
1.022199273109436,
0.23879311978816986,
0.006734064314514399,
0.2716015577316284,
-0.5771377086639404,
-0.5522721409797668,
-0.19227063655853271,
1.3040989637374878,
-0.25251907110214233,
-1.2648760080337524,
0.12767882645130157,
0.40697237849235535,
-0.36706671118736267,
-0.12501581013202667,
0.5065688490867615,
-0.9218728542327881,
0.3426528871059418,
0.08707401901483536,
-0.20164911448955536,
-0.2711517810821533,
0.19250504672527313,
0.29615214467048645,
0.001905642682686448,
-0.28689056634902954,
-0.5174313187599182,
-0.2920604944229126,
-0.3199501931667328,
0.4821156859397888,
1.1848863363265991,
0.3722670376300812,
0.10445631295442581,
-0.13053517043590546,
-0.4211858808994293,
-0.2753354012966156,
-1.0380173921585083,
0.45257848501205444,
-1.059801697731018,
-0.6589534282684326,
-0.4994981288909912,
-0.3598547875881195,
0.5290713310241699,
0.23528489470481873,
-0.33336910605430603,
0.20052389800548553,
-0.7397416234016418,
-0.4524012804031372,
0.1966603547334671,
-0.04582342877984047,
-0.0427401140332222,
-0.9833824634552002,
-0.2860319912433624,
-0.02370648831129074,
-0.0724191665649414,
-0.2757410705089569,
-0.029631495475769043,
0.29062458872795105,
-0.46003344655036926,
0.4732808470726013,
-0.14573179185390472,
0.8403195738792419,
-1.0569112300872803,
-0.8119416832923889,
-0.017974920570850372,
0.14300550520420074,
-0.6377939581871033,
0.3548569977283478,
0.1096000075340271,
0.21081854403018951,
0.2777203619480133,
-0.40567389130592346,
-0.17566412687301636,
-0.03700052946805954,
-0.49738776683807373,
-0.20038236677646637,
0.34133651852607727,
-0.05077125504612923,
-0.366254061460495,
-1.0507162809371948,
0.004018737468868494,
0.3621370494365692,
-1.2814650535583496,
0.26718610525131226,
-0.5501837730407715,
0.4131295680999756,
-0.7969344854354858,
0.10994461178779602,
-0.26432690024375916,
-0.01910710521042347,
0.046376585960388184,
1.0918174982070923,
-0.27026599645614624,
-0.1401136964559555,
0.33360883593559265,
0.20937718451023102,
-0.25817644596099854,
0.3494863212108612,
0.2939516007900238,
-0.44977304339408875,
0.3607325553894043,
0.25291043519973755,
-0.025132646784186363,
0.168979674577713,
-0.4345182776451111,
-0.2849005460739136,
0.04222598671913147,
-0.20988509058952332,
-0.5331873297691345,
0.5793183445930481,
0.8230128884315491,
-0.764569103717804,
-0.46530285477638245,
-0.5883175134658813,
-1.2705718278884888,
0.43803349137306213,
-0.7797740697860718,
-0.22187235951423645,
-0.05107061192393303,
-0.5804946422576904,
0.107742078602314,
0.1203608438372612,
0.22283527255058289,
0.35232290625572205,
-0.024756193161010742,
0.1965426355600357,
0.11228297650814056,
0.09809324890375137,
0.3508972227573395,
0.06258609890937805,
-0.9876077175140381,
-0.7214199304580688,
-0.37123599648475647,
0.3670142590999603,
-0.6718707084655762,
-0.59327632188797,
-1.0531840324401855,
0.6622641682624817,
0.04763578251004219,
-0.418804407119751,
-0.3236193358898163,
-0.6219007968902588,
-0.1572090983390808,
-0.14376863837242126,
-0.40103667974472046,
-0.1184224933385849,
-0.4987896680831909,
0.7102785110473633,
-0.1312667429447174,
-0.567559003829956,
0.4857129752635956,
-0.3671836853027344,
-0.18638870120048523,
-0.22856178879737854,
0.2893788814544678,
1.1376674175262451,
0.24401472508907318,
-0.6877377033233643,
1.3168365955352783,
-0.3815300464630127,
0.392301470041275,
0.7051771879196167,
-0.584886908531189,
0.13067501783370972,
0.5228551030158997,
0.2453732043504715,
0.8313279151916504,
0.4649202227592468,
0.30439743399620056,
0.5751887559890747,
-0.15428969264030457,
0.45720019936561584,
-0.015584005042910576,
0.45272502303123474,
0.3691668212413788,
0.2655923664569855,
-0.7927529811859131,
0.18716268241405487,
-0.058694105595350266,
0.09141514450311661,
-0.019965069368481636,
-0.32937508821487427,
0.18851572275161743,
0.1903114914894104,
0.2248460054397583,
0.570350706577301,
-0.9905493855476379,
-0.4084053933620453,
-0.0946040078997612,
0.49367544054985046,
0.22579094767570496,
0.42356806993484497,
0.15170486271381378,
0.7260543704032898,
0.30996719002723694,
-0.007100658491253853,
0.32535070180892944,
0.8403441905975342,
0.29052093625068665,
0.4437846541404724,
0.6107168793678284,
0.24145759642124176,
0.47142863273620605,
-0.04335925728082657,
0.3543664216995239,
-0.5276829600334167,
0.217251256108284,
0.48944833874702454,
-1.2085847854614258,
0.5184048414230347,
-0.2539893090724945,
-0.21797220408916473,
-0.6099351048469543,
-0.8842618465423584,
0.025716125965118408,
-0.6925270557403564,
0.31353625655174255,
0.9497231841087341,
-0.36123085021972656,
0.6251088976860046,
0.604803740978241,
0.08354032039642334,
0.10625290870666504,
0.48802435398101807,
0.0708041712641716,
-0.37491652369499207,
1.0755794048309326,
1.6634175777435303,
0.1881457269191742,
-0.06485681235790253,
0.0604458786547184,
-0.5026911497116089,
0.4569413661956787,
0.37550973892211914,
0.30670276284217834,
1.0136579275131226,
-0.58177250623703,
-0.4492824375629425,
0.6053375601768494,
-0.19132399559020996,
-0.4207204282283783,
-0.1152232214808464,
-0.3134308159351349,
0.27784135937690735,
-0.3610302209854126,
-0.5696254372596741,
0.9672030210494995,
0.47353246808052063,
-0.7573124766349792,
-0.5282554030418396,
-0.09715089201927185,
-0.29859110713005066,
-0.39837589859962463,
-0.5241953134536743,
0.5582259297370911,
0.18609614670276642,
0.3334142863750458,
0.0776771679520607,
-0.7963044047355652,
-0.7109653949737549,
-1.1465486288070679,
0.22530023753643036,
-0.2467374950647354,
0.5133600234985352,
0.13392850756645203,
-0.1428549736738205,
0.46457555890083313,
-0.5516512989997864,
0.5684931874275208,
0.5331507325172424,
1.0973130464553833,
-0.13877812027931213,
-0.35386738181114197,
0.31343093514442444,
0.4732353091239929,
-0.7020514607429504,
0.9212379455566406,
0.7678393721580505,
-0.6272128820419312,
0.37799254059791565,
-0.7594780325889587,
0.6350209712982178,
0.3804340362548828,
-0.08020853251218796,
0.42838752269744873,
0.337154746055603,
0.09082210063934326,
-0.2795102596282959,
-0.3095473349094391,
-0.36243996024131775,
-1.068681001663208,
-0.009601141326129436,
-0.6365938186645508,
-0.011958564631640911,
-0.2330309897661209,
0.33793899416923523,
0.49110835790634155,
-0.3590129315853119,
4.243029594421387,
1.3536708354949951,
0.5507707595825195,
0.3820708394050598,
0.36865609884262085,
0.6837841272354126,
-0.08567601442337036,
-0.3686169385910034,
0.39219552278518677,
-0.7274906039237976,
-0.897346019744873,
-0.03253958001732826,
0.26406237483024597,
-0.5595449209213257,
0.08325102925300598,
0.7434626817703247,
-0.46622344851493835,
-0.003712316742166877,
0.13301829993724823,
-0.5324006080627441,
-0.735682487487793,
0.2229871302843094,
0.4968535900115967,
0.04854991286993027,
0.3795944154262543,
0.6427233219146729,
0.2832433581352234,
-0.07533662021160126,
-0.6607314944267273,
-0.5338048338890076,
-0.9545131921768188,
-0.8390698432922363,
0.3780982196331024,
-0.24997955560684204,
-0.27900397777557373,
0.24197210371494293,
-0.3680802285671234,
-0.5993419289588928,
0.3168345093727112,
0.7634907960891724,
-0.05615776404738426,
-0.4285134971141815,
-0.00883667916059494,
0.09312420338392258,
-0.43455082178115845,
0.6361072659492493,
0.1024690493941307,
0.36513566970825195,
0.4726344048976898,
-0.3911300003528595,
0.6126646995544434,
-0.21321183443069458,
0.12224593758583069,
-0.17296914756298065,
-1.0156093835830688,
0.12224068492650986,
-0.4648092985153198,
-0.1864658147096634,
0.3597486913204193,
-0.10065647214651108,
0.20973677933216095,
-0.49987494945526123,
-0.5022181868553162,
0.14589117467403412,
0.12100740522146225,
0.7192419767379761,
0.1656784564256668,
0.08331550657749176,
-0.3258291780948639,
-0.5781903266906738,
-0.4299767315387726,
-0.09126153588294983,
-0.5248847007751465,
0.08100328594446182,
0.06143440678715706,
0.04076257348060608,
0.15237264335155487,
0.44833675026893616,
-0.46008574962615967,
0.0017215025145560503,
0.24182112514972687,
-0.11816529929637909,
-0.13714320957660675,
0.2517333924770355,
0.18570730090141296,
0.6156342029571533,
-0.4405946433544159,
0.35777685046195984,
0.061987727880477905,
0.3924857974052429,
0.21126583218574524,
1.5234651565551758,
0.27274683117866516,
0.24113057553768158,
-1.2195199728012085
] |
Four - Fermi Theories in Fewer Than Four Dimensions
|
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes relativistic fermions interacting non-trivially via exchange of scalar bound states. We calculate the $O(1/N_f)$ corrections to this picture, where $N_f$ is the number of fermion species, for a variety of models and confirm their renormalizability to this order. A connection between renormalizability and the hyperscaling relations between the theory's critical exponents is made explicit. We present results of extensive numerical simulations of the simplest model for $d=3$, performed using the hybrid Monte Carlo algorithm on lattice sizes ranging from $8^3$ to $24^3$. For $N_f=12$ species of massless fermions we confirm the existence of a second order phase transition where chiral symmetry is spontaneously broken. Using both direct measurement and finite size scaling arguments we estimate the critical exponents $\beta$, $\gamma$, $\nu$ and $\delta$. We also investigate symmetry restoration at non-zero temperature, and the scalar two-point correlation function in the vicinity of the bulk transition. All our results are in excellent agreement with analytic predictions, and support the contention that the $1/N_f$ expansion is accurate for this class of models.
|
Simon Hands, Aleksandar Kocic and John B. Kogut
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208022
|
hep-lat/9208023
|
[
0.21731920540332794,
-0.6532987952232361,
0.5427851676940918,
0.22524158656597137,
-0.30112797021865845,
-0.5584492683410645,
-0.4114376902580261,
-0.26565542817115784,
-0.5786734223365784,
2.0700182914733887,
0.567288339138031,
-0.15088215470314026,
0.8096985220909119,
-0.11905772238969803,
-0.35245516896247864,
0.36074745655059814,
0.3087940216064453,
-0.439075231552124,
-1.2643647193908691,
0.7970242500305176,
0.4079211354255676,
-0.33014941215515137,
-1.617667317390442,
-0.27518320083618164,
-0.5643286108970642,
0.9397534728050232,
0.32276538014411926,
0.22587865591049194,
0.5470105409622192,
0.11410119384527206,
0.07267638295888901,
-0.5782867074012756,
-0.042038388550281525,
-0.30729055404663086,
-0.6311084032058716,
-0.11460781842470169,
-0.6770301461219788,
-0.21442799270153046,
0.405303418636322,
0.3475680649280548,
0.6173848509788513,
-0.6417716145515442,
-0.1851767599582672,
-0.5585480332374573,
-0.7852426767349243,
0.022744184359908104,
-0.26602551341056824,
-0.07353407889604568,
-0.11735684424638748,
-1.0831611156463623,
0.2601488530635834,
0.47172966599464417,
0.393385648727417,
-0.48820745944976807,
-0.2983265221118927,
-0.5820300579071045,
0.19940975308418274,
0.2728533446788788,
-0.6905890703201294,
-0.48953568935394287,
0.3779902458190918,
0.4504583179950714,
0.4705392122268677,
-0.432648628950119,
-0.048911429941654205,
0.5065327882766724,
-0.5332539677619934,
1.2190570831298828,
0.11841573566198349,
-0.3359600305557251,
-0.46990785002708435,
-0.1676640659570694,
-0.880216658115387,
0.1732466071844101,
-0.8139162063598633,
0.11671137064695358,
-0.12153857201337814,
-0.470791757106781,
-0.8639466762542725,
-0.5609891414642334,
-0.6798100471496582,
-0.48338833451271057,
-0.4420848786830902,
-0.004750996828079224,
0.08244094997644424,
-0.03523661568760872,
-0.17235571146011353,
-0.1859259456396103,
-0.34701985120773315,
0.4785839915275574,
-0.02630884014070034,
0.4536701738834381,
-0.43170297145843506,
-0.06072768196463585,
-0.13939908146858215,
0.3451860845088959,
-0.11096248775720596,
0.35938650369644165,
0.2434358149766922,
0.26754575967788696,
0.2678055465221405,
0.3642808496952057,
-0.526770293712616,
0.20274057984352112,
-0.3086552023887634,
0.6172769665718079,
-0.7532064914703369,
0.8686010241508484,
0.418960303068161,
-0.6346256732940674,
0.44761836528778076,
-0.44661852717399597,
0.2802130877971649,
0.7181460857391357,
-0.11737153679132462,
0.6365084648132324,
0.034083291888237,
0.4128216803073883,
-0.9359161257743835,
-0.9545554518699646,
0.9284999966621399,
0.7973962426185608,
0.12296317517757416,
0.4887769818305969,
0.31552574038505554,
-0.15709275007247925,
0.5244573354721069,
0.5089390873908997,
-0.5659862756729126,
0.06838757544755936,
0.43870535492897034,
-0.3489529490470886,
-0.23228852450847626,
0.15230916440486908,
-0.6816609501838684,
-0.14325270056724548,
-0.37924855947494507,
0.3469899892807007,
-0.14731918275356293,
0.5024945735931396,
0.8309715390205383,
-0.06407324969768524,
0.16870926320552826,
1.0564815998077393,
0.48780831694602966,
-0.08386680483818054,
0.04538359120488167,
0.4290945529937744,
-0.09551218152046204,
0.1653442531824112,
-0.8786529898643494,
0.043602097779512405,
0.2574469745159149,
0.21512974798679352,
-0.31759780645370483,
0.3149869441986084,
-0.48914387822151184,
-0.0024483492597937584,
-0.8805771470069885,
-0.09203934669494629,
0.20073382556438446,
0.15558217465877533,
-0.6406760215759277,
0.7432666420936584,
-0.3358277976512909,
0.29925331473350525,
-0.44909000396728516,
-0.3120300769805908,
0.10230541229248047,
-0.9448239207267761,
-0.23553602397441864,
0.8000907301902771,
-0.35449355840682983,
1.0387564897537231,
0.6727199554443359,
0.2678127884864807,
0.3542757034301758,
-0.929934024810791,
0.024745838716626167,
0.38671308755874634,
-0.6770601868629456,
-0.3551700711250305,
0.3012837767601013,
-0.2951522171497345,
0.05479222536087036,
-0.5131428837776184,
-0.1360870897769928,
-0.4470573365688324,
-0.038108836859464645,
0.7394952178001404,
-0.004093259572982788,
-0.14417248964309692,
-0.3324238657951355,
0.8286862373352051,
-0.7394742369651794,
0.04622725024819374,
-1.4182454347610474,
0.11753930896520615,
-0.4075543284416199,
0.03718464821577072,
-0.31307512521743774,
-0.06815407425165176,
-1.3031798601150513,
0.4601496756076813,
-1.5328340530395508,
0.3556740880012512,
0.041518568992614746,
0.21123206615447998,
-0.7211986780166626,
-0.13257382810115814,
0.18847545981407166,
0.08680351823568344,
0.5560845136642456,
-0.32505664229393005,
-0.1743783950805664,
0.04702097922563553,
0.14361757040023804,
-0.38303717970848083,
0.49657055735588074,
0.7080459594726562,
0.5220116376876831,
0.34419816732406616,
-0.08142755180597305,
0.5476050972938538,
-0.5474430322647095,
-0.6285313367843628,
-0.22367194294929504,
0.4764328598976135,
0.07504817843437195,
-0.13751529157161713,
0.1741591989994049,
0.2955317795276642,
0.21798013150691986,
0.6911851167678833,
0.4153754711151123,
-0.05793621018528938,
0.3362290561199188,
0.5506097078323364,
0.606110155582428,
0.3865983188152313,
0.05890851840376854,
-0.13725684583187103,
0.4429035186767578,
-0.20693433284759521,
-0.6782683730125427,
0.3844636082649231,
-0.4935697317123413,
0.6088035106658936,
-0.08026950061321259,
0.48997971415519714,
0.8608974814414978,
0.6261913776397705,
0.28940901160240173,
0.25146737694740295,
-1.1137844324111938,
0.5133910775184631,
-0.12080128490924835,
0.18949905037879944,
0.23908637464046478,
-0.4885776937007904,
0.047819770872592926,
-0.025965681299567223,
-0.007619175128638744,
-0.6287845373153687,
-0.4459201991558075,
1.2487475872039795,
-0.17146801948547363,
-0.3109331429004669,
0.14941871166229248,
-0.13643909990787506,
-0.9239174723625183,
-0.11332187801599503,
-0.7478267550468445,
-0.004423797596246004,
-0.80086749792099,
0.4848191440105438,
0.653008759021759,
-0.6241620182991028,
0.5186678171157837,
0.3868582844734192,
-0.16547709703445435,
0.6467058062553406,
-0.49517321586608887,
0.12778352200984955,
0.37880364060401917,
0.7086816430091858,
-0.942818284034729,
0.10621169209480286,
-0.7973724603652954,
-0.4452623426914215,
0.004207572899758816,
0.03751938045024872,
0.9451621770858765,
-0.4754924476146698,
0.14550313353538513,
0.31961873173713684,
-0.49027305841445923,
-0.022043244913220406,
0.015927184373140335,
-0.40429797768592834,
0.47515738010406494,
0.981126070022583,
-0.12760226428508759,
-0.27138760685920715,
-0.9750862121582031,
0.44877779483795166,
-0.14791825413703918,
-0.3077543377876282,
0.1398472785949707,
0.5767078399658203,
-0.6844486594200134,
0.7848459482192993,
0.47544288635253906,
0.37353515625,
-0.130436509847641,
0.6582018136978149,
0.47655412554740906,
0.2024698257446289,
-0.24494419991970062,
-0.08122339099645615,
-0.630727231502533,
0.4665868282318115,
0.08427643030881882,
-0.06858736276626587,
0.20671676099300385,
0.029948409646749496,
0.47213032841682434,
-0.3589942157268524,
0.6564161777496338,
-0.9686735272407532,
-0.6371189951896667,
-0.08202457427978516,
-0.3107762634754181,
0.5232099890708923,
0.19155040383338928,
-0.09611735492944717,
-1.022361159324646,
-0.07455188035964966,
0.11328248679637909,
0.18485994637012482,
0.39865779876708984,
-0.1498856544494629,
0.39797553420066833,
0.2770286500453949,
1.2052364349365234,
-0.5008211731910706,
0.38450172543525696,
-0.12640473246574402,
-0.3117433786392212,
0.22925306856632233,
-0.47864198684692383,
0.38668206334114075,
0.020814497023820877,
0.3814298212528229,
0.059403784573078156,
0.6669954061508179,
-0.340241402387619,
-0.5209882855415344,
-0.4918089509010315,
-0.989734947681427,
0.18178397417068481,
1.1010037660598755,
-0.46066907048225403,
-0.04572363197803497,
-0.2765443027019501,
-0.6450476050376892,
0.3765176236629486,
0.27073368430137634,
0.7686314582824707,
-0.15502594411373138,
0.012662460096180439,
0.10969553887844086,
-0.5298707485198975,
0.23556742072105408,
-0.22763977944850922,
0.0761924460530281,
0.7386960983276367,
0.3147367537021637,
0.8839259147644043,
-0.5659509301185608,
-0.633757472038269,
0.3176586627960205,
0.9503276348114014,
0.7984510064125061,
0.5106306076049805,
0.6072177290916443,
-0.34629300236701965,
-0.11803042888641357,
-0.5416619181632996,
-0.3899374306201935,
0.13934427499771118,
-0.7580966949462891,
-0.014524965547025204,
-0.29531943798065186,
0.5555084943771362,
0.22112466394901276,
0.8299529552459717,
0.30016911029815674,
0.1360519379377365,
0.10964833199977875,
0.5337845683097839,
-0.29504144191741943,
0.18905755877494812,
0.0013281313003972173,
-0.058250077068805695,
0.5784082412719727,
-0.9692643880844116,
0.009864339604973793,
0.48955971002578735,
-0.033011965453624725,
0.07664725929498672,
-0.2673744559288025,
-0.4100117087364197,
-0.6408378481864929,
0.25342509150505066,
0.5752836465835571,
-0.6256409287452698,
0.5125510692596436,
-0.5191173553466797,
0.5461576581001282,
-0.33426132798194885,
-0.18499411642551422,
0.539064347743988,
0.28289684653282166,
0.783197283744812,
-1.0560284852981567,
0.32357048988342285,
-0.22173775732517242,
0.3873252272605896,
0.08945328742265701,
-0.6728945374488831,
-0.6768082976341248,
-0.5285468101501465,
-0.24016480147838593,
-0.2845921814441681,
-0.051342736929655075,
0.8636608719825745,
-0.3118661642074585,
0.006819064728915691,
-0.17094938457012177,
-0.45216813683509827,
1.1322026252746582,
-0.5780012011528015,
-0.13234762847423553,
0.3037925660610199,
0.13879907131195068,
-0.2248324155807495,
0.3385331928730011,
-0.11410155892372131,
-0.547723114490509,
-0.2059459388256073,
-0.3832300007343292,
0.4185416102409363,
-0.10938339680433273,
-0.5325671434402466,
-0.5864272713661194,
-0.2880478501319885,
0.19883224368095398,
0.3142964541912079,
-0.22413991391658783,
-0.287529319524765,
-0.0016066774260252714,
-0.10099697858095169,
-0.6494652628898621,
0.08849996328353882,
-0.0329645499587059,
0.14082837104797363,
1.2357354164123535,
0.5478293299674988,
0.8301055431365967,
0.11731113493442535,
-0.08520012348890305,
0.44159722328186035,
-0.5411525964736938,
0.397656112909317,
-0.11724765598773956,
-0.10836630314588547,
-0.4146910309791565,
0.22001732885837555,
-0.7857101559638977,
-0.43670693039894104,
0.10244906693696976,
-0.3288303017616272,
0.287282258272171,
-0.0015589514514431357,
-0.836039662361145,
-0.37871724367141724,
-0.12764525413513184,
-0.7722623944282532,
0.5192854404449463,
0.24143724143505096,
-0.19726958870887756,
-0.05471548065543175,
-0.24738414585590363,
-0.15193666517734528,
-0.7236757278442383,
0.011349278502166271,
-0.457048624753952,
0.08576222509145737,
0.47333449125289917,
0.7384699583053589,
0.6219274401664734,
-0.7908927798271179,
0.25743281841278076,
-0.5116674304008484,
0.30312222242355347,
-0.8152931332588196,
-0.40015316009521484,
0.11749337613582611,
-0.6213362216949463,
0.10494952648878098,
-0.19359703361988068,
0.09702779352664948,
-0.215611070394516,
0.13418526947498322,
0.2549116611480713,
-0.6224444508552551,
-0.435519814491272,
0.2728445827960968,
0.4665788412094116,
0.7899100184440613,
-0.637135922908783,
0.0507470965385437,
0.14513279497623444,
0.007481358014047146,
0.5233039259910583,
-0.40030524134635925,
-0.6993799209594727,
0.2791353762149811,
-0.13364934921264648,
0.7430985569953918,
-1.033340334892273,
-0.2808037996292114,
0.20511886477470398,
-0.38856831192970276,
-0.014133832417428493,
0.5100762844085693,
-0.23057079315185547,
-0.16010673344135284,
-0.6575531959533691,
-0.49876752495765686,
0.1840238720178604,
-0.575767993927002,
0.007302623707801104,
-0.4524543583393097,
-0.2531379163265228,
-0.63796466588974,
0.4533948600292206,
-0.044535789638757706,
0.22316820919513702,
0.6252370476722717,
-0.18727442622184753,
0.4025305509567261,
0.0471951887011528,
0.6612906455993652,
0.1687549650669098,
0.4459110200405121,
0.49056336283683777,
0.07224534451961517,
0.8548158407211304,
-0.14676018059253693,
0.14683310687541962,
-0.9494584798812866,
1.512900471687317,
-0.926392674446106,
-0.5966047048568726,
-0.017787467688322067,
0.2087068259716034,
0.801633894443512,
-0.8433269262313843,
0.11367260664701462,
0.18905670940876007,
-0.5446122884750366,
0.9378761053085327,
0.52569979429245,
-0.5753510594367981,
0.34338825941085815,
-0.24384677410125732,
-1.0241063833236694,
0.49143972992897034,
0.13457819819450378,
0.20230954885482788,
-0.4449409246444702,
-0.5322285294532776,
-0.30330705642700195,
0.06182088702917099,
-0.31588995456695557,
0.2749808132648468,
0.09632153064012527,
0.02747676707804203,
-0.18808430433273315,
0.031075909733772278,
-0.28437718749046326,
0.014144955202937126,
0.032714784145355225,
0.4017264246940613,
0.11007137596607208,
0.17366193234920502,
-0.07602895051240921,
-0.40104416012763977,
-0.09875617921352386,
0.22414937615394592,
0.06364387273788452,
-0.5050660371780396,
0.8686663508415222,
-0.7863979935646057,
-0.5268149375915527,
-0.585252046585083,
-0.3097866475582123,
0.36604365706443787,
0.10399526357650757,
0.2550375759601593,
0.19485092163085938,
0.7101986408233643,
-0.2894520163536072,
0.2906299829483032,
-0.4717828631401062,
-0.6109752655029297,
0.3082226812839508,
-0.5297714471817017,
-0.47720402479171753,
-0.02302001230418682,
0.04112577810883522,
-0.09800858050584793,
-0.4233447313308716,
-1.2226070165634155,
0.31679123640060425,
-0.5309593677520752,
-0.3134610950946808,
0.2725992798805237,
-0.6444141864776611,
0.023079363629221916,
0.07504730671644211,
0.5570975542068481,
0.04262423515319824,
-0.11116039007902145,
0.2015383541584015,
-0.07362241297960281,
-0.17928189039230347,
0.5185251235961914,
1.282193899154663,
-0.0573197677731514,
-0.7165615558624268,
-0.5959616899490356,
0.04186727851629257,
-0.420770525932312,
-0.4243961274623871,
0.7835595607757568,
-0.002940761623904109,
0.5266462564468384,
0.23498913645744324,
0.10597936809062958,
0.7606013417243958,
0.4943697452545166,
-0.2421090006828308,
-0.3129744529724121,
-0.1790408492088318,
-0.8080788850784302,
0.15115463733673096,
-0.8401999473571777,
0.09521526098251343,
0.7772117853164673,
0.019120147451758385,
0.30914533138275146,
-0.3463483154773712,
-0.46805644035339355,
-0.19856634736061096,
-0.7932537198066711,
0.34477344155311584,
-1.4377648830413818,
-0.2487184703350067,
-0.0886397510766983,
-0.018191082403063774,
0.13324949145317078,
0.5141404867172241,
0.442280113697052,
0.8667673468589783,
-0.48077917098999023,
-0.5575698614120483,
-0.11764900386333466,
-0.11427158862352371,
-0.7113252282142639,
-0.6880813837051392,
-0.20257504284381866,
-0.11619548499584198,
-0.29579368233680725,
-0.49333155155181885,
-0.1385883092880249,
0.23575752973556519,
0.04803181812167168,
0.27777090668678284,
-0.04553632065653801,
0.643292248249054,
-0.9702015519142151,
-1.186026692390442,
0.10525429248809814,
0.5301319360733032,
-0.25932905077934265,
0.028285624459385872,
0.49283891916275024,
1.3490207195281982,
0.2226352095603943,
0.14670898020267487,
-0.21764478087425232,
-0.02428450621664524,
-1.2715249061584473,
-0.2115437537431717,
0.09472332894802094,
-0.38966044783592224,
-0.4003896713256836,
-0.7824863195419312,
-0.25583404302597046,
-0.29155054688453674,
-1.379733681678772,
0.2916003167629242,
-0.4986102879047394,
0.7387232780456543,
-0.3404836058616638,
0.17744173109531403,
0.265610009431839,
0.08185518532991409,
0.10575789958238602,
0.9957363605499268,
-0.2151428610086441,
0.33673474192619324,
0.1890612542629242,
0.2732391059398651,
-0.30864137411117554,
0.23115010559558868,
0.6652989983558655,
0.08491557836532593,
-0.35260993242263794,
0.3057134449481964,
-0.1770039051771164,
0.1012256070971489,
0.11073020100593567,
-0.43959733843803406,
-0.05261386185884476,
-0.3317399024963379,
-0.5713465213775635,
0.18424192070960999,
0.5578979253768921,
-1.1252820491790771,
0.09052912145853043,
-0.5365632772445679,
-0.5209187269210815,
-0.10587412863969803,
-0.890705943107605,
-0.5340011119842529,
-0.05568693205714226,
-0.28872039914131165,
-0.10905560106039047,
0.39180484414100647,
-0.2060483992099762,
0.1382611095905304,
-0.12887762486934662,
0.5168607831001282,
-0.035721711814403534,
-0.29830706119537354,
-0.1367778331041336,
-0.25865885615348816,
-0.7248954176902771,
-0.16534891724586487,
-0.13639572262763977,
0.35271668434143066,
-0.5473911166191101,
-1.0222972631454468,
-0.30339276790618896,
0.29443344473838806,
0.4432348310947418,
0.24193471670150757,
-0.09059442579746246,
-0.06376665085554123,
-0.5922427773475647,
0.0786796435713768,
-0.5258595943450928,
-0.23798955976963043,
-0.7255910634994507,
0.5306731462478638,
-0.2132822424173355,
-0.6987541317939758,
0.7651383280754089,
-0.21039368212223053,
-0.26808443665504456,
-0.045461371541023254,
-0.14798282086849213,
0.8490896224975586,
0.421978622674942,
-0.1235022097826004,
0.6581472754478455,
-0.05963287502527237,
-0.2442101687192917,
-0.07441293448209763,
-0.19394318759441376,
0.5439121723175049,
0.6562812924385071,
0.3199489712715149,
0.7387294173240662,
0.02240566350519657,
0.03247189521789551,
0.25533202290534973,
0.11617209017276764,
0.202036052942276,
-0.13700005412101746,
0.4473991394042969,
0.5383965969085693,
0.8362324237823486,
0.3146650493144989,
0.0911514014005661,
0.22435659170150757,
0.34890255331993103,
0.1766544133424759,
-0.201702281832695,
-0.21369655430316925,
0.16362881660461426,
-0.31940925121307373,
0.05548197403550148,
-0.9200772643089294,
-0.3851088583469391,
0.027494700625538826,
-0.04166475683450699,
1.0048526525497437,
0.6350623965263367,
-0.09988457709550858,
0.7629704475402832,
0.4433915913105011,
0.15403978526592255,
-0.06855937838554382,
0.8413549661636353,
-0.1679576188325882,
1.1536821126937866,
0.8315145969390869,
-0.09768567234277725,
0.29857051372528076,
0.7407873272895813,
0.3774295747280121,
-0.439303457736969,
-0.17815247178077698,
0.2851419746875763,
-0.6711667776107788,
0.5308668613433838,
-0.37527260184288025,
0.5428131818771362,
-0.1320195347070694,
-0.6213354468345642,
0.2610003650188446,
-0.5328353047370911,
0.18503080308437347,
0.6161854863166809,
-0.3919043242931366,
0.20835906267166138,
0.6847421526908875,
-0.18433839082717896,
-0.3837287127971649,
0.5694913864135742,
-0.16576576232910156,
0.15625591576099396,
0.9495230913162231,
1.1717262268066406,
-0.13480515778064728,
0.31973710656166077,
0.2498701959848404,
-0.9530437588691711,
0.4200533926486969,
0.3610690236091614,
-0.3782863914966583,
0.4523157477378845,
-0.235345259308815,
-0.13110880553722382,
0.5735042691230774,
0.11454488337039948,
-0.23322437703609467,
-0.12844866514205933,
0.07380487024784088,
-0.10516209155321121,
0.23298433423042297,
-0.5893294811248779,
0.9393798112869263,
0.6972770690917969,
-0.32205238938331604,
-0.3899119198322296,
-0.06056811660528183,
-0.6231085062026978,
0.4307999312877655,
-1.0173417329788208,
0.5439836978912354,
-0.1263524740934372,
-0.419596403837204,
-0.6277390122413635,
-0.12198973447084427,
-0.10470079630613327,
-0.9549784660339355,
0.12294945120811462,
-0.2816261053085327,
0.1965397149324417,
0.12251148372888565,
-0.1819983422756195,
0.7340642809867859,
-0.6890831589698792,
0.08452300727367401,
0.40874484181404114,
1.081740140914917,
0.007086335215717554,
0.1617211103439331,
0.3224725127220154,
0.446424663066864,
-0.423128217458725,
0.42345163226127625,
0.6441799402236938,
-0.3376346230506897,
0.6030867695808411,
-0.34645530581474304,
0.3298082649707794,
0.06953190267086029,
-0.3333333134651184,
0.3211953341960907,
0.33516746759414673,
-0.37040242552757263,
-0.5117019414901733,
-0.419733464717865,
0.008804099634289742,
-0.4298931658267975,
-0.04782164469361305,
-0.6605902314186096,
0.3524657189846039,
-0.6089701652526855,
0.082098089158535,
0.3112375736236572,
-0.6562256813049316,
4.390357494354248,
0.9104025363922119,
0.33587774634361267,
0.3119228780269623,
0.6329525709152222,
0.8054183125495911,
-0.32234156131744385,
-0.678069531917572,
0.04994161054491997,
-0.5288999676704407,
-0.7150130271911621,
-0.24682672321796417,
0.007003504782915115,
-0.19880788028240204,
-0.01313750073313713,
0.7441964149475098,
-0.2719411551952362,
-0.1007075086236,
0.15456169843673706,
-0.6957865357398987,
-0.6250327229499817,
0.012312592007219791,
0.4542044401168823,
-0.14514337480068207,
0.24414126574993134,
0.6233152747154236,
-0.1346576064825058,
-0.30132439732551575,
-0.7681958675384521,
-0.47095999121665955,
-0.8818187117576599,
-1.018395185470581,
0.36873358488082886,
0.17425748705863953,
-0.8994174003601074,
-0.022285854443907738,
0.4145621359348297,
-0.4501998722553253,
-0.17691098153591156,
-0.13990171253681183,
0.030171122401952744,
-0.4771203100681305,
0.477970689535141,
-0.02127532847225666,
-0.4328959584236145,
0.8327502608299255,
-0.27066856622695923,
0.6874329447746277,
-0.08721975237131119,
-0.4213588535785675,
0.2598258852958679,
0.5209584832191467,
0.3924890160560608,
0.010614063590765,
-0.30087292194366455,
0.48842853307724,
-0.6320109367370605,
0.20257997512817383,
0.290897399187088,
-0.11622852087020874,
0.1283273547887802,
-0.4995535612106323,
0.013578456826508045,
0.26884278655052185,
-0.04295650124549866,
0.48841527104377747,
0.23172065615653992,
0.20654305815696716,
-0.514189600944519,
0.6140047907829285,
0.239385187625885,
-0.6262633800506592,
0.04901770502328873,
0.580991804599762,
0.4882178008556366,
-0.08130389451980591,
-0.456028550863266,
0.1463753879070282,
0.024524858221411705,
-0.29607120156288147,
0.464847207069397,
-0.3391443192958832,
-0.04265857860445976,
-0.07562725245952606,
0.11155225336551666,
0.22907204926013947,
-0.14998190104961395,
0.21027594804763794,
-0.20144318044185638,
0.5747038722038269,
0.29566213488578796,
0.9252262115478516,
0.421808123588562,
0.030934175476431847,
-0.39696308970451355
] |
Mixed Model of Induced QCD
|
The problems with the $Z_N$ symmetry breaking in the induced QCD are analyzed. We compute the Wilson loops in the strong coupling phase, but we do not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to bypass this problem by adding to the model a heavy fermion field in a fundamental representation of $ SU(N) $. Remarkably, the model still can be solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of flavors. At $ N_f \ll N \rightarrow \infty $ there is a new regime, with two vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear integral equation, with the kernel, depending upon the old density. The symmetry breaking requires certain eigenvalue condition, which takes some extra parameter adjustment of the scalar potential.
|
A.A. Migdal
|
hep-lat hep-th
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208023
|
hep-lat/9208024
|
[
0.42607614398002625,
0.6873795986175537,
0.8124290704727173,
0.3590037226676941,
-0.03996783494949341,
-0.30041399598121643,
0.367803156375885,
-0.13428762555122375,
-1.3443125486373901,
1.4440871477127075,
1.1072173118591309,
-0.040940798819065094,
0.7560371160507202,
-0.48398447036743164,
-0.25473183393478394,
0.8107219934463501,
-0.25635412335395813,
-0.522779643535614,
-0.8973764777183533,
-0.126607283949852,
-0.20250007510185242,
-0.33721429109573364,
-1.048268437385559,
-0.8964665532112122,
-0.30253639817237854,
0.5338758826255798,
-0.635404646396637,
0.2937042713165283,
1.4473676681518555,
0.6757208108901978,
0.10994541645050049,
-0.7972639799118042,
-0.5360562801361084,
-0.48095718026161194,
-0.3855275809764862,
-0.5860549211502075,
-0.28143778443336487,
0.27693286538124084,
0.5184773206710815,
-0.37001901865005493,
1.1474502086639404,
-0.17598015069961548,
1.155363917350769,
-0.05459901690483093,
-0.7224118709564209,
0.38322511315345764,
-0.17690517008304596,
-0.12441537529230118,
-0.6328410506248474,
-1.292952060699463,
0.3720969557762146,
0.42213061451911926,
0.6924890875816345,
-0.7173476815223694,
-0.20348435640335083,
-0.1643943339586258,
0.22571071982383728,
-0.00047276681289076805,
-1.0716018676757812,
-0.12034466862678528,
0.6862046122550964,
-0.139679417014122,
0.8674341440200806,
-0.5989975333213806,
0.20547428727149963,
0.19068720936775208,
-0.5586043000221252,
0.003122445661574602,
0.0564642995595932,
-0.3938153088092804,
-0.7426642775535583,
-0.6298632621765137,
0.1781710833311081,
0.24520526826381683,
-0.42107823491096497,
0.08890364319086075,
-0.38148829340934753,
-0.2889584004878998,
-1.0305875539779663,
-0.25291088223457336,
-0.15335209667682648,
-0.4408026337623596,
-0.6703413128852844,
0.2982499897480011,
-0.2027098685503006,
-0.04981847479939461,
-0.34831032156944275,
-0.07459330558776855,
0.41038477420806885,
0.5369871258735657,
0.27968767285346985,
0.9298098087310791,
-0.042105477303266525,
0.14530698955059052,
0.7251513004302979,
0.6501233577728271,
0.5741139650344849,
0.19669586420059204,
0.1376422941684723,
0.048386238515377045,
0.30048468708992004,
1.0049666166305542,
-0.24224554002285004,
0.31463631987571716,
-1.0254569053649902,
0.1765121966600418,
0.12016250193119049,
0.22550594806671143,
-0.7270750403404236,
-0.0660552904009819,
-0.04981781914830208,
0.6780568957328796,
0.7800685167312622,
0.9771094918251038,
0.008129609748721123,
0.1550835818052292,
0.3494044840335846,
-0.44919243454933167,
-0.8202906250953674,
-0.17558278143405914,
-0.12548278272151947,
0.2199554443359375,
-0.04270758107304573,
0.7310377359390259,
-0.33708885312080383,
-0.5324428081512451,
0.3253352642059326,
0.8927133679389954,
-0.5423417687416077,
-0.10467952489852905,
-0.01770716719329357,
0.10909558832645416,
0.21371717751026154,
0.7370494604110718,
0.33714020252227783,
0.15590454638004303,
-0.4902532994747162,
0.44808611273765564,
0.04306359961628914,
-0.21790136396884918,
0.27708518505096436,
-0.7294245362281799,
0.22666525840759277,
0.42083853483200073,
0.24464483559131622,
0.07583770155906677,
0.7290610671043396,
-0.6828516721725464,
-0.26707401871681213,
-0.0347779244184494,
-0.573789119720459,
-0.09304750710725784,
0.33804672956466675,
-0.1426066905260086,
0.518677294254303,
-0.2715553641319275,
-0.6624879240989685,
0.7676246762275696,
-0.42232364416122437,
-0.7808970808982849,
0.5952285528182983,
-0.23005107045173645,
-0.7305927276611328,
0.10625988990068436,
-1.044740915298462,
0.06746994704008102,
-0.31635141372680664,
-0.0002254812716273591,
0.5130816698074341,
-0.9537919759750366,
0.2349158674478531,
0.3314861059188843,
-0.17610760033130646,
0.5000519752502441,
-0.21261584758758545,
0.16272059082984924,
0.840602695941925,
-0.3317238688468933,
0.19517476856708527,
0.3179018199443817,
-0.33839303255081177,
-0.0789702907204628,
1.1027088165283203,
0.1959523856639862,
-0.2553058862686157,
0.5110196471214294,
-0.1978655457496643,
0.019074080511927605,
0.4831943213939667,
-0.4153560698032379,
0.2806098759174347,
0.3756788671016693,
-0.5336240530014038,
0.2947702407836914,
-0.7304216623306274,
-0.20774784684181213,
-0.6640692949295044,
0.7804349064826965,
-0.6865007877349854,
-1.1547636985778809,
-0.2256140261888504,
0.5747031569480896,
-1.127712368965149,
0.3357866704463959,
-1.2743351459503174,
0.0778314471244812,
0.30728423595428467,
-0.00534765375778079,
-0.04813840240240097,
-0.3187783658504486,
0.44620198011398315,
-0.3384253978729248,
0.4917111098766327,
0.1360052227973938,
-0.2675972580909729,
0.24228987097740173,
-0.1994498074054718,
-0.36435022950172424,
0.5774104595184326,
-0.17224861681461334,
0.8931361436843872,
0.0914950892329216,
-0.15327635407447815,
0.5397266745567322,
-0.02407316118478775,
-0.444963276386261,
0.5585612654685974,
0.2942129969596863,
0.37134984135627747,
-0.04275853559374809,
-0.25240179896354675,
0.8511227965354919,
-0.20410524308681488,
0.15823239088058472,
1.0645051002502441,
0.6404047012329102,
0.7513095736503601,
1.088400959968567,
0.32566317915916443,
0.5849199891090393,
-0.3835981786251068,
0.04668949171900749,
0.9006531238555908,
-0.14440137147903442,
0.3073924481868744,
0.20076298713684082,
-0.7648259997367859,
0.06299909949302673,
-1.0817663669586182,
0.6619827151298523,
0.00693289190530777,
0.9343746900558472,
0.3369293808937073,
0.30318892002105713,
-1.0581343173980713,
-0.06185343116521835,
-0.09593615680932999,
0.15978385508060455,
-0.4603556990623474,
-0.2573227286338806,
-0.4840058982372284,
0.046389028429985046,
-0.028295962139964104,
0.18426166474819183,
-0.48464542627334595,
1.0302139520645142,
0.2895829677581787,
0.16424956917762756,
-0.519612193107605,
-0.1879383772611618,
-1.5571234226226807,
-0.03520268574357033,
-0.7934982180595398,
-0.3866000175476074,
-0.26545649766921997,
0.06414099037647247,
1.2465687990188599,
-0.9575879573822021,
0.5712557435035706,
0.06371758878231049,
-0.3492291569709778,
0.9202280640602112,
-0.3700474798679352,
0.2968538701534271,
0.9015153646469116,
0.16678184270858765,
-1.354798436164856,
0.008085019886493683,
-0.34224236011505127,
0.20621924102306366,
0.29619067907333374,
0.30996331572532654,
0.716487467288971,
-0.08088419586420059,
0.15303467214107513,
-0.49067384004592896,
-0.8241791725158691,
-0.0829383060336113,
0.13978205621242523,
-0.2854350805282593,
0.32456621527671814,
0.48053666949272156,
-0.6332243084907532,
0.08992981910705566,
-0.5751495361328125,
1.015012264251709,
0.26527509093284607,
-0.44819360971450806,
0.9318017959594727,
0.6100087761878967,
0.08387646079063416,
0.1233585774898529,
-0.5441850423812866,
-0.1383342444896698,
0.011212380602955818,
0.9665495157241821,
0.9291542172431946,
0.028158938512206078,
0.5195648670196533,
-0.7505242228507996,
0.1091015487909317,
0.21111451089382172,
-0.16661636531352997,
-0.8628990650177002,
0.048850201070308685,
1.128747820854187,
-0.060604117810726166,
-1.0738645792007446,
0.3459773063659668,
-0.7873015403747559,
-0.9638179540634155,
-0.1825571209192276,
-0.44556692242622375,
0.30324581265449524,
-0.397185355424881,
0.12314995378255844,
-0.40514057874679565,
0.2492360919713974,
-0.04278186336159706,
0.4682346284389496,
0.23779140412807465,
-0.7396575212478638,
0.5151522159576416,
0.4245068430900574,
-0.0314856581389904,
-0.09649953246116638,
0.17310771346092224,
-0.36968305706977844,
-0.11165180802345276,
0.3845028579235077,
-0.8740509152412415,
0.5327779650688171,
0.6932722926139832,
0.2956445515155792,
-0.07461846619844437,
0.7394922971725464,
0.0050689601339399815,
-0.6514729261398315,
-0.5417742729187012,
-1.0222632884979248,
0.4159086048603058,
0.2844848334789276,
-0.3058435022830963,
0.4636699855327606,
-0.6956409215927124,
-0.13025213778018951,
0.6131293177604675,
0.38177934288978577,
0.7872776389122009,
-0.886950671672821,
0.2592163383960724,
0.2568877637386322,
0.022353466600179672,
0.04785192385315895,
-0.023542068898677826,
0.4267677068710327,
0.16929495334625244,
-0.025073153898119926,
1.0929079055786133,
-1.44521164894104,
-0.37518224120140076,
-0.17035900056362152,
0.7928304076194763,
1.1171619892120361,
0.6981492042541504,
1.0161609649658203,
0.13368116319179535,
0.10632647573947906,
-0.31410038471221924,
-0.2153916209936142,
-0.3570789396762848,
-0.04359683021903038,
-0.25415387749671936,
-0.07777499407529831,
-0.003539771307259798,
-0.5954389572143555,
-0.27340495586395264,
0.5328870415687561,
0.31921595335006714,
-0.00436128256842494,
0.3856467604637146,
0.13132718205451965,
0.8112640380859375,
1.1745728254318237,
-0.37211349606513977,
-0.3895089328289032,
-1.0109471082687378,
0.12926211953163147,
0.34875059127807617,
0.45988667011260986,
-0.19014672935009003,
-0.3281776010990143,
-0.4211001396179199,
-0.8416427969932556,
0.214650496840477,
0.020807569846510887,
-0.45665034651756287,
0.6285481452941895,
-0.6134180426597595,
-0.11157312989234924,
0.09930514544248581,
-0.36020857095718384,
-0.028136907145380974,
0.1871122419834137,
0.3222510814666748,
-1.157002329826355,
0.3829517364501953,
-0.10268596559762955,
0.9321501851081848,
0.497243195772171,
-0.49641865491867065,
-0.9485874772071838,
-0.6547873616218567,
0.12268856912851334,
-0.26380425691604614,
-0.3297368884086609,
0.5995564460754395,
-0.042583584785461426,
-0.3097819685935974,
-0.310019850730896,
0.019431279972195625,
0.33266639709472656,
-0.3612014353275299,
-0.4035175144672394,
-0.137473002076149,
-0.04761967435479164,
-0.13085414469242096,
0.6023338437080383,
0.23544633388519287,
-0.5922375321388245,
0.22061453759670258,
-0.22247610986232758,
-0.08094629645347595,
-0.5117219090461731,
-0.74835604429245,
-0.5575602650642395,
-0.5899208188056946,
-0.9353093504905701,
0.5831983685493469,
-0.24802729487419128,
0.11662668734788895,
0.20877107977867126,
0.2591205835342407,
-0.46518170833587646,
-0.31780770421028137,
0.025316424667835236,
0.5297834873199463,
0.5211726427078247,
1.2094131708145142,
0.5962836742401123,
0.3354259431362152,
0.8895930647850037,
0.05661679804325104,
0.02633984386920929,
0.7184945940971375,
0.11015740782022476,
-0.3392737805843353,
-0.3292812407016754,
-0.06121623143553734,
-0.9254987835884094,
-1.076677918434143,
0.7104107737541199,
-0.3816273808479309,
1.0202926397323608,
-0.20584721863269806,
-0.7787412405014038,
-0.30221322178840637,
-0.8753240704536438,
-0.6216238737106323,
0.4924657940864563,
0.1074393093585968,
-0.3350135087966919,
0.5602820515632629,
-0.635823130607605,
-0.08887337148189545,
-0.04608407989144325,
0.4043416380882263,
-0.584958553314209,
0.6187697649002075,
0.4339927136898041,
0.013261005282402039,
0.9206565022468567,
-0.5331504940986633,
0.41887199878692627,
-0.39376580715179443,
0.10825689882040024,
0.00586584210395813,
-0.675750732421875,
-0.16884088516235352,
-0.09758230298757553,
0.11461781710386276,
-0.6145715117454529,
0.5111153721809387,
-0.20158818364143372,
-0.12061721831560135,
0.2322179079055786,
-0.16601119935512543,
-0.1255294531583786,
-0.6435348391532898,
0.8131117820739746,
-0.06530128419399261,
-1.0609354972839355,
0.002442003460600972,
0.9354615807533264,
-0.15887451171875,
0.13116037845611572,
-0.04379909485578537,
-0.4845597445964813,
0.19240161776542664,
-0.6910112500190735,
0.0026119467802345753,
-0.39758750796318054,
-0.17476099729537964,
-0.3757534623146057,
-0.2681190073490143,
0.0674363523721695,
0.19802258908748627,
0.11297585815191269,
0.7551000118255615,
-0.07781950384378433,
-1.071427345275879,
0.06661694496870041,
-0.7689818143844604,
-0.5065465569496155,
-0.6105604767799377,
-0.45476919412612915,
-0.48887354135513306,
0.8140032887458801,
-0.185002863407135,
0.12691184878349304,
0.5075244903564453,
-0.5393343567848206,
-0.434111088514328,
1.1823484897613525,
0.034806594252586365,
-0.382864385843277,
0.5086010098457336,
0.5898705720901489,
0.5647045969963074,
-0.10912108421325684,
-1.0939440727233887,
0.6590715050697327,
-1.1776152849197388,
1.2062997817993164,
-0.2851579785346985,
-0.23587597906589508,
0.16351056098937988,
0.08909501135349274,
0.8136561512947083,
-0.7378183603286743,
0.5101763010025024,
-0.08195861428976059,
-0.4486311972141266,
0.9264932870864868,
0.5289703607559204,
-0.9739167094230652,
-0.4110011160373688,
-0.43208378553390503,
-1.0022319555282593,
0.8470929861068726,
-0.1697605401277542,
-0.11561711877584457,
-1.0042661428451538,
-0.776605486869812,
0.1307774782180786,
0.045207299292087555,
0.7080321311950684,
0.20642921328544617,
-0.23191437125205994,
-0.26818791031837463,
0.2337394505739212,
0.25307995080947876,
-0.7774615287780762,
-0.07715671509504318,
0.13568514585494995,
-0.10643599182367325,
-0.545331597328186,
-0.5279359817504883,
-0.4621034562587738,
-0.8626165986061096,
-0.2948461174964905,
0.384127140045166,
0.4677709639072418,
-0.6259693503379822,
0.6624987721443176,
-0.7602068781852722,
-0.7136064767837524,
-0.36544954776763916,
-0.09561469405889511,
-0.02660832181572914,
0.23431396484375,
0.633156955242157,
0.029065243899822235,
-0.03491387516260147,
-0.11889927834272385,
0.41847479343414307,
-0.535416841506958,
-0.4537811875343323,
0.4612707197666168,
-0.4260827302932739,
-0.33362704515457153,
0.2699710428714752,
0.21906565129756927,
-0.7034209370613098,
-0.974244236946106,
-0.9853048324584961,
-0.24633948504924774,
-0.3715086877346039,
-0.657224178314209,
0.6140156388282776,
-0.050933923572301865,
-0.3850376307964325,
0.5452675819396973,
0.32404378056526184,
-0.10253231227397919,
0.09147708117961884,
0.08770473301410675,
-0.49045342206954956,
-0.4195501208305359,
-0.15806250274181366,
1.2643157243728638,
-0.8765699863433838,
-0.3630852699279785,
-0.2188822478055954,
-0.06806065887212753,
-0.5549372434616089,
0.26950863003730774,
0.04761425405740738,
-0.5746957659721375,
0.25519150495529175,
0.20628689229488373,
0.4821641445159912,
0.3380500376224518,
0.23186095058918,
0.5604376792907715,
-0.04038432240486145,
-0.3921091854572296,
-0.8873339295387268,
-0.779041588306427,
-0.2964417338371277,
0.1346280574798584,
0.6315532922744751,
-0.08395343273878098,
0.5082514882087708,
-0.0658871978521347,
-0.24164144694805145,
-0.2705450654029846,
-0.7068994641304016,
0.5710639357566833,
-1.3001627922058105,
-0.15554623305797577,
-0.8188650012016296,
-0.19559533894062042,
0.16818270087242126,
0.3344835340976715,
0.020187905058264732,
0.027898253872990608,
-1.1590535640716553,
0.05838184803724289,
0.4189021587371826,
-0.1227412149310112,
0.03748263418674469,
-0.8956999182701111,
-0.6949601769447327,
-0.19343611598014832,
-0.4334276020526886,
-0.30598345398902893,
-0.27531757950782776,
-0.12886099517345428,
-1.0152510404586792,
0.30902910232543945,
-0.09017781913280487,
0.4779246747493744,
-0.199051633477211,
-0.6780138611793518,
-0.028458287939429283,
0.050147075206041336,
-0.47169286012649536,
-0.1574467122554779,
-0.6216650605201721,
0.4215298295021057,
0.00010325940093025565,
0.045807622373104095,
-0.46830129623413086,
0.33033543825149536,
-0.7575826048851013,
-0.4651353657245636,
-0.34800124168395996,
0.320072740316391,
-0.021321816369891167,
-0.6999613046646118,
0.12215418368577957,
-0.12718793749809265,
-0.4798203110694885,
0.22537606954574585,
-0.24140627682209015,
-0.3452024757862091,
0.14684517681598663,
-0.03362613916397095,
-0.10383377969264984,
0.6324611902236938,
-0.6084498167037964,
0.7260912656784058,
-0.5235744118690491,
-0.5827493667602539,
0.011950298212468624,
0.5401410460472107,
-0.16318143904209137,
0.5578240752220154,
0.6538456678390503,
-0.22835804522037506,
0.23430390655994415,
0.7173436284065247,
-0.11603496223688126,
0.29640135169029236,
-0.5481525659561157,
-0.13456936180591583,
0.01376071572303772,
0.020983077585697174,
-0.030117245391011238,
0.8130062818527222,
0.45648863911628723,
-0.3884929418563843,
-0.9463909864425659,
-0.8177217245101929,
-0.41860827803611755,
0.16978426277637482,
-0.9262750148773193,
-0.04776916280388832,
-0.20145277678966522,
-0.18036049604415894,
0.3510807454586029,
0.11387486010789871,
-0.29299619793891907,
-0.009797245264053345,
-0.11711587011814117,
-0.06396841257810593,
-0.15639181435108185,
0.11076561361551285,
-0.1496713012456894,
-0.3002229928970337,
-0.8812376856803894,
-0.5685229897499084,
0.08785130083560944,
0.8785343766212463,
-0.78012615442276,
-0.44854944944381714,
-0.6934720277786255,
0.41882428526878357,
-0.02741418033838272,
0.13409990072250366,
-0.28089815378189087,
-0.3961893618106842,
-0.08349771052598953,
0.1058024987578392,
0.2188270539045334,
0.3363322913646698,
0.17933684587478638,
0.9504762291908264,
0.24020443856716156,
-1.1011139154434204,
0.4674372971057892,
0.2649761140346527,
0.18324920535087585,
-0.5986813902854919,
-0.193710058927536,
0.23677945137023926,
-0.04276646673679352,
-0.717075526714325,
1.207326889038086,
-0.25864163041114807,
0.8056848645210266,
0.5373358130455017,
0.028502395376563072,
0.035374559462070465,
0.11397412419319153,
0.7835456728935242,
0.3737219572067261,
0.6988887786865234,
0.10633227229118347,
0.3043643534183502,
-0.0139091731980443,
0.39796459674835205,
-0.12167782336473465,
0.8115528225898743,
0.22448435425758362,
0.6817915439605713,
-0.2864516079425812,
0.93105548620224,
0.2916427254676819,
0.16452164947986603,
-0.2555883228778839,
-0.23155423998832703,
-0.09830956906080246,
0.18938584625720978,
0.23697836697101593,
0.7251966595649719,
-0.5988553166389465,
-0.15463963150978088,
-0.3132764399051666,
1.3154727220535278,
0.04003352299332619,
0.6166564226150513,
-0.5125065445899963,
0.54010009765625,
0.9219372272491455,
0.15799672901630402,
0.11994337290525436,
0.6597224473953247,
-0.044154174625873566,
0.5431111454963684,
0.6903269290924072,
0.47367340326309204,
1.0151984691619873,
-0.04096988961100578,
0.6748460531234741,
-0.9573130011558533,
-0.1011996790766716,
0.9462804794311523,
-1.4919594526290894,
0.5298303961753845,
0.0965961366891861,
-0.4661014676094055,
-0.29993560910224915,
-0.9988395571708679,
0.18597954511642456,
-0.7887037396430969,
0.8138860464096069,
0.8886692523956299,
-0.559369683265686,
0.06961304694414139,
0.8081547021865845,
-0.1851949393749237,
0.26339074969291687,
0.603890061378479,
0.1648326814174652,
0.2588788866996765,
0.9984263777732849,
1.6159006357192993,
0.2640124559402466,
0.42977237701416016,
0.26978600025177,
-0.8821134567260742,
0.27887338399887085,
0.3867005407810211,
-0.3450026214122772,
1.361108660697937,
-0.6554754376411438,
-0.7553725838661194,
0.5175259113311768,
0.14066460728645325,
0.14142435789108276,
-0.07045923173427582,
-0.5701395273208618,
0.599317193031311,
-0.5147889852523804,
-1.0318007469177246,
1.0723243951797485,
0.2597557008266449,
-0.422013521194458,
-0.23923847079277039,
-0.20912423729896545,
-0.14018575847148895,
-0.2154899537563324,
-0.745151162147522,
0.6419973969459534,
0.5469264984130859,
0.5539801120758057,
-0.2695581912994385,
-0.605717122554779,
-0.3238999843597412,
-1.0082814693450928,
0.010999339632689953,
-0.7562065124511719,
0.6102481484413147,
0.10494169592857361,
0.4453827142715454,
0.9390720129013062,
-0.6185747981071472,
0.39575204253196716,
0.5528942346572876,
0.8937113285064697,
-0.0774785652756691,
0.13064135611057281,
0.4857933521270752,
0.6385632157325745,
-0.7761238813400269,
1.0352966785430908,
0.5993341207504272,
0.028727728873491287,
0.10104622691869736,
-0.3561214506626129,
0.1808926910161972,
0.05851666256785393,
-0.21599586308002472,
1.2654261589050293,
-0.6659261584281921,
0.3596004247665405,
-0.02331382967531681,
-0.0665111318230629,
-0.42447465658187866,
-1.317952036857605,
-0.06975281238555908,
-0.8252409100532532,
0.20822741091251373,
-0.2713530361652374,
0.6448639035224915,
0.5763716697692871,
-0.5146669745445251,
3.9495837688446045,
0.967044472694397,
0.3895608186721802,
0.25831496715545654,
0.7074320316314697,
0.42726126313209534,
-0.06275822967290878,
-0.5074767470359802,
0.38620468974113464,
-1.1948156356811523,
-0.17025205492973328,
0.5105406045913696,
0.5043204426765442,
-0.5167638659477234,
-0.45365065336227417,
0.305841863155365,
0.2216215878725052,
0.28788501024246216,
0.26047688722610474,
-0.9253301620483398,
-0.11579633504152298,
0.5101633667945862,
0.10839807987213135,
-0.15692764520645142,
0.6197370290756226,
-0.570586085319519,
0.04060734808444977,
-0.9075192213058472,
-0.6104962229728699,
-0.4356900751590729,
-0.7876215577125549,
-1.0552371740341187,
-0.0013141045346856117,
-0.07741948217153549,
-0.4255668520927429,
0.9611791968345642,
-0.16198648512363434,
-0.5280171632766724,
0.19608117640018463,
0.6209132075309753,
-0.41869717836380005,
0.25081104040145874,
0.07347600907087326,
0.14471684396266937,
-1.1890968084335327,
0.7094146013259888,
0.7279866933822632,
0.9508724808692932,
-0.16214364767074585,
-0.24562610685825348,
0.2693720757961273,
-0.28767451643943787,
0.5155977010726929,
-0.2579497992992401,
-1.2932018041610718,
0.38732266426086426,
-0.5566725730895996,
-0.46803367137908936,
0.11345096677541733,
0.20718571543693542,
0.621364951133728,
-0.09474881738424301,
-0.5949755907058716,
0.2279941439628601,
0.28599071502685547,
0.381944864988327,
0.30075550079345703,
0.10157342255115509,
-0.3407157361507416,
-0.20313295722007751,
-0.13116809725761414,
-0.1460057646036148,
-0.3312782943248749,
-0.27131128311157227,
-0.2427016943693161,
-0.0932299792766571,
-0.13145552575588226,
0.6770525574684143,
-0.0005001481622457504,
0.17823456227779388,
0.17121116816997528,
-0.4567676782608032,
-0.357930451631546,
0.32523709535598755,
0.1615448296070099,
0.8922545909881592,
-0.4188247323036194,
0.2564595937728882,
-0.48036229610443115,
0.2788781225681305,
0.1616414338350296,
1.24033784866333,
0.5376744270324707,
-0.20677676796913147,
-1.1096247434616089
] |
Finite-Size Scaling on the Ising Coexistence Line
|
We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear evi consequences of the convexity of the free energy are not adequately treated in either of these approaches.\lb {\it Keywords}\/: Finite-size scaling, 2-d Ising, pure-phase susceptibility.
|
S.Gupta and A.Irbaeck
|
hep-lat cond-mat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208024
|
hep-lat/9208025
|
[
0.20008385181427002,
-0.08473114669322968,
-0.24484984576702118,
-0.35995686054229736,
-0.4315263032913208,
0.22831207513809204,
-0.19822877645492554,
-0.4476363956928253,
-0.48563629388809204,
1.3318066596984863,
0.1012607216835022,
0.07522033154964447,
0.04614647105336189,
-0.9150820970535278,
0.19663405418395996,
0.16602876782417297,
0.21020546555519104,
0.06465582549571991,
-0.9248079657554626,
0.0945032387971878,
0.26783353090286255,
-0.5445542931556702,
-0.8357383608818054,
-0.7337898015975952,
-0.1140141487121582,
0.8291194438934326,
0.004158215597271919,
0.09816671162843704,
1.156148910522461,
0.0077680060639977455,
0.03709559887647629,
-0.84247225522995,
-0.24714922904968262,
-0.810193657875061,
-0.11350096017122269,
-0.4534069299697876,
0.301251620054245,
-0.5530819296836853,
0.7841781973838806,
0.2688176929950714,
0.9837729930877686,
-0.28138333559036255,
-0.08441361039876938,
-0.002845326904207468,
-0.06575299799442291,
-0.1260896772146225,
-0.535891592502594,
-0.33034461736679077,
0.5476818680763245,
-1.4170740842819214,
0.8531966209411621,
0.3355671167373657,
0.7588557004928589,
-0.2787166237831116,
-0.6119354963302612,
-0.5108088254928589,
0.07659011334180832,
0.03770675137639046,
-0.49224653840065,
-0.10536568611860275,
-0.04162461310625076,
0.20331330597400665,
0.4145814776420593,
-1.0911706686019897,
-0.02520032227039337,
0.6822568774223328,
-0.5396707057952881,
0.8811716437339783,
-0.5538572072982788,
-0.4756142795085907,
-0.027872852981090546,
-0.2504201829433441,
-0.9691073894500732,
-0.07852748781442642,
-0.9909625053405762,
-0.10207892954349518,
-0.19928224384784698,
-0.5735364556312561,
-1.6026712656021118,
-0.5848811864852905,
-0.18962393701076508,
-0.3488667607307434,
-0.08685878664255142,
0.3816058039665222,
0.1510915905237198,
0.15071986615657806,
-0.01911647990345955,
-0.2630962133407593,
-0.10050006955862045,
0.896137535572052,
0.3052647113800049,
1.0254735946655273,
-0.4276057779788971,
0.0789053663611412,
0.434673935174942,
-0.10548026114702225,
0.3506574332714081,
-0.12405775487422943,
0.4247792363166809,
0.3858025074005127,
0.3272149860858917,
-0.09387218207120895,
-1.0064314603805542,
0.30582955479621887,
-0.4782491624355316,
0.8235378861427307,
-0.317687451839447,
0.29608818888664246,
-0.3917355239391327,
-0.5253470540046692,
0.3874671459197998,
-0.39961957931518555,
0.14715337753295898,
0.7254229187965393,
0.2270805835723877,
0.5640766620635986,
-0.47693538665771484,
0.3550829589366913,
-0.1855500042438507,
-0.5427931547164917,
0.45562899112701416,
-0.15494081377983093,
-0.02029447816312313,
0.40091097354888916,
-0.11638521403074265,
0.1922907829284668,
-0.16872133314609528,
0.016709066927433014,
-0.6365830302238464,
0.18717233836650848,
-0.12269286811351776,
0.08304440975189209,
0.0211605504155159,
0.3926592171192169,
-0.28385496139526367,
-0.24925848841667175,
-0.6886278986930847,
0.547568678855896,
0.3816220760345459,
-0.33919525146484375,
0.4051527976989746,
-0.6504292488098145,
0.33931228518486023,
0.9070817232131958,
0.2110012024641037,
0.5262448191642761,
-0.2752547860145569,
0.03868040069937706,
-0.11162912100553513,
0.24511480331420898,
-0.24811287224292755,
-0.11182834953069687,
-0.46936213970184326,
0.7987250685691833,
0.09112603962421417,
0.21709729731082916,
0.19773951172828674,
0.5956543684005737,
-0.19349008798599243,
-0.32292571663856506,
0.07259179651737213,
-0.5394834876060486,
-0.2240266501903534,
0.24236364662647247,
-0.1787939816713333,
-0.1318824142217636,
-0.37923750281333923,
-0.8907973766326904,
0.19832341372966766,
-0.607930064201355,
-0.2761608064174652,
0.5754504799842834,
-0.10496866703033447,
0.5126422643661499,
-0.0671147033572197,
0.4415760934352875,
0.5576223731040955,
-0.5066497921943665,
-0.2616564929485321,
0.09527638554573059,
-0.0602726936340332,
-0.017163829877972603,
0.3243448734283447,
0.04236610233783722,
0.0630345419049263,
-0.0031628208234906197,
-0.4930724799633026,
-0.337764710187912,
-0.23000119626522064,
0.5364794731140137,
-0.053991060703992844,
-0.2762593924999237,
0.35029375553131104,
0.45808807015419006,
-0.8592443466186523,
-0.2376369833946228,
-0.6450666785240173,
0.1790998876094818,
-0.20763005316257477,
-0.48893770575523376,
0.024286439642310143,
-0.0013075958704575896,
-0.3813006281852722,
-0.2740395963191986,
-1.154767632484436,
-0.21925422549247742,
0.9286724925041199,
0.2615957260131836,
-0.7912878394126892,
-0.1822100430727005,
0.4894110858440399,
0.20225954055786133,
0.1111619770526886,
-0.6305509209632874,
0.1518978476524353,
0.2016105204820633,
0.2756935954093933,
-0.11666334420442581,
-0.05781741812825203,
0.37526020407676697,
0.18916693329811096,
0.15693503618240356,
0.07382875680923462,
0.5954676270484924,
-0.9652039408683777,
-0.47772738337516785,
-0.27597224712371826,
0.3853769600391388,
0.7438319325447083,
-0.12953011691570282,
0.26380351185798645,
0.40252670645713806,
0.2371201068162918,
0.806094229221344,
0.27401143312454224,
0.2635970115661621,
0.3502761423587799,
-0.3600100576877594,
0.5328002572059631,
0.7382541298866272,
0.3440859913825989,
-0.38712838292121887,
0.33784642815589905,
-0.3499069809913635,
-0.10710704326629639,
0.22192542254924774,
-0.5226780772209167,
0.5259529948234558,
-0.6875787377357483,
0.694171130657196,
-0.06348550319671631,
0.03442290797829628,
-0.2720487713813782,
0.6542465090751648,
-0.5932723879814148,
-0.40692198276519775,
0.1361440271139145,
0.4135744869709015,
0.2220294326543808,
-0.4919581413269043,
0.2764608860015869,
-0.0713430717587471,
-0.4484848976135254,
-0.20331381261348724,
0.3993080258369446,
1.3204389810562134,
-0.08692063391208649,
-0.1509731411933899,
0.8253430128097534,
-0.1028822660446167,
-0.9703580141067505,
0.16183139383792877,
-0.9376577138900757,
0.14564189314842224,
-0.4947567582130432,
-0.38346245884895325,
0.46870702505111694,
-0.8517854809761047,
1.1013644933700562,
-0.31974393129348755,
0.19155701994895935,
0.7411249279975891,
-0.5757025480270386,
0.5218326449394226,
0.25424841046333313,
0.3567436933517456,
-0.3877484202384949,
0.9992883801460266,
-0.9529720544815063,
-0.1620658040046692,
-1.1484571695327759,
0.399818480014801,
0.5302839279174805,
-0.588085949420929,
-0.0295606330037117,
-0.2098277062177658,
-0.30846095085144043,
0.4067034423351288,
0.5358515977859497,
-0.711245596408844,
-0.3498065769672394,
1.0133157968521118,
-0.2719557285308838,
-0.4530543088912964,
-1.512365698814392,
0.23240138590335846,
0.2295868843793869,
0.3808336555957794,
0.41232746839523315,
-0.13530290126800537,
-0.22837865352630615,
0.7019320726394653,
0.3146442770957947,
-0.592339038848877,
-0.20551139116287231,
0.37312567234039307,
0.9685234427452087,
0.1491769552230835,
-0.1607075333595276,
-0.3115573823451996,
-0.24079225957393646,
0.3182407319545746,
0.3094450831413269,
-0.7824247479438782,
-0.10003987699747086,
0.5235697627067566,
-0.024213889613747597,
-0.4918070435523987,
0.5215877294540405,
-0.391451895236969,
-0.5717188119888306,
0.40234655141830444,
-0.4442902207374573,
0.7154595255851746,
-0.3487652838230133,
0.19411823153495789,
-0.42547085881233215,
0.13166937232017517,
0.6888403296470642,
0.23220881819725037,
0.14010296761989594,
0.38151493668556213,
0.2581014633178711,
0.33029159903526306,
0.28406983613967896,
0.019724678248167038,
-0.2344813197851181,
-0.3780421316623688,
-0.37731656432151794,
-0.02223927713930607,
-0.630079448223114,
0.07558847218751907,
0.08112160861492157,
0.42957887053489685,
0.3494831919670105,
1.0357223749160767,
-0.23442699015140533,
-0.41966554522514343,
-0.31746232509613037,
-0.6349026560783386,
0.1816202998161316,
0.5615620017051697,
-0.1825399398803711,
-0.4292798340320587,
-0.48932722210884094,
-0.530475914478302,
0.0947066992521286,
0.054643113166093826,
-0.2605126202106476,
-0.42053306102752686,
-0.12464819103479385,
0.07956601679325104,
-0.27207067608833313,
-0.12263872474431992,
-0.06316176056861877,
0.622698962688446,
0.32422366738319397,
0.5766415596008301,
1.2407073974609375,
-0.3645820915699005,
-0.3379484713077545,
0.015414335764944553,
0.7348019480705261,
0.3849858045578003,
0.381503164768219,
0.08359791338443756,
-0.03469487279653549,
0.2115514874458313,
-0.3469308018684387,
-0.6569563150405884,
-0.6921901702880859,
-0.17608028650283813,
-0.18859359622001648,
0.4885980188846588,
0.16296271979808807,
0.15747274458408356,
0.64696204662323,
-0.10650105774402618,
0.7393710017204285,
0.25373736023902893,
0.6046642065048218,
0.0687713548541069,
0.35438862442970276,
0.3394930362701416,
0.03473637253046036,
0.3184822201728821,
-0.6090382933616638,
-0.3102883994579315,
0.07592770457267761,
0.2511029839515686,
-0.15888671576976776,
-0.1895817369222641,
-0.12499399483203888,
-0.15272672474384308,
-0.09239304065704346,
0.92831951379776,
-0.9262887239456177,
0.5510981678962708,
0.1644751876592636,
1.250925898551941,
-0.16758817434310913,
0.2821228802204132,
0.28651687502861023,
0.16256122291088104,
0.5469258427619934,
-0.508601188659668,
0.28332871198654175,
-0.8253271579742432,
0.22213974595069885,
0.431879460811615,
-1.4069911241531372,
-0.8737378716468811,
-0.5654026865959167,
0.0325772762298584,
-0.5241169333457947,
0.6969364285469055,
1.3381850719451904,
0.11550669372081757,
0.002404330763965845,
-0.3524734079837799,
-0.4948733150959015,
1.0679030418395996,
-0.36951348185539246,
-0.5083552002906799,
0.39386415481567383,
0.008995305746793747,
-0.11707338690757751,
0.5201047658920288,
0.06643576920032501,
-0.6842783093452454,
0.012700176797807217,
-0.17333048582077026,
0.7793857455253601,
-0.6993349194526672,
-0.528269350528717,
-0.19746677577495575,
-0.3723806142807007,
-0.11363447457551956,
0.3335726857185364,
0.02473939210176468,
0.28551119565963745,
0.5185656547546387,
0.3102954626083374,
0.14522379636764526,
0.0705869272351265,
-0.18584153056144714,
-0.5677565336227417,
1.1275757551193237,
0.4959607422351837,
0.2215554416179657,
0.14958710968494415,
0.08554445207118988,
-0.3290179967880249,
0.06644309312105179,
0.0722123384475708,
0.5155179500579834,
-0.1925501674413681,
-0.22656868398189545,
-0.16964608430862427,
-0.5971089005470276,
-0.43004512786865234,
0.12435556203126907,
-0.06922896206378937,
0.433904230594635,
-0.05172950401902199,
-0.45753172039985657,
-0.4110049307346344,
0.31144988536834717,
-0.9456201791763306,
0.5116247534751892,
0.02212715707719326,
-0.9801414012908936,
0.9980064034461975,
-0.6740766167640686,
-0.25951215624809265,
-0.9120646119117737,
0.11452358216047287,
-0.26600390672683716,
0.21038247644901276,
0.5020467042922974,
0.911787748336792,
0.4104325771331787,
-0.9052706956863403,
0.6821728944778442,
-0.28682973980903625,
0.09658621996641159,
-0.49160072207450867,
-0.5683186650276184,
0.20930646359920502,
-0.21717002987861633,
0.19046249985694885,
0.48561617732048035,
-0.12889286875724792,
-0.3699057698249817,
0.12065267562866211,
-0.313005656003952,
0.2969282567501068,
-0.3507314920425415,
-0.3155006468296051,
0.4825116991996765,
0.30167967081069946,
-0.3413781225681305,
-0.08374550193548203,
0.6483720541000366,
-0.3892224133014679,
0.4201478064060211,
0.44126608967781067,
-0.8313184976577759,
0.2485436350107193,
-0.01648724637925625,
0.19603006541728973,
-0.8076778650283813,
-0.4028281569480896,
-0.26293423771858215,
-1.024623990058899,
0.17232631146907806,
0.08814812451601028,
0.1403273046016693,
-0.7246416807174683,
-1.1889230012893677,
-0.44604334235191345,
0.3540733754634857,
-0.15235616266727448,
-0.441342830657959,
-1.017102837562561,
0.06549204140901566,
-0.34623631834983826,
1.0321474075317383,
-0.008388839662075043,
0.16480201482772827,
-0.03780112415552139,
-0.23426620662212372,
0.08607354760169983,
0.5186218023300171,
-0.03552813455462456,
0.040574073791503906,
0.0592317208647728,
0.22164717316627502,
-0.1516767144203186,
0.5190945267677307,
-0.76352459192276,
0.7979354858398438,
-0.6086879968643188,
0.6354913115501404,
-0.2878803610801697,
0.0798296108841896,
-0.03272058814764023,
-0.32873260974884033,
0.5591035485267639,
-0.19259896874427795,
0.1808793544769287,
0.663657546043396,
0.022562341764569283,
0.4361327588558197,
0.29745522141456604,
-0.8135975003242493,
0.08180408179759979,
-0.682773232460022,
-0.49451494216918945,
0.36341536045074463,
-0.08540601283311844,
-0.15397435426712036,
-0.017373407259583473,
-0.4347724914550781,
-0.24911528825759888,
0.06964966654777527,
0.8087814450263977,
0.589406430721283,
0.08865136653184891,
0.19035089015960693,
-0.20221522450447083,
-0.3986867070198059,
-0.1442376971244812,
0.4088907837867737,
0.02180374227464199,
-0.25622859597206116,
-0.3293277323246002,
0.3125781714916229,
-0.4066678583621979,
-0.9021618366241455,
-0.4712264835834503,
0.42377570271492004,
0.27415958046913147,
-0.3513789176940918,
1.0602253675460815,
-0.22491738200187683,
-0.4968746304512024,
0.13797709345817566,
0.2708706855773926,
0.07410358637571335,
0.5701228380203247,
0.65816730260849,
0.11767180263996124,
0.8220086693763733,
0.5814173221588135,
0.9967491626739502,
-0.2059083729982376,
-0.13164573907852173,
0.4951760768890381,
-0.08005164563655853,
-0.33389803767204285,
0.2906133532524109,
0.23603390157222748,
-0.5660210847854614,
0.1647842973470688,
-0.7990493178367615,
0.45083126425743103,
-0.5486997365951538,
0.0010713161900639534,
-0.6870031356811523,
0.33117952942848206,
-0.7051620483398438,
0.558039665222168,
0.4085492491722107,
0.3009862005710602,
-0.5345969796180725,
-0.6218682527542114,
-0.5200967192649841,
-0.41576021909713745,
-0.49089357256889343,
1.5512155294418335,
0.13266386091709137,
-0.392225980758667,
0.49053117632865906,
-0.245441272854805,
-0.3460094928741455,
0.46477189660072327,
0.866769552230835,
-0.42628273367881775,
-0.03814822435379028,
-0.2172798216342926,
0.29415997862815857,
0.5099480748176575,
0.7264264822006226,
0.23291750252246857,
0.24401739239692688,
0.010104321874678135,
-0.8044062852859497,
-0.3348195254802704,
-0.21428273618221283,
0.0466286763548851,
-0.17933624982833862,
0.12052210420370102,
0.08815740793943405,
0.19619587063789368,
-0.8283992409706116,
-0.15226276218891144,
-0.3725738227367401,
-0.06296151131391525,
-0.8257137537002563,
0.10786005854606628,
0.06706944853067398,
-0.1775040179491043,
0.04661490395665169,
1.1320372819900513,
0.2593538761138916,
-0.6529322266578674,
-0.4730512797832489,
0.2953551411628723,
0.6496251821517944,
0.16315266489982605,
-0.0429864339530468,
-1.2135655879974365,
0.3358950614929199,
-0.31814077496528625,
-0.5147424340248108,
0.02624308131635189,
-0.3835325539112091,
0.12698420882225037,
-0.04754350334405899,
0.4618091881275177,
0.09341146051883698,
1.3167524337768555,
-1.0982110500335693,
-0.4767162501811981,
-0.3221794068813324,
-0.5545016527175903,
-0.6191228032112122,
0.23908774554729462,
0.15869782865047455,
0.501524806022644,
0.9097166061401367,
-0.33381181955337524,
-0.17872774600982666,
0.27073970437049866,
-0.5709412693977356,
0.19911709427833557,
0.19939886033535004,
0.8183141350746155,
-0.5426257848739624,
-0.6210070848464966,
-0.503565788269043,
0.4126940071582794,
-1.430798888206482,
0.059444352984428406,
-1.0465401411056519,
0.25327014923095703,
0.20050831139087677,
-0.06399549543857574,
-0.3612658381462097,
0.8147044777870178,
0.37297216057777405,
1.1252830028533936,
-0.6218222975730896,
-0.287605345249176,
0.5301515460014343,
0.18860755860805511,
-0.24666360020637512,
-0.14775879681110382,
-0.4267856478691101,
-0.3632987141609192,
-0.48778218030929565,
1.0367335081100464,
0.16408857703208923,
-0.1386854201555252,
-0.38817647099494934,
-0.10511761903762817,
-0.2448016107082367,
-0.4935324490070343,
-0.8702837228775024,
0.3261737823486328,
0.30772730708122253,
-0.6038476228713989,
-0.18013224005699158,
-0.8006392121315002,
-0.7691093683242798,
0.4299774765968323,
-0.420139342546463,
-0.14850005507469177,
0.4241073727607727,
-0.761502206325531,
0.28282105922698975,
-0.007088115438818932,
-0.4855089783668518,
-0.0905606746673584,
0.03658756613731384,
0.771267831325531,
0.2653498649597168,
0.029656706377863884,
-0.7388186454772949,
0.14617295563220978,
-0.8589000701904297,
0.3717517852783203,
-0.9301071763038635,
0.44667601585388184,
-0.8463904857635498,
-1.5601388216018677,
0.3530419170856476,
0.0752527117729187,
-0.30399325489997864,
-0.12863776087760925,
-0.35692355036735535,
0.27580103278160095,
-0.434205561876297,
-0.20655831694602966,
-0.7830014824867249,
-0.47442513704299927,
-0.34839507937431335,
0.28273800015449524,
-0.3334037959575653,
0.06080032140016556,
0.20420783758163452,
0.21884439885616302,
0.7750632762908936,
-0.4717857241630554,
-0.3685230612754822,
0.9865174889564514,
0.3136463165283203,
-0.5614410638809204,
0.3401387929916382,
0.5044413805007935,
-0.09974118322134018,
-0.04730953276157379,
-1.1767574548721313,
0.3980596959590912,
0.2848636507987976,
0.37257811427116394,
0.6691151261329651,
0.5161927938461304,
0.12360772490501404,
0.2047559767961502,
0.4585682451725006,
0.4434250295162201,
-0.4979970455169678,
0.8502289652824402,
-0.19509759545326233,
0.747369110584259,
0.4294483959674835,
0.16462530195713043,
0.09956841915845871,
-0.21781973540782928,
-0.08563879877328873,
0.261905699968338,
0.011172805912792683,
-0.403579980134964,
-0.324070543050766,
-0.15769580006599426,
-0.5075845122337341,
-0.40866100788116455,
-0.41625121235847473,
0.1430407613515854,
0.7208484411239624,
-0.0546700619161129,
-0.18594352900981903,
0.5878533720970154,
0.4382105767726898,
0.23840521275997162,
-0.22233615815639496,
0.428914338350296,
-0.13954123854637146,
0.9197934865951538,
0.15966612100601196,
0.7702818512916565,
0.28519096970558167,
0.30085763335227966,
0.44094523787498474,
-1.1762102842330933,
0.3461340069770813,
0.7585917115211487,
-0.46301522850990295,
-0.3454039692878723,
-0.4730062186717987,
-0.24660620093345642,
-0.1618385910987854,
-0.18838798999786377,
0.18730191886425018,
-0.47113993763923645,
-0.0411803312599659,
0.5705220103263855,
-0.27619701623916626,
0.5090934038162231,
0.7451136112213135,
-0.2382834404706955,
-0.0942210927605629,
0.40661951899528503,
-0.0811346173286438,
-0.08479005098342896,
1.372471570968628,
1.3312063217163086,
-0.06443969905376434,
0.7117013335227966,
0.403076171875,
-0.4380800724029541,
0.11178311705589294,
0.5185886025428772,
-0.4802415668964386,
0.9632738828659058,
-0.26965001225471497,
-0.1906491070985794,
0.5359341502189636,
-0.0017008762806653976,
-0.2723162770271301,
-0.13148514926433563,
0.7946414947509766,
-0.23096565902233124,
-0.2102455198764801,
-0.7619690299034119,
1.132390022277832,
0.49224165081977844,
-0.48594000935554504,
-0.2538244426250458,
0.2690262794494629,
-0.2772744297981262,
-0.9000083208084106,
-0.47898367047309875,
0.10639600455760956,
-0.4263967275619507,
-0.23460593819618225,
-0.566510021686554,
-0.15731211006641388,
-0.2345808893442154,
-0.8510111570358276,
-0.34307074546813965,
-0.6365163326263428,
0.35106271505355835,
0.7026945352554321,
0.2487482726573944,
-0.030594471842050552,
-0.46508070826530457,
-0.47038665413856506,
-0.35445454716682434,
0.5434028506278992,
0.011471578851342201,
-0.25406360626220703,
0.7398105263710022,
0.7596604824066162,
-0.06076878681778908,
-0.0035017775371670723,
0.39877429604530334,
-1.0619741678237915,
0.4933216869831085,
-0.2435932755470276,
0.28367936611175537,
0.7833597660064697,
-0.10116245597600937,
0.41868826746940613,
0.8519436717033386,
0.04835137352347374,
0.49881601333618164,
-0.1726299673318863,
-0.3932890295982361,
-0.3657200336456299,
0.13221138715744019,
-0.5433762073516846,
0.23052774369716644,
-0.02336968667805195,
0.06832367181777954,
0.05757221207022667,
-0.9921807646751404,
4.319180965423584,
0.1623525619506836,
0.728279709815979,
0.5384532809257507,
0.08691872656345367,
0.792497456073761,
-0.04726545512676239,
-0.42224469780921936,
0.26558205485343933,
-0.5940777063369751,
0.009106948040425777,
0.29648855328559875,
0.36717918515205383,
-0.6227870583534241,
-0.130829319357872,
0.8824233412742615,
-0.30780652165412903,
-0.3437291979789734,
0.20235183835029602,
-0.7772164940834045,
-0.32107576727867126,
-0.6150927543640137,
0.17204654216766357,
0.5455982089042664,
0.2247268557548523,
-0.07069583237171173,
0.2832268178462982,
-0.6328705549240112,
0.11020475625991821,
-0.20703557133674622,
-0.8090180158615112,
-0.8827722072601318,
0.20375706255435944,
-0.23826907575130463,
-0.3797970414161682,
0.03830050677061081,
0.3776092231273651,
-0.5228905081748962,
-0.3590385317802429,
-0.11523184925317764,
-0.706672728061676,
-0.4661814570426941,
0.6032194495201111,
-0.5908353328704834,
-0.7431582808494568,
1.1424827575683594,
-0.47842615842819214,
0.6295733451843262,
0.493347704410553,
-0.402544766664505,
0.8690118789672852,
-0.176979660987854,
0.47875314950942993,
-0.3773301839828491,
-0.6042848229408264,
0.7130902409553528,
-0.3147900700569153,
-0.4023697078227997,
0.29301342368125916,
0.004922434221953154,
-0.18148617446422577,
-0.6369146704673767,
-0.15673474967479706,
0.3126845359802246,
0.48073431849479675,
0.48576048016548157,
-0.07000888884067535,
0.13655933737754822,
-0.288394957780838,
0.3609626889228821,
-0.035331059247255325,
-0.7099653482437134,
-0.6638470888137817,
0.5879119038581848,
0.509982705116272,
-0.055331990122795105,
-0.3261989951133728,
-0.09790131449699402,
0.31895384192466736,
-0.01935461349785328,
0.7281460165977478,
0.026754815131425858,
-0.7766770720481873,
-0.4452369809150696,
0.10331682860851288,
0.6402112245559692,
-0.18452486395835876,
-0.49000680446624756,
0.2738248407840729,
0.8865101337432861,
0.3665047585964203,
0.9166183471679688,
0.08467840403318405,
0.2581166923046112,
-0.6267295479774475
] |
Decuplet Baryon Structure from Lattice QCD
|
The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented giving the first model independent insight to the shape of the quark distribution in the baryon ground state. As in our octet baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent experimental measurements are available. The lattice prediction of the $\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good agreement with the experimental ratio.
|
Derek B. Leinweber, Terrence Draper, and R.M. Woloshyn
|
hep-lat hep-ph
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208025
|
hep-lat/9208026
|
[
0.3036125600337982,
-0.30608007311820984,
0.6559069156646729,
0.21787339448928833,
-0.13543078303337097,
-0.1284961849451065,
-0.04837454855442047,
-0.018053751438856125,
-0.46978574991226196,
1.5881136655807495,
1.1289783716201782,
-0.11838137358427048,
0.598145604133606,
-0.6589216589927673,
-0.6489084959030151,
0.8959463238716125,
-0.23519067466259003,
-0.6863703727722168,
-0.7730693221092224,
0.1557137668132782,
-0.10335402935743332,
-0.47980430722236633,
-1.464411735534668,
-0.9505606293678284,
-0.20914870500564575,
0.6474773287773132,
0.10250641405582428,
0.11963344365358353,
1.2874879837036133,
0.7034379243850708,
0.5278719067573547,
-0.7850565314292908,
0.32493671774864197,
-0.247602641582489,
-1.0461665391921997,
-0.48933035135269165,
-0.02320113219320774,
-0.33082956075668335,
0.17919914424419403,
-0.47232794761657715,
1.318086862564087,
-0.6537719964981079,
0.9336175918579102,
-0.03634544461965561,
-0.35226163268089294,
0.23493117094039917,
-0.29425889253616333,
-0.15633557736873627,
-0.2480522245168686,
-1.2469301223754883,
-0.05963672325015068,
0.13247238099575043,
-0.0239300187677145,
0.12701450288295746,
-0.5320513844490051,
0.04389939829707146,
0.3484591841697693,
-0.4061671793460846,
-0.6159748435020447,
0.11548501998186111,
0.6163589954376221,
-0.0384012795984745,
0.4381507635116577,
-0.6322036981582642,
0.05532645806670189,
0.4619027376174927,
-0.18666276335716248,
0.230891615152359,
0.517800509929657,
-0.6262068152427673,
-1.0807132720947266,
-0.7298906445503235,
0.19684040546417236,
-0.23267154395580292,
-0.252875417470932,
-0.1079750508069992,
0.15904419124126434,
-0.6382805705070496,
-0.6876116991043091,
0.06817809492349625,
-0.12819579243659973,
-0.05425495654344559,
-0.8312827348709106,
-0.07386752218008041,
-0.7323444485664368,
-0.3679948151111603,
-0.1503911167383194,
0.01298674289137125,
0.3486142158508301,
0.5616318583488464,
0.6544663310050964,
0.970384955406189,
0.5582779049873352,
-0.22552987933158875,
0.45467132329940796,
0.9508917331695557,
0.1279788315296173,
0.8102601766586304,
0.3967289924621582,
-0.21501880884170532,
0.2501789629459381,
1.1211485862731934,
-0.34103861451148987,
0.2873833477497101,
-1.0847327709197998,
0.32485994696617126,
0.38487327098846436,
0.461608350276947,
-0.3173429071903229,
-1.0117621421813965,
-0.5430914163589478,
0.38255834579467773,
-0.052319396287202835,
0.03444577008485794,
-0.4690510928630829,
0.8836922645568848,
0.4013485908508301,
-0.7275267839431763,
-0.8214690089225769,
0.2706715762615204,
0.22710582613945007,
0.23851752281188965,
0.42803308367729187,
0.5237129926681519,
0.46559765934944153,
-0.6089591383934021,
0.1529524028301239,
1.0714781284332275,
-0.38037627935409546,
-0.19904763996601105,
0.24228157103061676,
-0.21002773940563202,
-0.41599875688552856,
0.8812485933303833,
0.34714555740356445,
0.18323810398578644,
0.19516617059707642,
0.18060559034347534,
0.20713791251182556,
-0.29565176367759705,
0.7075147032737732,
-0.3242727518081665,
0.1120532751083374,
1.2781251668930054,
0.43961983919143677,
0.08472216129302979,
0.5783392190933228,
-0.5837263464927673,
-0.25188252329826355,
-0.007448090240359306,
-1.1472176313400269,
0.1168881431221962,
-0.21545884013175964,
0.5937581658363342,
0.33608680963516235,
0.3661479353904724,
-0.2939416766166687,
0.401668518781662,
-0.871601939201355,
-0.33552366495132446,
0.577689528465271,
-0.24160276353359222,
-0.7936245799064636,
0.42201387882232666,
-1.3211191892623901,
0.39664316177368164,
-0.3434465527534485,
0.7288496494293213,
-0.02321299910545349,
-0.8654670715332031,
0.1557440608739853,
0.3387172222137451,
-0.3861560523509979,
0.7909318208694458,
0.36297616362571716,
1.0821839570999146,
0.893435001373291,
-0.22954343259334564,
0.3067655563354492,
0.3392638564109802,
-0.213904470205307,
-0.48314300179481506,
0.4954129159450531,
0.5254009366035461,
0.6485603451728821,
-0.16506139934062958,
-0.0028083883225917816,
-0.24120645225048065,
0.4758964478969574,
0.21939411759376526,
0.14436842501163483,
0.48292580246925354,
-0.45577767491340637,
0.3845263421535492,
-0.332745760679245,
-0.5267224311828613,
-0.4315017759799957,
0.7728655338287354,
-0.8797224760055542,
-1.0397909879684448,
-0.1491764634847641,
0.6562687754631042,
-1.0823982954025269,
0.5281647443771362,
-1.2233928442001343,
0.40528905391693115,
0.14735066890716553,
0.3322944939136505,
-0.34354469180107117,
-0.25347837805747986,
0.2464333325624466,
-0.15200617909431458,
0.5605917572975159,
0.14690656960010529,
-0.20308925211429596,
0.3223133385181427,
-0.37449219822883606,
0.5761564373970032,
0.41302844882011414,
-0.07462544739246368,
0.7292214632034302,
-0.058928027749061584,
-0.6450822353363037,
0.3758223354816437,
-0.3999054431915283,
-0.3639736771583557,
0.6272996664047241,
0.1985068917274475,
0.27038753032684326,
0.19815483689308167,
-0.5917631983757019,
0.44820019602775574,
-0.5080428719520569,
0.4321304261684418,
0.7616217732429504,
0.21820923686027527,
0.6175408959388733,
1.0445002317428589,
-0.2487102448940277,
0.3586031198501587,
0.12724339962005615,
0.07520555704832077,
0.473444402217865,
0.07135792821645737,
0.2297830581665039,
0.14437544345855713,
-0.7435411810874939,
0.053104087710380554,
-0.5104101300239563,
0.7405157685279846,
-0.7717466354370117,
1.2945492267608643,
0.5168505311012268,
-0.129737988114357,
-0.70076984167099,
0.29234156012535095,
0.10223623365163803,
0.6074653267860413,
-0.8953076601028442,
-0.4982122480869293,
0.3941742479801178,
0.09675800800323486,
-0.26159006357192993,
-0.19116905331611633,
0.11814495921134949,
1.479061484336853,
-0.32292723655700684,
0.9147465229034424,
-0.35253405570983887,
-0.5331562161445618,
-1.4926925897598267,
-0.29131728410720825,
-0.7032161951065063,
-0.588192343711853,
-0.01596021093428135,
0.1922520101070404,
1.0542875528335571,
-0.509843111038208,
1.1338906288146973,
-0.1056135818362236,
-0.6228264570236206,
0.5128310322761536,
-0.2658900022506714,
1.0301077365875244,
0.7361174821853638,
-0.1387186348438263,
-0.9449514150619507,
0.9806475639343262,
-0.4222843050956726,
0.1903643012046814,
0.10919896513223648,
-0.23446018993854523,
0.3799830675125122,
-0.25243303179740906,
0.4808763265609741,
-0.04530070722103119,
-0.21373531222343445,
0.14143382012844086,
-0.031054114922881126,
-0.4590533673763275,
0.17726564407348633,
0.355487197637558,
-0.4397164285182953,
-0.5772940516471863,
-0.3550218641757965,
0.9547787308692932,
0.41575804352760315,
-0.9901094436645508,
0.8381562232971191,
0.5522975325584412,
0.0808413028717041,
0.005418726708739996,
-0.4072314202785492,
0.38515543937683105,
-0.048977311700582504,
1.3546359539031982,
0.973666787147522,
-0.2759071886539459,
-0.06209788843989372,
-0.9227533936500549,
-0.138386070728302,
0.3241497874259949,
-0.12336668372154236,
-0.5807857513427734,
-0.25847122073173523,
1.0698177814483643,
-0.032867152243852615,
-0.9540942311286926,
0.354592889547348,
-0.861455500125885,
-0.2057299166917801,
0.4020199477672577,
-0.609246015548706,
0.6836091876029968,
0.2681318521499634,
0.16405627131462097,
-0.20903268456459045,
-0.4672679603099823,
0.14221833646297455,
0.2908845543861389,
0.12375745177268982,
-0.616113007068634,
-0.049806106835603714,
0.5896244049072266,
0.39073240756988525,
-0.14791738986968994,
0.4081698954105377,
-0.37766680121421814,
-0.04975443705916405,
-0.013197986409068108,
-0.32014545798301697,
0.6740937829017639,
0.35061144828796387,
0.2115900069475174,
-0.25646352767944336,
0.6056886911392212,
-0.7767966985702515,
-0.9247568845748901,
-0.46998462080955505,
-0.5096918940544128,
-0.1623263657093048,
-0.0870366245508194,
-0.8012765645980835,
0.2567046582698822,
-0.8198844790458679,
-0.11296384036540985,
0.8133940100669861,
0.3718161880970001,
1.1236560344696045,
-0.8096250891685486,
0.5768019556999207,
-0.027968743816018105,
0.17883014678955078,
0.0820876881480217,
0.2807365953922272,
0.1980646401643753,
0.17076809704303741,
0.0363273099064827,
0.7711260914802551,
-0.8696252107620239,
-0.6353175640106201,
-0.3970997631549835,
0.07757338881492615,
1.1418708562850952,
0.8742538094520569,
1.1089797019958496,
-0.20759767293930054,
-0.3586423695087433,
-0.25123050808906555,
-0.3855949938297272,
-0.4514659643173218,
-0.5607094168663025,
0.16044044494628906,
-0.49902600049972534,
-0.2800782024860382,
-0.0322851836681366,
0.3571033775806427,
0.8459205031394958,
0.5004869103431702,
0.6552636623382568,
0.08014755696058273,
-0.05845586955547333,
0.2771266996860504,
0.7258267402648926,
-0.7853265404701233,
0.12695035338401794,
-1.1617698669433594,
0.5289124250411987,
-0.014564457349479198,
0.08973730355501175,
0.013438181951642036,
-0.842653214931488,
-0.12943598628044128,
-0.5820632576942444,
0.22842946648597717,
-0.08868366479873657,
-0.33590710163116455,
0.40007904171943665,
-0.14418672025203705,
0.3828842043876648,
-0.5116885304450989,
-0.5818934440612793,
0.41367581486701965,
0.7895399928092957,
-0.05426609516143799,
-1.2397047281265259,
-0.21591824293136597,
-0.27469441294670105,
1.242079734802246,
0.7248086333274841,
-0.2875920832157135,
-1.1171458959579468,
0.10518745332956314,
-0.18134836852550507,
-0.7965418100357056,
-0.129516139626503,
1.1207361221313477,
-0.5893165469169617,
0.024275073781609535,
-0.3134858012199402,
-0.2691132128238678,
0.615132212638855,
-0.3830747902393341,
-0.7029314041137695,
0.19771930575370789,
0.050319500267505646,
0.10571986436843872,
0.5478968620300293,
-0.4641113877296448,
-0.0854988619685173,
-0.0844314768910408,
-0.058454014360904694,
0.14873860776424408,
-0.4590481221675873,
-0.279972106218338,
-0.2710326910018921,
-0.8254391551017761,
-0.42649441957473755,
0.5350938439369202,
0.3687443137168884,
0.26590585708618164,
0.24667109549045563,
0.07179480791091919,
-0.60476154088974,
-0.519977867603302,
0.09234729409217834,
0.4821512997150421,
0.03307917341589928,
1.0047996044158936,
0.10010939091444016,
0.08812297880649567,
0.5415641069412231,
0.15245398879051208,
-0.1503400057554245,
0.8063077330589294,
0.7837775945663452,
-0.07277557253837585,
-0.02558300457894802,
-0.1294255405664444,
-0.7099456787109375,
-0.326358824968338,
0.17642493546009064,
-0.251660019159317,
0.8737632036209106,
0.07624588906764984,
-0.7565131187438965,
-0.4890584349632263,
-0.3969906270503998,
-0.32174474000930786,
0.2787633538246155,
-0.010628574527800083,
-0.018703769892454147,
0.6700606942176819,
-0.9677819609642029,
0.3322273790836334,
0.31243133544921875,
0.3168621361255646,
-0.4065794050693512,
-0.011284868232905865,
1.043337345123291,
-0.18924294412136078,
0.9004698395729065,
-0.7983768582344055,
0.010291198268532753,
-0.8356186151504517,
0.4948975145816803,
-0.27832546830177307,
0.18734444677829742,
-0.17396683990955353,
0.19541361927986145,
-0.09882467240095139,
-0.7089192271232605,
0.8850154280662537,
-0.3909122943878174,
-0.009613771922886372,
-0.14448018372058868,
0.033538080751895905,
0.45597657561302185,
-0.783207356929779,
0.7533603310585022,
-0.3741932511329651,
-0.992963969707489,
0.24290814995765686,
0.9146848320960999,
-0.09603036940097809,
0.871715784072876,
-0.4843527376651764,
-0.44342437386512756,
0.15105539560317993,
-0.9802325963973999,
0.49108290672302246,
-0.6075651049613953,
-0.5254393815994263,
-0.47109454870224,
-0.4981629550457001,
0.38631683588027954,
0.28808024525642395,
0.2640671730041504,
0.4769672155380249,
-0.03166084736585617,
-0.9433849453926086,
-0.05253166705369949,
-0.7060452699661255,
-0.5501466989517212,
-0.647221028804779,
-0.2821153700351715,
-1.0430430173873901,
0.53741455078125,
-0.3210676312446594,
-0.3368251323699951,
0.2892930507659912,
-0.27910006046295166,
-0.12519317865371704,
0.27422070503234863,
-0.4177565276622772,
-0.21033410727977753,
-0.3413769006729126,
0.962094783782959,
0.03795367106795311,
0.5076425671577454,
-0.6310800909996033,
0.5959909558296204,
-1.0906801223754883,
0.9711055755615234,
-0.16753411293029785,
-0.5072314143180847,
0.40615037083625793,
-0.2296406626701355,
0.9875906109809875,
-0.2560780346393585,
0.3644265830516815,
-0.23093833029270172,
-0.37940824031829834,
0.5077971816062927,
0.5238616466522217,
-0.9444422125816345,
-0.3607049882411957,
-0.4372680187225342,
-0.8277990221977234,
0.6274039149284363,
-0.24886910617351532,
-0.6094561815261841,
-0.875852644443512,
-0.5997520685195923,
0.3658679723739624,
0.041724320501089096,
0.5532491207122803,
0.7876477837562561,
-0.5824265480041504,
0.19000524282455444,
0.24014391005039215,
0.44428926706314087,
-0.2980433404445648,
-0.13643641769886017,
-0.07017166912555695,
0.08655355870723724,
-0.7223116755485535,
-0.08924414962530136,
-0.882925271987915,
-1.0104495286941528,
-0.3893214762210846,
0.06100231409072876,
0.12483061850070953,
0.12411872297525406,
0.5164262652397156,
-0.43815839290618896,
-0.7964878082275391,
-0.4442886412143707,
0.07007535547018051,
0.07628235220909119,
0.1775090992450714,
0.14926029741764069,
-0.17664247751235962,
-0.47160789370536804,
0.24687743186950684,
0.7338980436325073,
-0.8357535004615784,
-0.49436208605766296,
0.7621914148330688,
-0.15089261531829834,
-0.7176030278205872,
0.44747576117515564,
-0.07837717235088348,
-0.5829039216041565,
-0.6537638902664185,
-0.8960428833961487,
-0.4097711741924286,
-0.12858541309833527,
-0.4411196708679199,
0.4312034845352173,
0.24254070222377777,
-0.3205718696117401,
0.9167591333389282,
0.654942512512207,
-0.46607574820518494,
0.30247506499290466,
0.1482427567243576,
-0.07040300220251083,
-0.4939902126789093,
0.4550376832485199,
0.8688839077949524,
-0.4849108159542084,
-0.501148521900177,
-0.31246423721313477,
-0.7431224584579468,
0.21328981220722198,
0.0008692345581948757,
-0.014937911182641983,
0.07470262050628662,
0.652280867099762,
0.26734909415245056,
0.2469741553068161,
-0.2633899748325348,
0.41478097438812256,
0.6285465955734253,
0.43399232625961304,
-0.3360059857368469,
-0.8461532592773438,
-0.8594375848770142,
-0.3132617473602295,
0.29283496737480164,
1.1902974843978882,
-0.3204061686992645,
0.5630024075508118,
-0.16623671352863312,
-0.33198171854019165,
-0.8413463830947876,
-1.113147258758545,
0.3384303152561188,
-1.5163196325302124,
-0.5729473829269409,
-0.811893880367279,
-0.5771843194961548,
0.7965320348739624,
0.17812515795230865,
0.29517465829849243,
-0.07879873365163803,
-0.5940790176391602,
0.21287737786769867,
0.3555637001991272,
0.11099498718976974,
-0.3149947226047516,
-0.4568759500980377,
-0.5758663415908813,
-0.5165224075317383,
-0.8628117442131042,
0.2505125105381012,
0.2452925592660904,
-0.016738271340727806,
-0.5188067555427551,
0.3706718385219574,
-0.3187005817890167,
0.4734864830970764,
-0.637844443321228,
-0.901475727558136,
-0.01051248423755169,
-0.22548703849315643,
-0.7398786544799805,
-0.2430541068315506,
-0.7120265364646912,
0.1861501783132553,
-0.07176868617534637,
-0.24887406826019287,
-0.07742058485746384,
-0.1238003522157669,
-0.8147016763687134,
-0.09133236110210419,
0.04048500582575798,
0.4541964530944824,
-0.578088104724884,
-0.6791839599609375,
0.6177145838737488,
0.44031912088394165,
-1.0162043571472168,
0.6775580644607544,
-0.6165553331375122,
0.02370632067322731,
-0.30794811248779297,
0.19675405323505402,
-0.28665822744369507,
1.0039503574371338,
-0.08470083028078079,
1.053997278213501,
-0.34549766778945923,
-0.11323725432157516,
0.12653565406799316,
0.5801169276237488,
0.19280961155891418,
0.7004024982452393,
-0.12583096325397491,
-0.6935134530067444,
0.706635594367981,
0.19748230278491974,
-0.562476634979248,
0.045647162944078445,
-0.17617729306221008,
-0.3826720118522644,
0.10211978852748871,
0.3815547227859497,
-0.49185827374458313,
0.7158712148666382,
-0.14697358012199402,
-0.5748946070671082,
0.07884712517261505,
-0.42990434169769287,
-0.6346156001091003,
0.21350641548633575,
-1.3876848220825195,
-0.35158097743988037,
-0.6238229870796204,
0.012703207321465015,
-0.5943713188171387,
0.02760825678706169,
-0.6572657227516174,
-0.37470099329948425,
-0.32725346088409424,
-0.20366577804088593,
-0.15704457461833954,
0.022987201809883118,
-0.36635416746139526,
-0.027904028072953224,
-0.8726941347122192,
-0.6510259509086609,
-0.19443188607692719,
0.8072230219841003,
-0.4732958674430847,
-0.4416201710700989,
-0.29853346943855286,
-0.15807068347930908,
-0.014919562265276909,
0.03712679073214531,
-0.35263529419898987,
-0.47243520617485046,
0.348526269197464,
0.224766805768013,
0.12202432006597519,
0.07353101670742035,
-0.29919371008872986,
0.44394564628601074,
0.4463798403739929,
-1.1343485116958618,
0.3700093924999237,
0.17608551681041718,
0.3355134129524231,
-0.05377640947699547,
-0.5493800640106201,
1.3607944250106812,
0.6157454252243042,
-0.9382206797599792,
0.9292508959770203,
-0.72698974609375,
0.9380853176116943,
0.11713887751102448,
-0.05933883413672447,
0.13773974776268005,
0.2941431701183319,
0.5626628994941711,
0.5806474089622498,
0.7648692727088928,
0.27927136421203613,
0.9159595966339111,
-0.4111928939819336,
-0.1384071260690689,
-0.18004918098449707,
0.5437494516372681,
-0.04328984394669533,
0.17327478528022766,
-0.20846933126449585,
0.5278122425079346,
-0.5796513557434082,
-0.18111789226531982,
-0.35835790634155273,
0.0045964838936924934,
-0.12582388520240784,
0.2895950973033905,
0.2064199000597,
0.5440065860748291,
-0.31902024149894714,
-0.35680118203163147,
-0.7369399070739746,
0.3199239671230316,
0.14624731242656708,
0.2376457303762436,
-0.12786510586738586,
0.289897620677948,
0.6806337237358093,
0.5035174489021301,
0.15354493260383606,
0.8766065835952759,
-0.3560042083263397,
0.27244728803634644,
0.08376572281122208,
1.1132709980010986,
0.8095914125442505,
-0.17949527502059937,
-0.055688876658678055,
-0.8638573288917542,
-0.06922189891338348,
1.1931782960891724,
-1.7716561555862427,
0.6230840086936951,
-0.12613104283809662,
-0.34665781259536743,
-0.1257535070180893,
-0.8501824140548706,
0.4886758029460907,
-0.4943619668483734,
0.5947564840316772,
0.9680249094963074,
0.23963266611099243,
-0.46277835965156555,
0.6019204258918762,
0.08432549983263016,
0.19701455533504486,
0.4903050661087036,
0.08701738715171814,
-0.32088929414749146,
0.987747311592102,
1.4607231616973877,
-0.0752178505063057,
0.7613173127174377,
0.386496365070343,
-0.8627992272377014,
0.17966832220554352,
0.3050200939178467,
-0.6026774644851685,
0.97999107837677,
-0.6028884649276733,
-0.9110174775123596,
0.27313360571861267,
0.30793339014053345,
-0.0482763834297657,
0.10021962970495224,
-0.6906886696815491,
0.6308885216712952,
-0.42828792333602905,
-0.750294029712677,
1.0834094285964966,
0.7312256097793579,
-0.2643808424472809,
-0.5787541270256042,
-0.10834584385156631,
-0.25097376108169556,
0.2896656095981598,
0.03051748313009739,
0.22002632915973663,
0.30732277035713196,
0.1593625396490097,
-0.3062986135482788,
-0.9827282428741455,
0.03068743273615837,
-1.1614094972610474,
-0.06094896420836449,
-0.09022513777017593,
0.6263795495033264,
0.182166188955307,
0.6431775689125061,
0.15942420065402985,
-0.6088595390319824,
0.04653463512659073,
0.29069268703460693,
1.0214120149612427,
0.01325512956827879,
-0.028692876920104027,
0.848900318145752,
0.26891714334487915,
-0.6206731796264648,
0.8031413555145264,
0.5032039284706116,
-0.1290774792432785,
0.3495587706565857,
-0.2658575177192688,
0.30064019560813904,
0.1709604263305664,
-0.2996752858161926,
0.8300437927246094,
0.0713425949215889,
0.4579783082008362,
-0.4635702967643738,
-0.08922452479600906,
-0.08933894336223602,
-1.180838942527771,
0.11079641431570053,
-0.8237259387969971,
0.083367720246315,
-0.22010943293571472,
0.6564954519271851,
0.40311500430107117,
0.06104811280965805,
3.796806812286377,
2.027183771133423,
0.6177417039871216,
0.08139931410551071,
0.5264384150505066,
0.4319600462913513,
0.2613056004047394,
-0.5102184414863586,
0.5747716426849365,
-1.310753345489502,
-0.18115819990634918,
0.014417302794754505,
0.4384576082229614,
-0.14639031887054443,
-0.18656988441944122,
0.5403976440429688,
-0.36226367950439453,
0.5333151817321777,
0.5446036458015442,
-0.5204635262489319,
-0.7175952792167664,
0.41166916489601135,
0.23778292536735535,
0.6559453010559082,
0.19590994715690613,
-0.2872448265552521,
0.5671551823616028,
-1.4585527181625366,
-0.9104968905448914,
-0.6500911116600037,
-0.6704267859458923,
-1.0906448364257812,
0.0075202020816504955,
-0.8493250012397766,
-0.8845827579498291,
0.6066527366638184,
0.2747819721698761,
-0.04846908897161484,
0.24003392457962036,
0.7343972325325012,
-0.01185622252523899,
0.6635257005691528,
0.20639824867248535,
-0.2599608600139618,
-1.1511318683624268,
0.7641879320144653,
-0.14508263766765594,
0.6634954214096069,
0.25426924228668213,
-0.41018936038017273,
0.36488524079322815,
-0.45306092500686646,
1.020617127418518,
-0.3865845203399658,
-1.1084485054016113,
-0.19747206568717957,
-0.20111703872680664,
-1.2289516925811768,
-0.14642854034900665,
0.31108927726745605,
0.47009173035621643,
-0.10551692545413971,
-0.27421873807907104,
0.12259800732135773,
-0.19267232716083527,
0.7777101993560791,
-0.17358869314193726,
-0.16144044697284698,
-0.3125059902667999,
-0.2975319027900696,
0.2688899338245392,
-0.7798025012016296,
-0.3161045014858246,
-0.26045191287994385,
0.4704722464084625,
-0.3100942373275757,
0.1563410758972168,
0.8423592448234558,
0.44274622201919556,
0.017459776252508163,
-0.4967145621776581,
-0.5381803512573242,
0.3857346177101135,
0.5731232166290283,
0.54830002784729,
0.7978082895278931,
-0.6868119239807129,
-0.6157862544059753,
0.4709272086620331,
0.23468635976314545,
0.7391560673713684,
1.853902816772461,
0.1952676624059677,
-0.0799834206700325,
-1.3717069625854492
] |
Numerical Study of Finite Size Scaling for First Order Phase Transitions
|
I present results of simulations of the q=10 and q=20 2-d Potts models in the transition region. The asymptotic finite size behavior sets in only for extremely large lattices. We learn from this simulation that finite size scaling cannot be used to decide that a transition is first order.
|
Alain Billoire
|
hep-lat cond-mat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208026
|
hep-lat/9208027
|
[
0.04783569648861885,
-0.30060118436813354,
-0.15470784902572632,
-0.08683333545923233,
-0.0567636601626873,
-0.2556473910808563,
0.05477641522884369,
-0.2029835432767868,
-0.5025392770767212,
1.4282644987106323,
0.1271732747554779,
-0.11382245272397995,
0.04633926600217819,
-0.13001126050949097,
0.3252885937690735,
0.4212884306907654,
-0.41105911135673523,
-0.5089799761772156,
-2.323180675506592,
1.1692520380020142,
0.4764084219932556,
-0.039742399007081985,
-0.8479874134063721,
-0.7638348937034607,
0.07293716073036194,
0.7593357563018799,
0.39620524644851685,
0.8351863622665405,
0.8084552884101868,
0.49536511301994324,
0.20714564621448517,
-0.12566162645816803,
-0.47036921977996826,
-0.5327244400978088,
-0.22530503571033478,
-0.18736936151981354,
-0.17246069014072418,
-0.6209672689437866,
0.9419825673103333,
-0.6973598599433899,
0.12455415725708008,
-0.4920385181903839,
-0.05564604327082634,
-0.5595831871032715,
-0.5703397393226624,
0.10051815211772919,
0.2970145344734192,
-0.12004664540290833,
-0.01808418147265911,
-1.453080654144287,
0.04334909841418266,
0.041830338537693024,
0.403799831867218,
-1.0435905456542969,
-0.22953833639621735,
0.1041450947523117,
0.21287092566490173,
-0.6054231524467468,
-1.0255781412124634,
0.01005723886191845,
0.3546120524406433,
0.11596596240997314,
0.44431114196777344,
-1.263565182685852,
-0.23298762738704681,
0.8674178719520569,
0.1492810994386673,
0.4810763895511627,
0.11238986253738403,
-0.6664866805076599,
-0.01673292927443981,
-0.2836292088031769,
-1.130861759185791,
-0.056775033473968506,
-0.12898924946784973,
0.23013654351234436,
0.11405650526285172,
-0.2058776170015335,
-0.12947483360767365,
-0.33602389693260193,
0.3005174398422241,
0.6874745488166809,
0.0672498419880867,
0.6041526794433594,
-0.5593560934066772,
-0.17202147841453552,
0.2921285927295685,
-0.13635140657424927,
0.23816455900669098,
-0.028999416157603264,
0.27704325318336487,
0.7393440008163452,
-0.37908467650413513,
0.21374911069869995,
0.5951288938522339,
0.5050517916679382,
-0.26400455832481384,
1.0643318891525269,
-0.05498639494180679,
0.3511820137500763,
0.12921321392059326,
1.3846218585968018,
-0.44415441155433655,
0.7307761311531067,
-1.2611981630325317,
-0.2105693370103836,
-0.6006141901016235,
0.21353043615818024,
-0.6070879101753235,
-0.7877638936042786,
0.6577437520027161,
-0.057404980063438416,
0.31199657917022705,
0.6978656649589539,
0.5385261178016663,
0.5697723031044006,
0.13518232107162476,
0.28370583057403564,
-0.6841879487037659,
-0.1379237174987793,
-0.19194383919239044,
-0.025717079639434814,
-0.00996344443410635,
0.3774716258049011,
-0.49791496992111206,
-0.6349987983703613,
0.033331409096717834,
0.11484707146883011,
-0.3105025291442871,
0.05960915610194206,
0.20438435673713684,
-0.007093227468430996,
0.08042117208242416,
0.5455867648124695,
-0.42385801672935486,
-0.20255617797374725,
-0.30826956033706665,
-0.025750821456313133,
-0.2417190819978714,
-0.33967986702919006,
0.38065439462661743,
-0.4993726909160614,
0.4008668065071106,
1.0452322959899902,
-0.2753552794456482,
-0.023308493196964264,
0.5776085257530212,
0.3142814040184021,
-0.1178286075592041,
-0.17417216300964355,
-0.11081448942422867,
-0.46102818846702576,
0.16665424406528473,
-0.039958979934453964,
0.30304282903671265,
0.09384132921695709,
-0.868989884853363,
0.53937828540802,
-0.5808801054954529,
-0.33594006299972534,
-0.31311628222465515,
0.25915369391441345,
0.11017299443483353,
0.8159233927726746,
-0.378030925989151,
-0.11098819971084595,
-0.3482927680015564,
-0.7773230671882629,
0.3504007160663605,
-0.9444388151168823,
-0.44510143995285034,
0.5065547823905945,
0.08572525531053543,
0.9426950812339783,
1.0889918804168701,
0.08358081430196762,
0.13498152792453766,
-0.11259867995977402,
0.03347094729542732,
0.8996755480766296,
-0.10629437118768692,
-0.9187576174736023,
0.8249313831329346,
0.3573935031890869,
-0.9760235548019409,
-0.5320501923561096,
0.01435003336519003,
-0.8582273721694946,
-0.2424803078174591,
-0.1705770641565323,
-0.36599865555763245,
0.49754634499549866,
-0.3400282859802246,
0.5633840560913086,
-1.3580248355865479,
0.7347385287284851,
-1.4104876518249512,
-0.24318499863147736,
-0.5663427710533142,
-0.17993545532226562,
-0.08217880129814148,
0.37727227807044983,
-1.2077924013137817,
0.1423020362854004,
-0.5864604711532593,
-0.043325819075107574,
0.38531509041786194,
0.4083951711654663,
-0.45567190647125244,
-0.4757513999938965,
0.2324698120355606,
-0.6337862610816956,
0.34085604548454285,
0.06516027450561523,
0.741589367389679,
-0.4000498950481415,
-0.28835368156433105,
-0.2073815017938614,
0.16130125522613525,
0.37316542863845825,
0.7221209406852722,
0.5176945924758911,
-0.22089187800884247,
1.0924614667892456,
-0.36864525079727173,
-0.2507982552051544,
-0.4661530554294586,
0.6262581944465637,
-0.08784029632806778,
0.35535046458244324,
-0.07501354813575745,
-0.2639894485473633,
0.46444615721702576,
0.7880092263221741,
0.8951261639595032,
-0.11707831174135208,
1.2760264873504639,
0.6181018948554993,
0.487527459859848,
0.35408979654312134,
-0.028820307925343513,
-0.054569777101278305,
0.5084432363510132,
-0.16245579719543457,
-0.41828683018684387,
0.6511309742927551,
-0.06922584772109985,
-0.35720258951187134,
-0.8414256572723389,
0.49582046270370483,
-0.9690340757369995,
0.6899966597557068,
-0.10231780260801315,
0.14370638132095337,
-1.3003597259521484,
0.377544105052948,
-0.3364778161048889,
0.21338380873203278,
-0.5405614972114563,
-0.4823228418827057,
0.3161132037639618,
0.05641549825668335,
0.14446218311786652,
-0.8239797949790955,
-0.2688685357570648,
0.956315815448761,
-0.10754654556512833,
-0.2967923879623413,
0.6671411991119385,
-0.2681429982185364,
-1.2548353672027588,
0.49877211451530457,
-1.0688215494155884,
0.24134497344493866,
-0.5574809312820435,
-0.05953042954206467,
0.5180174708366394,
0.09970062971115112,
0.39729368686676025,
-0.0962706208229065,
0.06878611445426941,
0.27530890703201294,
-0.012344574555754662,
-0.2539524435997009,
0.2436290979385376,
-0.03357677161693573,
-0.9057061672210693,
0.295397013425827,
-1.0856724977493286,
0.03441782295703888,
-0.6963160037994385,
-0.2607332468032837,
0.14010456204414368,
-0.009511653333902359,
0.2259092926979065,
-0.26083117723464966,
0.21047799289226532,
0.12746495008468628,
-0.09716375917196274,
-0.36021536588668823,
-0.16987167298793793,
0.5725776553153992,
0.16443641483783722,
-0.12414772808551788,
-0.8476823568344116,
1.1530348062515259,
0.0832662507891655,
-0.013998210430145264,
0.8453480005264282,
0.17116281390190125,
-0.49658650159835815,
0.8592839241027832,
0.33640891313552856,
-0.07691529393196106,
-0.05124036222696304,
0.9156332015991211,
1.2389318943023682,
-0.24052420258522034,
0.14307311177253723,
-0.14604124426841736,
-0.45908239483833313,
0.4497322142124176,
0.09919604659080505,
-0.852317750453949,
-0.11163226515054703,
1.0053421258926392,
0.13623328506946564,
-0.5318046808242798,
0.5655807256698608,
-1.1695550680160522,
-0.8016000390052795,
-0.208685040473938,
0.16320744156837463,
0.19439034163951874,
0.45552825927734375,
0.2526024580001831,
-1.2822157144546509,
-0.42676591873168945,
-0.4079408347606659,
0.1742534190416336,
0.9605239629745483,
-0.40448126196861267,
0.9869008660316467,
0.22874067723751068,
0.21019534766674042,
-0.6140934824943542,
0.42459988594055176,
-0.44952142238616943,
-0.011227953247725964,
0.05501868575811386,
-0.20808705687522888,
0.19596733152866364,
-0.2383642941713333,
-0.41990557312965393,
-0.19917532801628113,
0.3386695086956024,
-0.7963581085205078,
-0.39927762746810913,
-0.6852760910987854,
-0.06564979255199432,
0.12224327772855759,
0.8323277235031128,
0.04413830116391182,
-0.28253206610679626,
-1.0667297840118408,
-0.502889096736908,
-0.23307567834854126,
0.5600186586380005,
0.35119375586509705,
-1.0002504587173462,
0.6857468485832214,
0.34899047017097473,
-0.3620155155658722,
-0.20113635063171387,
0.028842167928814888,
0.5005168318748474,
0.5060263872146606,
0.7045396566390991,
0.6189985871315002,
-0.11085601150989532,
-0.483516663312912,
0.0877206027507782,
0.5492587089538574,
0.21229757368564606,
0.7346944212913513,
-0.0012894172687083483,
-0.0932764783501625,
-0.17043207585811615,
-0.31133684515953064,
-0.2828691005706787,
-0.27300912141799927,
-0.8533937931060791,
0.22699905931949615,
0.33374133706092834,
0.19709070026874542,
-0.06031375378370285,
0.41071170568466187,
0.9839739203453064,
0.37433698773384094,
-0.3814336657524109,
0.4003180265426636,
0.5474463701248169,
0.36088740825653076,
0.26606449484825134,
-0.37127020955085754,
-0.14439977705478668,
-0.3267308175563812,
0.7157001495361328,
0.22541677951812744,
-0.11387833952903748,
-0.04154062643647194,
-0.48319146037101746,
-0.064055897295475,
0.03772931918501854,
0.37901079654693604,
0.8266969919204712,
-0.8788253664970398,
0.21054278314113617,
0.09452545642852783,
0.19400453567504883,
-0.4774450659751892,
0.16403828561306,
1.210856318473816,
0.5593046545982361,
0.09935474395751953,
-0.5531625747680664,
0.20909731090068817,
0.015362491831183434,
0.10005474835634232,
0.5808148384094238,
-0.6610826849937439,
-0.5451566576957703,
-0.4856838285923004,
0.20888453722000122,
0.056770697236061096,
0.27699461579322815,
1.1084046363830566,
-0.14269304275512695,
0.2999669909477234,
-0.12918610870838165,
0.10221846401691437,
0.8091967701911926,
-0.604804277420044,
-0.281907856464386,
-0.24120977520942688,
0.03060152195394039,
0.03489179164171219,
1.1974769830703735,
-0.3159080147743225,
-0.19277122616767883,
-0.4859292507171631,
-0.015332958661019802,
0.04662717506289482,
-0.11330320686101913,
-0.5916013717651367,
-0.08098071813583374,
-0.06104153394699097,
-0.1206868439912796,
0.5749845504760742,
0.10994034260511398,
0.4734167754650116,
0.14424404501914978,
0.47205618023872375,
-0.3691903054714203,
-0.061874061822891235,
0.16347810626029968,
-0.4919271767139435,
0.9176576137542725,
0.23600797355175018,
0.5080169439315796,
-0.19980843365192413,
0.5577347874641418,
0.32445207238197327,
-0.26748281717300415,
0.166534423828125,
-0.16630838811397552,
-0.4375009834766388,
-0.12997910380363464,
-0.5965673327445984,
-0.09256491810083389,
-0.2147340476512909,
0.6012310981750488,
-0.28836771845817566,
0.5255438685417175,
0.16859927773475647,
-0.7030897736549377,
-1.1918443441390991,
-0.10701059550046921,
-0.20577239990234375,
0.4707823395729065,
-0.5039283037185669,
-0.07474693655967712,
0.5900252461433411,
-0.5717149376869202,
-0.003696171101182699,
-1.0731489658355713,
0.20055803656578064,
-0.19834767282009125,
-0.06591176241636276,
0.7180694341659546,
0.5925206542015076,
0.6805693507194519,
-0.5272629261016846,
0.434433251619339,
-0.5978830456733704,
-0.12972554564476013,
-0.7329541444778442,
-0.19631686806678772,
-0.14083506166934967,
-0.4221973419189453,
0.22900086641311646,
0.07389772683382034,
0.019101232290267944,
0.08828286826610565,
0.0770285576581955,
0.7595217823982239,
0.16773448884487152,
-0.8709542155265808,
-0.013460943475365639,
0.37865692377090454,
0.3912340998649597,
-0.752856969833374,
-0.15756241977214813,
0.38901177048683167,
0.3760709762573242,
-0.09607776254415512,
0.2057437002658844,
0.03970997780561447,
0.11856137216091156,
-0.6199960708618164,
0.4523746967315674,
-0.8506316542625427,
-0.5087412595748901,
-0.16669610142707825,
-0.606025218963623,
0.3846185803413391,
0.39148280024528503,
-0.07033485919237137,
-0.5350548624992371,
-0.38285133242607117,
-0.2744501829147339,
0.25354450941085815,
-0.9238648414611816,
0.672313928604126,
-1.1221414804458618,
-0.5184534192085266,
-0.4074728488922119,
0.9132816791534424,
-0.04983195662498474,
0.02120216377079487,
-0.08761968463659286,
0.28074467182159424,
-0.13072419166564941,
0.11514785885810852,
0.34193161129951477,
-0.19596904516220093,
-0.5288271903991699,
0.4148963987827301,
0.16968800127506256,
0.5314798951148987,
-0.236266627907753,
0.8529844284057617,
-0.19735917448997498,
0.8259879350662231,
-0.6352561116218567,
-0.3537448048591614,
0.17096535861492157,
0.21255621314048767,
0.5399661064147949,
-0.6551657915115356,
0.022781558334827423,
0.604546844959259,
0.2944512665271759,
0.4893418252468109,
-0.14749766886234283,
-0.31758248805999756,
-0.36991265416145325,
-0.5882347822189331,
-0.5477883815765381,
0.298304945230484,
-0.18086329102516174,
-0.04568065330386162,
-0.6896930932998657,
-1.063422441482544,
0.04976844787597656,
0.256111741065979,
0.5463535189628601,
0.5797144770622253,
0.20404107868671417,
0.004323819186538458,
-0.2969730794429779,
-0.014285905286669731,
-0.010243812575936317,
0.416068971157074,
-0.18173068761825562,
-0.5142049789428711,
-0.025587450712919235,
0.04378499835729599,
-0.6155222654342651,
-0.3241303861141205,
-0.49486327171325684,
-0.1636456996202469,
0.4425763487815857,
-0.5503203868865967,
1.072713017463684,
0.32162174582481384,
-0.34515541791915894,
-0.4266517460346222,
-0.1564030796289444,
0.20298002660274506,
0.2564983367919922,
0.4449823796749115,
-0.1477576047182083,
0.14406903088092804,
0.2363356649875641,
0.26171791553497314,
-0.7745645642280579,
-0.5399570465087891,
1.0240626335144043,
-1.0354623794555664,
-0.46033012866973877,
0.6154997944831848,
0.32988113164901733,
-0.20187799632549286,
-1.0917478799819946,
-1.4932235479354858,
-0.15072216093540192,
-0.24320019781589508,
-0.8885044455528259,
-0.3639310300350189,
-0.4007747173309326,
-0.6012141108512878,
0.502250075340271,
0.6180570721626282,
0.3451767563819885,
0.19440515339374542,
0.11939875036478043,
-0.05871336907148361,
-0.37628084421157837,
-0.20230107009410858,
1.0132426023483276,
0.17873607575893402,
-0.6968194246292114,
-0.02431698702275753,
-0.27903279662132263,
-0.23499704897403717,
0.19292813539505005,
0.6581301093101501,
0.04878326877951622,
0.0947345644235611,
-0.556723415851593,
0.315500944852829,
0.42000049352645874,
0.25884851813316345,
0.056179847568273544,
-0.3318868577480316,
-0.7063043713569641,
-0.7660218477249146,
0.0033643378410488367,
-0.3308609127998352,
0.2235913872718811,
0.3497726023197174,
-0.237919881939888,
-0.3168119490146637,
0.3135705590248108,
-0.039480868726968765,
-0.0010791149688884616,
-1.2110713720321655,
-0.25157514214515686,
-0.9114282131195068,
-0.006959906313568354,
-1.1042718887329102,
0.20433877408504486,
-0.2774412930011749,
0.13166648149490356,
-0.9451965093612671,
0.2761092483997345,
-0.5155482888221741,
-0.1403375267982483,
0.15707404911518097,
0.3578527867794037,
-0.6884735822677612,
-0.7319809794425964,
-0.8265621066093445,
-0.29301682114601135,
-0.10179666429758072,
-0.5245541334152222,
-0.6613309383392334,
-0.039128627628088,
-0.3478199541568756,
0.4939388334751129,
0.25571298599243164,
0.7362440824508667,
-0.3945876359939575,
-0.6844441294670105,
0.00714112538844347,
0.018995078280568123,
-0.5969933867454529,
0.3183550536632538,
0.06795737147331238,
1.0430519580841064,
0.5674523115158081,
0.24041099846363068,
0.28020966053009033,
0.37892845273017883,
-0.9119442105293274,
0.5833398103713989,
-0.0759415477514267,
0.7015163898468018,
0.065498948097229,
-0.8023512959480286,
0.507335364818573,
-0.07867584377527237,
-0.7504110932350159,
0.1361304223537445,
-0.40944603085517883,
0.523117184638977,
-0.3454824984073639,
0.30178534984588623,
0.8437198996543884,
-0.08282580226659775,
-0.20715972781181335,
0.2240176498889923,
0.01809840090572834,
-0.09463053196668625,
0.23917509615421295,
0.19717612862586975,
-0.6462215185165405,
0.24248377978801727,
0.37595823407173157,
0.36128857731819153,
-0.3498519957065582,
0.487080454826355,
-0.059573978185653687,
0.44253671169281006,
0.02995552495121956,
0.09810960292816162,
-0.38061124086380005,
0.22945848107337952,
-0.31323012709617615,
0.47756972908973694,
0.5247844457626343,
-0.0370340533554554,
0.7160085439682007,
-0.530335009098053,
-0.41291841864585876,
0.03913575038313866,
-0.53401118516922,
-0.7460870742797852,
0.3719882369041443,
-0.3010060489177704,
-0.6168347597122192,
0.15206009149551392,
-0.6136536002159119,
0.03529069945216179,
-0.3590552806854248,
1.1500531435012817,
0.22904011607170105,
-0.3271336257457733,
-0.13760145008563995,
0.400610089302063,
-0.5797759294509888,
-0.742465615272522,
-0.07385819405317307,
1.0409566164016724,
-0.32636284828186035,
-0.7179455757141113,
0.26472803950309753,
0.14359745383262634,
-0.06897538155317307,
-0.049487847834825516,
0.07745932787656784,
-0.3245648741722107,
-0.1795884370803833,
0.17074798047542572,
-0.2332591563463211,
-0.016190646216273308,
-0.5903133153915405,
0.3441235423088074,
-0.09741484373807907,
-0.8203173875808716,
-0.16764336824417114,
0.3908693492412567,
-0.001523081329651177,
-0.033974044024944305,
-0.05407390743494034,
0.8168811798095703,
-0.10345232486724854,
-0.03548207879066467,
0.03198409080505371,
0.02058377116918564,
0.4960445463657379,
-0.04680657759308815,
-0.7405721545219421,
0.6117078065872192,
-0.11851181834936142,
0.8219448924064636,
0.64870285987854,
-0.21996238827705383,
0.26139959692955017,
0.3635299503803253,
0.2289966642856598,
-0.009516127407550812,
0.4566764533519745,
0.10761303454637527,
0.041358496993780136,
0.43490102887153625,
-0.4340764284133911,
-0.44915640354156494,
-0.27563777565956116,
0.051217105239629745,
0.23805955052375793,
0.07211585342884064,
-0.6165044903755188,
-0.7882435321807861,
-0.3316129744052887,
0.6368716359138489,
-0.5253043174743652,
-0.6540655493736267,
-0.1726820170879364,
0.27657994627952576,
0.5885250568389893,
0.5062903761863708,
0.09579768031835556,
-0.04419508948922157,
1.043587327003479,
0.07008437812328339,
-0.7633271217346191,
0.49840182065963745,
0.4778619706630707,
0.7458469271659851,
0.5787438154220581,
0.27642855048179626,
0.9416412711143494,
0.6501185297966003,
-0.39241793751716614,
-1.145399570465088,
-0.318636029958725,
0.3031083643436432,
-0.6030486822128296,
0.6479358077049255,
-0.27538296580314636,
-0.09154524654150009,
-0.33863696455955505,
-0.7145949602127075,
0.3133837580680847,
-0.5869354605674744,
-0.18540455400943756,
0.3667425215244293,
-0.4253464937210083,
-0.20253531634807587,
0.8098604679107666,
0.46678051352500916,
0.6368409395217896,
0.692496120929718,
0.2091541588306427,
0.7642250657081604,
1.2222875356674194,
0.8496041893959045,
-0.27083873748779297,
0.805198609828949,
-0.4062323272228241,
-0.6099469065666199,
0.7555080056190491,
0.7052545547485352,
-0.2318355143070221,
0.36576077342033386,
-0.5054616332054138,
-0.1787002831697464,
0.4934597611427307,
0.21535690128803253,
-0.09972910583019257,
0.2407573014497757,
0.427029550075531,
0.6005740165710449,
-0.8408321142196655,
-0.12504765391349792,
1.3508479595184326,
0.8744437098503113,
-0.40741756558418274,
0.04281875863671303,
0.22612951695919037,
-0.8488695621490479,
0.11122258007526398,
-1.1768579483032227,
0.43564140796661377,
-0.24118828773498535,
0.0664970800280571,
-0.47854796051979065,
-0.5849472284317017,
-0.3477190434932709,
-0.8969104290008545,
-0.17629148066043854,
-0.45619669556617737,
0.6101053953170776,
0.9629229307174683,
0.1907617747783661,
-0.06994718313217163,
-0.7145175933837891,
-0.5717741847038269,
0.05216885358095169,
0.946118950843811,
0.34413835406303406,
-0.03612438216805458,
0.7303929328918457,
0.28014516830444336,
-0.7710016369819641,
-0.18896006047725677,
0.49442431330680847,
-0.48920145630836487,
0.6297199130058289,
-0.3162185549736023,
-0.35418447852134705,
0.35759541392326355,
-0.5013037919998169,
0.08699485659599304,
0.07535281032323837,
0.32906419038772583,
0.17185384035110474,
-0.14829568564891815,
-0.3808284103870392,
-0.7665948867797852,
-0.15287266671657562,
-0.701543390750885,
0.6254752278327942,
0.42867085337638855,
-0.2346859872341156,
-0.15067245066165924,
-0.7239647507667542,
4.233124732971191,
0.6820260286331177,
1.065065622329712,
0.27777358889579773,
1.1183239221572876,
0.7852722406387329,
-0.47161275148391724,
-0.10898610204458237,
0.26488634943962097,
-0.7939731478691101,
0.24997229874134064,
0.1577146351337433,
0.30558106303215027,
-0.07594884186983109,
0.263221800327301,
0.3461143970489502,
0.02062978781759739,
0.29676929116249084,
0.011465770192444324,
-0.8859605193138123,
-0.8381951451301575,
0.05663817375898361,
0.31348103284835815,
0.30845528841018677,
0.5075816512107849,
0.02448359504342079,
-0.12219750881195068,
-1.0375053882598877,
-0.31942319869995117,
-0.886462390422821,
-0.5955433249473572,
-0.6124516129493713,
0.17335642874240875,
-0.345112681388855,
-0.9254700541496277,
0.25767508149147034,
0.37789830565452576,
-0.26688337326049805,
0.07862390577793121,
0.07581103593111038,
-0.19127026200294495,
-0.7400650978088379,
0.1350378394126892,
-0.042923565953969955,
0.22103099524974823,
1.328123927116394,
-0.08045540004968643,
0.3900202512741089,
0.8971725106239319,
-0.4331563115119934,
0.13334594666957855,
-0.3346027433872223,
-0.239803284406662,
-0.18313659727573395,
-0.4231792092323303,
-0.0757206603884697,
-0.5290842652320862,
0.26520079374313354,
0.05243929103016853,
-0.5394629240036011,
0.7066537141799927,
-0.04998227581381798,
-0.3063091039657593,
0.20256288349628448,
-0.14062975347042084,
0.12732931971549988,
-0.26833558082580566,
0.6561872363090515,
0.3388250172138214,
-0.11326543241739273,
-0.007956264540553093,
-0.19200611114501953,
0.03554427996277809,
-0.12008770555257797,
-0.1703881174325943,
0.4686804711818695,
-0.21350978314876556,
0.01700788550078869,
0.10021930187940598,
0.004585375543683767,
-0.6236509680747986,
0.09701281785964966,
-0.46926555037498474,
0.602275550365448,
0.12925246357917786,
0.1824234426021576,
-0.0907631516456604,
-0.4390926659107208,
-0.0003451094089541584,
0.18475575745105743,
0.5023923516273499,
1.3025723695755005,
0.034268442541360855,
0.5753164887428284,
-0.6314077377319336
] |
Non-perturbative analysis, Gribov horizons and the boundary of the fundamental domain
|
In this contribution to the proceedings we will describe some of the details for constructing the Gribov horizon and the boundary of the fundamental modular domain, when restricting to some low energy modes of pure SU(2) gauge theory in a spherical spatial geometry. The fundamental domain is a one-to-one representation of the set of gauge invariant degrees of freedom, in terms of transverse gauge fields. Boundary identifications are the only remnants of the Gribov copies.
|
Pierre van Baal and R.E. Cutkosky
|
hep-lat hep-th
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208027
|
hep-lat/9208028
|
[
0.6352142095565796,
-0.1047079861164093,
-0.0575709342956543,
0.9233106374740601,
-0.4481434226036072,
0.0026386950630694628,
-0.34504979848861694,
-0.22301827371120453,
-0.7362514138221741,
1.1887104511260986,
0.6628552675247192,
-0.0520927757024765,
-0.28590357303619385,
-0.6717801690101624,
-0.4367837607860565,
0.7995603680610657,
0.27980953454971313,
-0.295343816280365,
-1.1189448833465576,
0.45379242300987244,
-0.03338733687996864,
-0.22449959814548492,
-1.5962835550308228,
-0.4379314184188843,
-0.006752797868102789,
0.8054654002189636,
-0.0739825889468193,
0.3931535482406616,
1.007531762123108,
0.18226900696754456,
0.3789323568344116,
-0.7025973796844482,
0.045960091054439545,
-0.31527644395828247,
-0.9537820816040039,
-0.31287989020347595,
0.09829376637935638,
0.01961914636194706,
0.6952115893363953,
-0.5209236741065979,
0.8380767107009888,
-0.4553993046283722,
-0.02439979836344719,
-0.3658146262168884,
-0.7252336144447327,
0.0011306136148050427,
-0.4555172324180603,
-0.5475061535835266,
-0.1693151742219925,
-1.2131015062332153,
-0.2500104308128357,
0.6746625900268555,
0.8501770496368408,
-0.7892128229141235,
-0.3487488031387329,
-0.08371173590421677,
0.24947403371334076,
0.295326292514801,
-0.6986873149871826,
0.026251787319779396,
0.35027360916137695,
-0.0006665747496299446,
0.7490254044532776,
-0.3704681098461151,
0.08013296127319336,
0.9652737379074097,
-0.30800068378448486,
0.8058285713195801,
0.2402469962835312,
-0.36455002427101135,
0.013261747546494007,
0.058435454964637756,
-1.0024484395980835,
-0.018785906955599785,
-0.8707412481307983,
-0.03757280111312866,
-0.12951087951660156,
-0.8152651786804199,
-0.7371935844421387,
0.10509153455495834,
-0.18620437383651733,
-0.306741327047348,
-0.25745701789855957,
0.007270814850926399,
-0.4349133372306824,
-0.26566946506500244,
-0.3527495265007019,
-0.17992015182971954,
-0.07592558860778809,
0.8367181420326233,
0.5222744941711426,
0.7281925678253174,
-0.2633446455001831,
-0.025290215387940407,
0.43763014674186707,
-0.003583758370950818,
0.24282142519950867,
0.27795350551605225,
0.19101585447788239,
0.3864801824092865,
0.16484838724136353,
0.5728697776794434,
-0.8807702660560608,
0.09943585842847824,
-0.7751363515853882,
0.6236352324485779,
-0.08213155716657639,
-0.26583045721054077,
0.20818625390529633,
-0.9091244339942932,
0.33980292081832886,
-0.1936943233013153,
0.3250032961368561,
0.5073888301849365,
-0.24318620562553406,
0.4014217257499695,
-0.22576852142810822,
0.16077996790409088,
-0.1907239854335785,
-0.5704714059829712,
0.06027074530720711,
-0.010029775090515614,
0.2107381969690323,
0.3565835654735565,
-0.3805201053619385,
-0.529596209526062,
0.04771554097533226,
0.13808436691761017,
-0.5542557239532471,
-0.07917740941047668,
-0.1458730548620224,
-0.24336248636245728,
-0.8851960897445679,
0.410747766494751,
-0.3697700500488281,
0.013658466748893261,
-0.1316254436969757,
0.16111767292022705,
-0.059156887233257294,
-0.318868488073349,
0.6385590434074402,
-0.6731177568435669,
0.2882993519306183,
1.316269040107727,
-0.1946866363286972,
0.32827845215797424,
0.005130925215780735,
0.6854895353317261,
-0.3968396782875061,
0.39448562264442444,
-0.462157666683197,
0.047802917659282684,
-0.3129637837409973,
0.2036823034286499,
0.3806050717830658,
0.45394453406333923,
-0.29798176884651184,
0.3932640850543976,
-0.17783331871032715,
-0.46400970220565796,
0.30658724904060364,
0.2557934820652008,
-0.5326926112174988,
0.1393984854221344,
-0.34968137741088867,
-0.5036062598228455,
-0.5979506373405457,
-0.46082982420921326,
0.8843669891357422,
-0.32585352659225464,
0.006324869580566883,
0.4180452227592468,
-0.24297401309013367,
0.7842580080032349,
0.30040284991264343,
0.7734431028366089,
0.08417867124080658,
-0.4267409145832062,
0.02411940135061741,
0.26102501153945923,
-0.1378968507051468,
-0.22062112390995026,
0.17772814631462097,
0.31272029876708984,
-0.07675076276063919,
-0.43977758288383484,
-0.07721811532974243,
-0.17379224300384521,
0.10377698391675949,
0.5009015202522278,
-0.4922608435153961,
0.7804361581802368,
-0.1672583967447281,
0.7840313911437988,
-0.43821752071380615,
-0.17065414786338806,
-0.8000128269195557,
0.11271802335977554,
-0.4858925938606262,
-0.41192924976348877,
0.3253313899040222,
-0.2533034086227417,
-0.20394304394721985,
-0.0962492823600769,
-1.4097553491592407,
0.2341490238904953,
0.9555050730705261,
0.08780862390995026,
-0.4069212079048157,
-0.38583138585090637,
0.3385196030139923,
-0.07435131818056107,
0.2675745189189911,
0.24717332422733307,
0.17330175638198853,
0.045002274215221405,
-0.031694330275058746,
0.4517093896865845,
0.6839936971664429,
0.4867120385169983,
0.0976409986615181,
0.3505645990371704,
-0.04685978218913078,
1.0615477561950684,
-1.0191112756729126,
-0.9138995409011841,
0.33504024147987366,
0.3454808294773102,
0.378307968378067,
-0.26269471645355225,
0.06180243939161301,
0.7165430784225464,
-0.30482229590415955,
0.35820168256759644,
0.4027332663536072,
-0.10796412080526352,
0.5896618366241455,
0.24998140335083008,
0.25682204961776733,
0.24521099030971527,
-0.2669518291950226,
0.2401479035615921,
0.027683958411216736,
0.08595302700996399,
-0.16345053911209106,
-0.23175056278705597,
-0.6630250215530396,
0.11665268987417221,
-1.0053470134735107,
0.15678207576274872,
-0.2645814120769501,
0.39253705739974976,
0.04922344908118248,
0.486298143863678,
-1.1288316249847412,
-0.007421914953738451,
0.11495384573936462,
0.2648574709892273,
-0.23762542009353638,
0.0971723422408104,
0.19911356270313263,
0.011970303021371365,
-0.30316880345344543,
-0.0838819369673729,
0.2656670808792114,
0.9848520159721375,
-0.13280849158763885,
0.3741399049758911,
0.6594477891921997,
-0.2698589861392975,
-1.0283676385879517,
0.5025970935821533,
-0.6563581228256226,
0.03123437613248825,
-0.4025753438472748,
0.23144038021564484,
0.8819299340248108,
-0.49529263377189636,
0.758775532245636,
-0.29507872462272644,
-0.25612303614616394,
0.5989598035812378,
-0.9383724331855774,
0.16604194045066833,
0.1307973861694336,
-0.4311676621437073,
-0.48930659890174866,
0.32264915108680725,
-0.9836368560791016,
-0.16448098421096802,
-0.3759346008300781,
0.4730752110481262,
0.6382452845573425,
-0.34325656294822693,
0.3862774670124054,
-0.16171294450759888,
-0.4868983030319214,
0.5290122032165527,
0.27498358488082886,
-0.5179678797721863,
0.4562821090221405,
0.3980385661125183,
0.11967798322439194,
-0.7388501763343811,
-1.3894857168197632,
0.7478157877922058,
0.3146347105503082,
-0.09707240015268326,
0.2948843240737915,
0.22540850937366486,
-0.6529914140701294,
0.28541895747184753,
-0.14162655174732208,
0.4682367146015167,
-0.0832865983247757,
1.427179217338562,
0.31203052401542664,
0.050285112112760544,
0.04817008599638939,
-0.5947100520133972,
-0.32178550958633423,
0.35938143730163574,
0.29717016220092773,
-0.5923269987106323,
-0.1357293725013733,
0.9174109101295471,
-0.08851338922977448,
-0.5956727862358093,
0.45433416962623596,
-0.8594876527786255,
-0.18421809375286102,
0.17012597620487213,
-0.46509918570518494,
0.23899461328983307,
-0.6419939398765564,
0.23536144196987152,
-0.6260208487510681,
0.37722811102867126,
-0.28186020255088806,
0.1806638538837433,
0.5494074821472168,
-0.35864540934562683,
0.4488067924976349,
0.5119470357894897,
0.2636551856994629,
-0.20116381347179413,
-0.2551717162132263,
-0.09988763183355331,
-0.47128844261169434,
0.20319277048110962,
-1.252784252166748,
0.21361087262630463,
0.02957005240023136,
0.5947602391242981,
0.3441384434700012,
0.26144081354141235,
-0.32353150844573975,
-0.34286579489707947,
-0.5289281010627747,
-0.7504924535751343,
-0.2072354406118393,
0.8252700567245483,
-0.07648346573114395,
0.02352854050695896,
-0.5248093008995056,
-0.5366958379745483,
0.25916799902915955,
-0.05992009490728378,
0.41722288727760315,
-0.5035954117774963,
-0.08020130544900894,
-0.1627306193113327,
-0.21838971972465515,
-0.07571360468864441,
0.3569064140319824,
0.7928385138511658,
0.02750755287706852,
0.11084672808647156,
0.8431530594825745,
-0.1552492380142212,
-0.6013946533203125,
0.3461335003376007,
0.7285777926445007,
0.7666340470314026,
0.18883830308914185,
0.3752140402793884,
0.16597433388233185,
0.11840961128473282,
-0.38906580209732056,
-0.4417381286621094,
-0.22352708876132965,
-0.015308068133890629,
0.3586089313030243,
-0.2892923653125763,
0.450052946805954,
-0.1364082247018814,
0.3879142105579376,
0.14802882075309753,
0.44363564252853394,
-0.18454818427562714,
0.35307803750038147,
0.2700561285018921,
0.7911075949668884,
0.6706222891807556,
0.44014525413513184,
0.3194541335105896,
-0.9927611947059631,
0.05779089406132698,
-0.17718324065208435,
0.5497252941131592,
-0.1588052660226822,
-0.4094908833503723,
-0.07272461801767349,
-0.2776602506637573,
0.38141295313835144,
0.1741485893726349,
-0.7117516994476318,
0.2625858783721924,
-0.41196176409721375,
0.6852982640266418,
0.08861927688121796,
0.2883850038051605,
0.4964289963245392,
0.17148759961128235,
0.5664346218109131,
-0.4452962279319763,
0.49460041522979736,
-0.3679317533969879,
0.7804948687553406,
0.33559390902519226,
-1.147081732749939,
-0.3751322031021118,
-0.7150802612304688,
-0.26732537150382996,
-0.7249531149864197,
0.4718188941478729,
1.1342508792877197,
0.03235379979014397,
0.06330595165491104,
-0.621623694896698,
-0.6920796632766724,
0.45722588896751404,
-0.4277615249156952,
-0.8878800272941589,
0.195437490940094,
0.040236569941043854,
-0.30537790060043335,
0.6642035245895386,
-0.3038214147090912,
-0.6207029223442078,
0.33319854736328125,
-0.4501323699951172,
0.16976520419120789,
-0.5496638417243958,
-0.29574257135391235,
-0.21449971199035645,
-0.5189130306243896,
-0.5276498198509216,
0.2747204601764679,
0.42681267857551575,
-0.07210028171539307,
0.08025554567575455,
0.02893194369971752,
-0.2673647403717041,
0.3557894825935364,
0.057481858879327774,
-0.43918099999427795,
0.7456873655319214,
0.6117645502090454,
0.1319398581981659,
0.1738709807395935,
0.026888633146882057,
-0.05848183110356331,
0.007467803079634905,
0.3982336223125458,
0.03909337893128395,
0.18994084000587463,
-0.40194207429885864,
0.21075136959552765,
-1.2833685874938965,
-0.8499718308448792,
0.2576407194137573,
-0.12075994163751602,
0.5593810081481934,
0.3134797215461731,
-0.24761740863323212,
0.13282793760299683,
-0.3071516156196594,
-0.7851712107658386,
0.6508088111877441,
-0.25306254625320435,
-0.5987173318862915,
0.7042059898376465,
-0.3422969579696655,
-0.08202439546585083,
-0.35761868953704834,
0.24172000586986542,
-0.33383652567863464,
0.2951180040836334,
0.7415488958358765,
0.1198112964630127,
0.21240423619747162,
-0.9273485541343689,
0.621385931968689,
-0.6080259084701538,
-0.13026505708694458,
-0.5690537095069885,
-0.23168545961380005,
0.24481084942817688,
0.08083077520132065,
0.28771519660949707,
-0.18286846578121185,
-0.24024982750415802,
0.17218247056007385,
-0.7006064653396606,
0.09864097833633423,
0.3870109021663666,
-0.2602249085903168,
-0.08814726024866104,
0.7327271699905396,
0.2841704487800598,
-0.35410839319229126,
-0.04518863558769226,
0.9107598066329956,
-0.0688881203532219,
0.3040251135826111,
-0.11647504568099976,
-0.5826956629753113,
0.19135822355747223,
-0.30047348141670227,
0.32826340198516846,
-0.3982141613960266,
-0.11100981384515762,
0.262907475233078,
-0.600302517414093,
0.005155801773071289,
0.2518838047981262,
0.11172441393136978,
-0.17406772077083588,
-1.0000827312469482,
-0.385195255279541,
0.5289385914802551,
0.10830719769001007,
0.3298546373844147,
-0.4142638146877289,
0.13474731147289276,
-0.08124158531427383,
0.8859346508979797,
-0.27458256483078003,
0.6198391318321228,
0.24226312339305878,
0.019939256832003593,
0.561614990234375,
0.6410182118415833,
0.29101958870887756,
-0.45949530601501465,
0.4155409336090088,
0.4347723722457886,
-0.2596701383590698,
0.4562723934650421,
-0.5917918682098389,
0.20639006793498993,
-0.5345414876937866,
1.0060495138168335,
-0.6431832313537598,
-0.30405887961387634,
0.21251879632472992,
0.1733274906873703,
0.46006330847740173,
-0.2523094713687897,
0.3846454620361328,
1.078782081604004,
0.15230771899223328,
0.14631803333759308,
0.48033514618873596,
-0.5088619589805603,
-0.14695075154304504,
-0.8441900610923767,
-0.5956977009773254,
0.1971004158258438,
0.33150166273117065,
-0.47877004742622375,
-0.38054218888282776,
-0.5046555995941162,
0.011481247842311859,
-0.39259207248687744,
0.37332600355148315,
0.5684264898300171,
-0.17831659317016602,
0.5331789255142212,
-0.032563336193561554,
-0.03985331952571869,
-0.5027742385864258,
0.39173442125320435,
0.22332479059696198,
-0.038472387939691544,
0.22337090969085693,
0.14629808068275452,
-1.1511719226837158,
-0.28730258345603943,
-0.257114440202713,
0.28075772523880005,
0.3884181082248688,
-0.4068034291267395,
0.7027956247329712,
0.1580929011106491,
-0.6557326316833496,
-0.25280338525772095,
0.631860613822937,
0.29871028661727905,
0.18371637165546417,
0.2574944794178009,
-0.04321249946951866,
0.34680140018463135,
-0.44090375304222107,
0.47692248225212097,
0.1885307878255844,
-0.7675444483757019,
0.7824475169181824,
-0.8010371923446655,
0.04218832775950432,
0.5076645612716675,
0.021638836711645126,
-0.667998731136322,
-0.4331777095794678,
-1.0991382598876953,
0.3665572702884674,
-0.6623480319976807,
-0.38010480999946594,
-0.35494789481163025,
-0.44537967443466187,
-0.051301728934049606,
0.3816453814506531,
0.6523034572601318,
0.021858420222997665,
0.3520994782447815,
-0.4293209910392761,
-0.249699667096138,
-0.09297704696655273,
-0.4860133230686188,
1.4402419328689575,
0.3698614239692688,
-0.7329657077789307,
0.009439298883080482,
-0.04318719729781151,
-0.26867905259132385,
0.16693739593029022,
0.9139877557754517,
-0.6660390496253967,
0.4383799731731415,
-0.16385535895824432,
0.2274661660194397,
0.2870338261127472,
1.0957131385803223,
0.5010783672332764,
0.3198185861110687,
-0.10286980122327805,
-0.6304689049720764,
0.03400721773505211,
-0.32917550206184387,
0.18431121110916138,
1.0557631254196167,
0.2158064842224121,
0.31773579120635986,
-0.48746341466903687,
-0.5032966136932373,
0.06562266498804092,
-0.7951775789260864,
-0.08665813505649567,
-0.918951690196991,
-0.3174152374267578,
-0.43093234300613403,
-0.6689332723617554,
-0.0814635381102562,
0.805210292339325,
-0.21176545321941376,
-0.19554497301578522,
-0.8925513029098511,
0.12418915331363678,
0.032146427780389786,
0.5375598669052124,
-0.4888349175453186,
-0.5660199522972107,
0.1154988631606102,
0.10273514688014984,
0.01899585872888565,
-0.32567039132118225,
-0.3721221685409546,
0.16349676251411438,
-0.3171598017215729,
0.1991254836320877,
-0.19525068998336792,
0.8127840757369995,
-1.0198639631271362,
-0.7894502282142639,
0.03543641045689583,
-0.1500912457704544,
-1.2059218883514404,
0.3648686110973358,
0.09885463118553162,
0.8512961864471436,
0.3968155086040497,
-0.10939747095108032,
-0.41643479466438293,
-0.07002868503332138,
-0.5592156052589417,
0.1587246209383011,
0.1633727103471756,
0.36191779375076294,
-0.5668447017669678,
-0.5392361879348755,
-0.21569055318832397,
0.3949408531188965,
-0.7868593335151672,
0.3478567600250244,
-0.5932748317718506,
0.13501182198524475,
-0.41210073232650757,
-0.0188982505351305,
0.16366827487945557,
0.49964290857315063,
0.08331073075532913,
0.8393306732177734,
0.16800305247306824,
0.1813930869102478,
0.4420309364795685,
0.05127307027578354,
-0.1075364425778389,
-0.0486312098801136,
0.22607466578483582,
-0.4475650489330292,
0.06346029043197632,
0.7067487239837646,
-0.08701734244823456,
-0.04554864764213562,
-0.34939494729042053,
-0.18081273138523102,
-0.04335658252239227,
-0.6442959308624268,
-0.6792885661125183,
0.372752845287323,
0.07399868965148926,
-0.31198012828826904,
-0.4089982807636261,
-0.5500057935714722,
-0.2938315272331238,
0.7921748161315918,
-1.088706612586975,
-0.44517090916633606,
-0.2755054533481598,
-0.4974590241909027,
-0.13450594246387482,
0.3555491864681244,
-0.5062289237976074,
0.07206734269857407,
0.03691887483000755,
-0.22245755791664124,
-0.15950074791908264,
0.24686746299266815,
-0.3046191334724426,
0.29092708230018616,
-0.2455025166273117,
-0.25460919737815857,
-0.43188902735710144,
0.582270622253418,
-1.0830591917037964,
-0.894992470741272,
-0.16505666077136993,
0.3915673494338989,
0.2190885692834854,
-0.20010103285312653,
-0.4211987853050232,
0.10287841409444809,
-0.30839136242866516,
0.17372269928455353,
-1.0063753128051758,
0.004500341136008501,
-0.40943101048469543,
0.32292962074279785,
0.1755267232656479,
-0.2957146465778351,
0.29933416843414307,
0.03783123940229416,
0.44483715295791626,
-0.04721812531352043,
-0.3806549608707428,
0.7265991568565369,
0.39302706718444824,
-0.017124781385064125,
0.4453486204147339,
-0.06461963057518005,
0.20069286227226257,
0.5603046417236328,
-0.7753928899765015,
0.17066942155361176,
0.3597618341445923,
0.47396278381347656,
0.4836859703063965,
0.1937510371208191,
0.06115220859646797,
0.3464226722717285,
0.11434698849916458,
-0.27173206210136414,
-0.494791179895401,
0.22113056480884552,
-0.16997584700584412,
0.47619742155075073,
0.029611598700284958,
-0.38795286417007446,
0.0758773609995842,
-0.11140386015176773,
-0.3299393057823181,
-0.5847952365875244,
-0.4410567283630371,
-0.4367705285549164,
0.11017283797264099,
0.33304324746131897,
-0.39033862948417664,
-0.6096346974372864,
-0.008859546855092049,
-0.13603933155536652,
0.45357346534729004,
-0.030003584921360016,
0.02617970108985901,
0.5832715630531311,
0.34780386090278625,
0.3962238132953644,
-0.02981669083237648,
0.20530059933662415,
0.19560007750988007,
1.358771562576294,
0.443832129240036,
0.5447579026222229,
0.06720845401287079,
0.7340089678764343,
0.2777523994445801,
-0.672303318977356,
0.35890132188796997,
0.7662369608879089,
-0.8833265900611877,
0.44783705472946167,
-0.6229891180992126,
-0.16530831158161163,
-0.5953486561775208,
-0.3085068166255951,
0.23647446930408478,
-0.7522493004798889,
0.04429052025079727,
0.7663502097129822,
-0.26995229721069336,
0.027007635682821274,
0.7569311261177063,
0.1636010706424713,
-0.043899279087781906,
0.901837170124054,
-0.2810855507850647,
0.22137998044490814,
0.9683008193969727,
1.4632842540740967,
0.19818489253520966,
0.00015137266018427908,
0.065420962870121,
-0.38687413930892944,
0.3406391441822052,
0.2850119471549988,
-0.5622752904891968,
0.8332322835922241,
-0.8052282333374023,
-0.07209648936986923,
0.07758890092372894,
0.31454628705978394,
-0.4644310474395752,
-0.637840986251831,
0.3330117166042328,
0.03740188851952553,
-0.6051450371742249,
-0.8357598781585693,
1.4357004165649414,
0.45183974504470825,
-0.23395715653896332,
-0.5052700042724609,
0.17850685119628906,
-0.2450125366449356,
-0.00970546342432499,
-0.05954499915242195,
0.02041621506214142,
-0.359777569770813,
0.03452746942639351,
0.1518734097480774,
-0.46291303634643555,
-0.8786611557006836,
-0.596935510635376,
0.4182884395122528,
-0.6837700605392456,
0.44039100408554077,
0.5148040056228638,
0.2680428922176361,
-0.05019134655594826,
-0.5565258860588074,
-0.07595198601484299,
0.030400589108467102,
1.266262173652649,
0.24680392444133759,
-0.09686272591352463,
1.023356556892395,
0.10639079660177231,
-1.000035047531128,
0.6919798254966736,
0.5597672462463379,
-1.1639344692230225,
0.4098806083202362,
-0.3573245108127594,
0.7965154647827148,
0.5251491665840149,
0.044139523059129715,
0.40788885951042175,
-0.2816388010978699,
0.45616093277931213,
0.13028845191001892,
-0.2877950668334961,
-0.2854997515678406,
-0.7418913245201111,
-0.10361333936452866,
-0.19951477646827698,
0.2971839904785156,
0.44327598810195923,
0.16997109353542328,
0.14526227116584778,
-0.9883765578269958,
4.457171440124512,
0.1060817763209343,
0.3711569905281067,
0.23427541553974152,
0.21012558043003082,
0.6026264429092407,
-0.08813748508691788,
-0.8935189843177795,
0.10703203827142715,
-0.6782562136650085,
-0.2642820477485657,
0.07119080424308777,
0.1605149209499359,
-0.19648487865924835,
0.15639320015907288,
0.6964266300201416,
-0.37328100204467773,
-0.3776963949203491,
0.2464074343442917,
-0.8586233258247375,
-0.2747257947921753,
0.0241397637873888,
-0.10268135368824005,
0.02382303588092327,
0.2913304269313812,
0.4009334444999695,
0.21607902646064758,
-0.40592944622039795,
-0.3859531879425049,
-0.36352744698524475,
-0.30733442306518555,
-0.6871936917304993,
0.2921420931816101,
-0.510452151298523,
-0.866609513759613,
0.6022117137908936,
0.5815693736076355,
-0.28930044174194336,
-0.10688328742980957,
0.362461119890213,
-0.11202721297740936,
-0.3471169173717499,
0.11365407705307007,
-0.5155013203620911,
-0.6265251636505127,
0.5371490120887756,
-0.14041151106357574,
0.8913885354995728,
0.13312500715255737,
-0.8141794204711914,
0.26647186279296875,
0.12539680302143097,
0.6419791579246521,
-0.09148110449314117,
-1.150630235671997,
0.30190137028694153,
-0.5083630681037903,
0.04356994852423668,
0.10952428728342056,
0.3400854468345642,
0.3016433119773865,
-0.6293781399726868,
-0.3133009374141693,
0.19654086232185364,
-0.11655349284410477,
0.5148594975471497,
-0.3042033314704895,
0.45976004004478455,
-0.2972085177898407,
0.2652736008167267,
-0.40082085132598877,
-0.7110180258750916,
-0.22951491177082062,
-0.07591156661510468,
0.2984175384044647,
0.00809415802359581,
0.07393033802509308,
0.5008253455162048,
0.2952239513397217,
0.19801729917526245,
0.4038131833076477,
-0.18645048141479492,
-0.8480790853500366,
0.06193918734788895,
-0.16320405900478363,
0.9567371010780334,
-0.5618131160736084,
-0.2472517490386963,
0.16563574969768524,
0.4482925534248352,
0.12204344570636749,
1.0720090866088867,
-0.1231236457824707,
-0.13333632051944733,
-0.6525487899780273
] |
Running Coupling and the Lambda-Parameter from SU(3) Lattice Simulations
|
We present new results on the static qq-potential from high statistics simulations on 32^4 and smaller lattices, using the standard Wilson beta = 6.0, 6.4, and 6.8. Within our statistical errors we do not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9fm up to 3.3fm. We are able to see and quantify the running of the coupling from the Coulomb behaviour of the interquark force. From this we extract the ratio \sqrt{sigma}/Lambda_L. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safe extrapolation of \Lambda_L to its continuum value. Both methods yield consistent values for Lambda: Lambda_MSbar = 0.558_{-0.007}^{+0.017}\sqrt{sigma} = 246_{-3}^{+7}MeV. At the highest energy scale attainable to us we find alpha(5 GeV) = 0.150(3)
|
Gunnar S. Bali and Klaus Schilling
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208028
|
hep-lat/9208029
|
[
0.5345533490180969,
-0.5551929473876953,
0.24283672869205475,
0.27788203954696655,
-0.34538379311561584,
-0.6434755325317383,
-0.2724204957485199,
-0.08170226961374283,
-0.7460814118385315,
1.547093152999878,
0.4686446487903595,
-0.3669203519821167,
0.714967668056488,
-0.4589994549751282,
-0.3614490330219269,
0.8003243803977966,
-0.02008722350001335,
-0.6680265069007874,
-1.224555492401123,
0.351618230342865,
0.5593516230583191,
-0.3391360342502594,
-1.7239958047866821,
-0.7639843225479126,
-0.4791920483112335,
0.9127479791641235,
0.061454709619283676,
-0.2026970535516739,
0.5261256694793701,
0.30048906803131104,
0.2670047879219055,
-0.27264413237571716,
-0.6008421778678894,
-0.5617302656173706,
-0.45621898770332336,
-0.09880722314119339,
-0.3534468114376068,
-0.5576382875442505,
0.5013694167137146,
-0.1665804535150528,
0.7588067650794983,
-0.5261325836181641,
-0.47475120425224304,
-0.44538500905036926,
-0.5805424451828003,
0.1672956645488739,
-0.12336517125368118,
-0.3669446110725403,
0.28598541021347046,
-0.8507187366485596,
0.21611955761909485,
0.3155837953090668,
0.9136174917221069,
-0.9776626825332642,
-0.7390145063400269,
-0.5263521671295166,
0.04595109820365906,
0.015582693740725517,
-0.5003862380981445,
-0.4951998293399811,
0.2719598114490509,
0.157600536942482,
0.602415144443512,
-0.8951425552368164,
0.001257730764336884,
0.6034001111984253,
-0.2849905490875244,
1.0212397575378418,
0.019809944555163383,
-0.30091238021850586,
-0.8300594091415405,
-0.2590567171573639,
-0.7097879648208618,
-0.015538150444626808,
-0.7509362101554871,
0.20823292434215546,
-0.3214972913265228,
-0.7503861784934998,
-0.5309149026870728,
-0.44403818249702454,
-0.27685463428497314,
0.08419517427682877,
-0.36192187666893005,
0.5865558385848999,
-0.0995250716805458,
0.16450674831867218,
-0.09219945967197418,
-0.11309412866830826,
-0.16052821278572083,
0.7289654016494751,
0.23161542415618896,
0.5484533905982971,
-0.21820572018623352,
-0.1836162805557251,
0.5345309376716614,
0.5705116987228394,
0.23368588089942932,
0.8295353651046753,
0.34609147906303406,
0.10974816977977753,
0.13877254724502563,
1.0433533191680908,
-0.7529019117355347,
-0.09503308683633804,
-0.15853555500507355,
0.482555091381073,
-0.5175151824951172,
-0.1888362020254135,
-0.45102858543395996,
-0.5441589951515198,
0.42442354559898376,
-0.11010351777076721,
0.3091981112957001,
0.6272771954536438,
-0.031567107886075974,
0.8482670783996582,
-0.03758513554930687,
0.04643525183200836,
-0.913152813911438,
-1.0140407085418701,
0.41448161005973816,
0.7739772200584412,
-0.2718553841114044,
0.35017794370651245,
0.2353491485118866,
-0.20178066194057465,
1.1066478490829468,
0.6192030310630798,
-0.9901859164237976,
0.24563269317150116,
0.5233103036880493,
-0.21519941091537476,
-0.32534313201904297,
0.7374352812767029,
-0.6791822910308838,
0.07120879739522934,
-0.6393895149230957,
0.24579335749149323,
0.4018501937389374,
0.24691540002822876,
0.8056764602661133,
-0.23808801174163818,
0.12863732874393463,
1.2031906843185425,
0.603204071521759,
-0.06562240421772003,
0.5415621995925903,
-0.11504533886909485,
-0.21847163140773773,
0.379159152507782,
-0.7092697024345398,
-0.09023894369602203,
0.6095284819602966,
0.1317068487405777,
-0.25932028889656067,
0.6472771763801575,
-0.9490029215812683,
0.6177465915679932,
-0.7196655869483948,
-0.6138835549354553,
0.37257710099220276,
-0.10298218578100204,
-0.6072536110877991,
0.7287553548812866,
-0.5308243036270142,
0.35679763555526733,
-0.7740293145179749,
-0.23420561850070953,
0.14250458776950836,
-0.8310968279838562,
-0.03797072172164917,
0.6298560500144958,
-0.41043877601623535,
0.7257601618766785,
0.6287320256233215,
0.06453293561935425,
0.29693686962127686,
-0.8475991487503052,
0.08747152239084244,
0.463537335395813,
-0.41870594024658203,
-0.30058425664901733,
0.476105660200119,
0.05560705438256264,
0.17124880850315094,
0.23270337283611298,
-0.40904250741004944,
-0.5274006128311157,
0.5417733788490295,
0.5160462260246277,
-0.061580803245306015,
0.32158714532852173,
-0.028821729123592377,
0.5571631789207458,
-0.7712844014167786,
-0.15928557515144348,
-1.2049463987350464,
0.46111205220222473,
-0.9535506963729858,
-0.20746608078479767,
0.2660008668899536,
0.7234067916870117,
-1.3177292346954346,
0.424734503030777,
-1.4357025623321533,
0.3115209937095642,
0.1647370606660843,
0.14067023992538452,
-0.7989855408668518,
-0.42119917273521423,
0.8371294736862183,
-0.2822214365005493,
0.41827839612960815,
-0.6555569171905518,
0.40591347217559814,
0.10156306624412537,
-0.49516212940216064,
-0.3177098035812378,
0.39188238978385925,
0.34122928977012634,
0.7929150462150574,
0.3027331233024597,
-0.1004633679986,
0.7902305722236633,
-0.7214875817298889,
-0.5949327945709229,
-0.40981101989746094,
0.6966559290885925,
0.37138694524765015,
-0.11571931093931198,
0.17460666596889496,
0.5233832597732544,
0.3395911753177643,
0.3708452880382538,
0.9890155792236328,
0.4598205089569092,
0.4619116187095642,
0.4772181510925293,
0.2834341824054718,
0.28305578231811523,
-0.32657232880592346,
0.5207109451293945,
0.787201464176178,
0.28403279185295105,
-0.574941098690033,
0.24961541593074799,
-0.6563395857810974,
0.10710352659225464,
-0.5403261184692383,
0.22135744988918304,
0.025338858366012573,
1.0518285036087036,
-0.37421539425849915,
0.12297825515270233,
-0.8470864295959473,
-0.29684650897979736,
0.16483129560947418,
0.00013614997442346066,
0.2659968137741089,
-0.08429490029811859,
0.2660978138446808,
0.0007445561932399869,
-0.018250342458486557,
-1.0011968612670898,
-0.4061700999736786,
1.625584602355957,
-0.3688315153121948,
-0.27911481261253357,
0.6062655448913574,
-0.6793044805526733,
-0.9932765364646912,
-0.051487620919942856,
-0.6792343258857727,
-0.003893821267411113,
-0.7121071815490723,
0.3144751489162445,
0.7915734648704529,
-0.8445695638656616,
0.5881049036979675,
0.2636403441429138,
-0.2484045922756195,
0.6311541795730591,
-0.629511296749115,
0.014992770738899708,
0.25265073776245117,
0.16310259699821472,
-1.1757012605667114,
0.5834609270095825,
-0.9451086521148682,
-0.238475501537323,
-0.46503946185112,
0.07151497900485992,
0.6207786202430725,
-0.22093653678894043,
0.368499755859375,
-0.31330356001853943,
0.12430974841117859,
-0.19045060873031616,
-0.048156946897506714,
-0.5836493968963623,
0.41256457567214966,
1.1867384910583496,
0.2136332243680954,
0.06148279085755348,
-0.6205087304115295,
0.35199248790740967,
-0.13388241827487946,
-0.2847854495048523,
0.3150222599506378,
0.7580104470252991,
-0.5084071755409241,
0.5118563175201416,
-0.07175276428461075,
0.4066269099712372,
-0.20098870992660522,
0.8897569179534912,
0.7078810930252075,
0.13629688322544098,
-0.07873184978961945,
0.1243743747472763,
-0.7024620175361633,
0.6779535412788391,
-0.11243818700313568,
-0.29937657713890076,
0.2146487981081009,
0.6326648592948914,
0.3552264869213104,
-0.4025302231311798,
0.017329173162579536,
-0.908804178237915,
-0.6665472984313965,
-0.5628768801689148,
-0.5447762608528137,
0.6420841217041016,
0.44387808442115784,
-0.15353311598300934,
-0.9390976428985596,
0.08470117300748825,
-0.16403828561306,
0.217056542634964,
0.12219713628292084,
-0.14356181025505066,
0.885992705821991,
0.18694645166397095,
0.7978813052177429,
-0.03693031892180443,
0.0554407499730587,
-0.4651722311973572,
0.012212523259222507,
0.1776147186756134,
-0.8662494421005249,
0.17832393944263458,
-0.2796584665775299,
0.4131277799606323,
-0.2022794932126999,
0.7873597741127014,
-0.3137957751750946,
-0.8533408641815186,
-0.3795590102672577,
-0.8762385845184326,
0.05638521909713745,
1.0928350687026978,
-0.5016512870788574,
-0.11038114875555038,
-0.265746533870697,
-0.5427117347717285,
0.11070957779884338,
0.3588525354862213,
0.5688614845275879,
-0.5170120000839233,
0.3141879439353943,
0.09886470437049866,
-0.06684493273496628,
-0.11134514957666397,
-0.35178419947624207,
0.21231356263160706,
0.22079366445541382,
-0.22268113493919373,
1.0278593301773071,
-0.2998545467853546,
-0.8054726719856262,
0.0009404643205925822,
0.48476535081863403,
0.6834515929222107,
1.1920474767684937,
0.19622819125652313,
0.07689805328845978,
0.33325842022895813,
-0.4680722951889038,
-0.444220632314682,
-0.04637358710169792,
-0.6251131296157837,
-0.30548688769340515,
0.031563058495521545,
0.2883699834346771,
0.24087265133857727,
0.31238141655921936,
0.6831403970718384,
0.22613674402236938,
0.10106021165847778,
0.48350289463996887,
0.2831149697303772,
0.07235486805438995,
0.3320578634738922,
-0.5707074999809265,
0.4015188217163086,
-0.6521015763282776,
0.07349062711000443,
0.1081366315484047,
-0.1326208859682083,
-0.2738301455974579,
-0.4888782203197479,
-0.5637196898460388,
-0.33658233284950256,
0.6937218904495239,
0.6330291032791138,
-0.9163682460784912,
0.6471273899078369,
-0.3805076479911804,
0.42132195830345154,
-0.4703686237335205,
-0.14607661962509155,
1.0671710968017578,
0.3714947998523712,
0.3435385823249817,
-0.8349131941795349,
0.25340187549591064,
-0.591824471950531,
0.41683539748191833,
-0.026028087362647057,
-0.7418208718299866,
-0.7038317322731018,
-0.6626107692718506,
-0.054740045219659805,
-0.1527549922466278,
0.054198987782001495,
0.7159721851348877,
0.08579742908477783,
0.11108795553445816,
-0.6052928566932678,
-0.4632047712802887,
0.7767108082771301,
-0.43377336859703064,
-0.5792125463485718,
0.3815186619758606,
-0.347561776638031,
-0.30441975593566895,
0.7542293667793274,
-0.688498318195343,
-0.26572704315185547,
-0.1855708211660385,
-0.4280301630496979,
0.3192838430404663,
-0.28879961371421814,
-0.13986128568649292,
-0.21210572123527527,
-0.6976748704910278,
-0.01777372695505619,
0.507192850112915,
-0.01827286370098591,
0.15050487220287323,
0.5174899101257324,
0.1342918425798416,
-0.4839290976524353,
0.4263315498828888,
-0.269698828458786,
0.029625188559293747,
1.044320821762085,
0.7059444785118103,
0.2296840399503708,
0.130863755941391,
0.25448912382125854,
0.10546476393938065,
-0.23945562541484833,
0.3074738085269928,
0.11040705442428589,
-0.15643081068992615,
-0.27515938878059387,
0.07670792192220688,
-0.6423504948616028,
-0.5786271095275879,
-0.045490920543670654,
-0.32995352149009705,
0.8567261099815369,
-0.025028031319379807,
-0.6443331241607666,
-0.36855584383010864,
-0.22833143174648285,
-0.3510446846485138,
0.5699034333229065,
-0.10126142203807831,
-0.5288636684417725,
0.09691516309976578,
-0.6481596827507019,
-0.27521970868110657,
-0.7547405362129211,
0.1528356522321701,
-0.16254395246505737,
-0.13229374587535858,
0.6825482845306396,
-0.026310544461011887,
0.9401060938835144,
-0.8444098234176636,
0.23452018201351166,
-0.6055117249488831,
0.15589052438735962,
-0.6000470519065857,
-0.4874119162559509,
-0.06968796998262405,
-0.8852890133857727,
0.033514756709337234,
-0.29082900285720825,
0.0957997590303421,
-0.2215634435415268,
-0.16686148941516876,
0.10962630808353424,
-0.08928731828927994,
-0.27823349833488464,
-0.0857163667678833,
0.5366182923316956,
0.05026445537805557,
-0.85610431432724,
-0.11767671257257462,
0.2761678695678711,
0.25884148478507996,
0.3952940106391907,
-0.06113571673631668,
-0.7763097286224365,
0.2638208568096161,
-0.08532175421714783,
0.4706169068813324,
-0.5264626741409302,
-0.4443649351596832,
0.287440687417984,
-0.3967892527580261,
0.15943172574043274,
0.39034417271614075,
-0.08296879380941391,
-0.31394317746162415,
-0.6605766415596008,
-0.42537012696266174,
0.34871020913124084,
-0.7212432026863098,
-0.14442434906959534,
-0.475658118724823,
-0.5522491335868835,
-0.6643084287643433,
0.748811662197113,
-0.010659590363502502,
0.33859261870384216,
0.6116711497306824,
-0.07205371558666229,
-0.23812873661518097,
0.20724278688430786,
0.38662704825401306,
0.012485555373132229,
-0.13179488480091095,
0.8585275411605835,
-0.5635537505149841,
0.6508087515830994,
-0.28828248381614685,
0.4215024411678314,
-0.8440543413162231,
1.2761479616165161,
-0.3338607847690582,
-0.219694584608078,
-0.15583942830562592,
-0.1381203532218933,
1.1150656938552856,
-1.0960536003112793,
0.40074625611305237,
0.4271564781665802,
-0.33823034167289734,
0.7212014198303223,
0.3982144594192505,
-0.6648243069648743,
-0.2318107932806015,
-0.49687910079956055,
-0.8411216139793396,
1.0410420894622803,
0.3851458728313446,
-0.13725270330905914,
-0.9249473214149475,
-0.6082171201705933,
0.2615322172641754,
0.35355088114738464,
0.27887842059135437,
0.34753361344337463,
-0.4180741310119629,
-0.18863916397094727,
0.32069775462150574,
-0.024035844951868057,
-0.38832029700279236,
0.1438625305891037,
0.3113742470741272,
0.18861177563667297,
-0.04982513561844826,
0.11780247092247009,
-0.48609253764152527,
-0.4542001485824585,
0.09141708165407181,
0.12153460830450058,
0.26679685711860657,
-0.37839800119400024,
0.3974941670894623,
-0.4656789302825928,
-0.6462880373001099,
-0.3942697048187256,
-0.11650096625089645,
0.41475337743759155,
0.3117333948612213,
0.5917437076568604,
0.608605146408081,
0.583115816116333,
0.07652644068002701,
0.6831822395324707,
-0.6098626852035522,
-0.2822880446910858,
0.3253211975097656,
-0.4161468744277954,
-0.4768325686454773,
0.2596420645713806,
0.2410174161195755,
-0.37274670600891113,
-0.844313383102417,
-1.0933434963226318,
-0.046340081840753555,
-0.42780616879463196,
0.02405114658176899,
0.13745634257793427,
-0.30594542622566223,
-0.304849773645401,
0.7059689164161682,
0.7399925589561462,
0.23280423879623413,
-0.17957289516925812,
0.10464593768119812,
-0.6520925760269165,
-0.4341563582420349,
0.2884857952594757,
1.308963656425476,
-0.20616468787193298,
-0.6924704313278198,
-0.3211933970451355,
-0.10041942447423935,
-0.5401275753974915,
-0.24331414699554443,
0.24423463642597198,
0.05986347794532776,
0.5094888806343079,
-0.04219279810786247,
0.1815042495727539,
0.9132567048072815,
0.6938830614089966,
0.2160988748073578,
-0.3140289783477783,
-0.23219071328639984,
-0.8672959208488464,
-0.21562354266643524,
-0.7184244394302368,
0.40971916913986206,
0.7481349110603333,
0.05255281552672386,
0.432641863822937,
-0.14687465131282806,
-0.5556568503379822,
-0.2840302884578705,
-0.4621308147907257,
0.11149325221776962,
-0.9546762108802795,
-0.2543487548828125,
-0.18011465668678284,
-0.19300010800361633,
-0.23661847412586212,
0.6080068349838257,
0.05236155167222023,
0.24021433293819427,
-0.9345397353172302,
-0.012282727286219597,
0.08755715936422348,
0.22261284291744232,
-0.23490843176841736,
-1.2395817041397095,
-0.5370594263076782,
-0.007118115667253733,
-0.5121076107025146,
-0.14928460121154785,
-0.26424556970596313,
0.1419733166694641,
-0.5750171542167664,
0.38522762060165405,
0.024714093655347824,
0.9912182092666626,
-1.0284149646759033,
-1.1183068752288818,
0.36736446619033813,
-0.27024850249290466,
-0.4794493615627289,
0.22475673258304596,
0.177232027053833,
0.9248640537261963,
0.29802435636520386,
-0.09280409663915634,
-0.07177780568599701,
0.32011857628822327,
-1.0100148916244507,
0.2522558271884918,
0.3261442184448242,
0.5458677411079407,
-0.2793506383895874,
-0.4757252633571625,
-0.3458676338195801,
0.14242027699947357,
-1.0458208322525024,
0.5411346554756165,
-0.4749555289745331,
0.7276500463485718,
-0.3397896885871887,
0.1672392040491104,
0.1643189936876297,
0.19204583764076233,
0.29939743876457214,
0.5949667692184448,
-0.6189824938774109,
0.651620090007782,
0.22747290134429932,
0.38906532526016235,
-0.6369427442550659,
0.22647595405578613,
0.6438798308372498,
-0.0039524901658296585,
-0.09059008955955505,
0.5392959117889404,
-0.3732604682445526,
0.385756254196167,
0.013444628566503525,
0.018769675865769386,
-0.10320524871349335,
-0.14966189861297607,
-0.5737581849098206,
0.6127637028694153,
0.40163910388946533,
-0.5368266701698303,
0.13740547001361847,
-0.6028591990470886,
-0.4596545100212097,
-0.09516249597072601,
-0.6821838021278381,
-0.34744107723236084,
-0.11231465637683868,
-0.1349470466375351,
-0.1997850090265274,
0.3875395357608795,
-0.2711475193500519,
-0.10761500149965286,
0.20953039824962616,
0.4868669807910919,
0.15956532955169678,
-0.7149302363395691,
-0.33759260177612305,
-0.10765212774276733,
-0.680597186088562,
-0.4176628589630127,
0.07259172946214676,
0.5229536294937134,
-0.4443874657154083,
-0.7525927424430847,
0.22637853026390076,
0.07361242920160294,
0.24715249240398407,
0.09927590191364288,
-0.23888550698757172,
-0.2596428096294403,
-0.7007593512535095,
-0.1730974167585373,
-0.41165754199028015,
-0.09905174374580383,
-0.7169385552406311,
0.3773917853832245,
-0.38822343945503235,
-0.5746415257453918,
0.433491587638855,
0.003973116632550955,
0.41639524698257446,
-0.16789332032203674,
0.059450458735227585,
0.8157137632369995,
0.23853549361228943,
-0.561997652053833,
0.1372973918914795,
0.26539263129234314,
-0.3609860837459564,
0.02594124712049961,
-0.38939929008483887,
0.44705671072006226,
0.48360782861709595,
0.24717749655246735,
0.8817981481552124,
0.40322333574295044,
0.4584898054599762,
0.05533815920352936,
0.28872400522232056,
0.11110308021306992,
-0.15672911703586578,
0.28096163272857666,
0.58872389793396,
0.5098062753677368,
-0.0025454505812376738,
-0.02977382391691208,
-0.2612746059894562,
-0.027003372088074684,
0.22311437129974365,
0.2516772449016571,
-0.2923639714717865,
-0.2831759750843048,
-0.15249653160572052,
0.05565119534730911,
-0.7597396969795227,
-0.5365694761276245,
-0.022945459932088852,
0.5094231963157654,
0.654184103012085,
0.5218490362167358,
-0.09890260547399521,
0.41005247831344604,
0.38384297490119934,
0.05459519103169441,
-0.07717514783143997,
0.5099847912788391,
-0.0742555484175682,
1.118265151977539,
0.747356653213501,
0.47589820623397827,
0.5736508965492249,
0.41221344470977783,
0.7854164838790894,
-0.9821529388427734,
0.02905343845486641,
0.3838479518890381,
-0.7604940533638,
0.39290663599967957,
-0.33792752027511597,
0.38031071424484253,
-0.06922348588705063,
-0.8639847040176392,
0.34069550037384033,
-0.5334046483039856,
0.5281778573989868,
0.1617773026227951,
-0.37469226121902466,
0.10966654121875763,
0.9739143252372742,
0.09571225196123123,
0.3831031918525696,
0.7869985103607178,
-0.14129677414894104,
0.5129216909408569,
1.01333749294281,
1.1336203813552856,
-0.0724654346704483,
0.7092105746269226,
0.36257192492485046,
-0.7009258270263672,
0.08150019496679306,
0.45824262499809265,
-0.5503552556037903,
0.6109443306922913,
-0.5538822412490845,
-0.5013524293899536,
0.18380795419216156,
0.2853575646877289,
-0.2256062775850296,
-0.31821852922439575,
0.6090106964111328,
-0.07185959070920944,
-0.20099610090255737,
-0.5478324890136719,
1.1668789386749268,
0.49088120460510254,
-0.38945046067237854,
-0.16430023312568665,
0.29600170254707336,
-0.9509392976760864,
0.2500074803829193,
-1.0151952505111694,
0.49793973565101624,
-0.11504776775836945,
-0.2633334696292877,
-0.2327331304550171,
-0.056983582675457,
-0.10620232671499252,
-0.7948254942893982,
-0.10401619970798492,
-0.8081480860710144,
0.43455877900123596,
0.4284217655658722,
0.3481449484825134,
0.34010496735572815,
-0.5719946026802063,
0.03152649477124214,
-0.05388238653540611,
0.7343831658363342,
0.2854248583316803,
-0.09157425910234451,
0.9738495945930481,
0.6662604808807373,
-0.6030743718147278,
0.09477017819881439,
0.5064139366149902,
-0.34393563866615295,
0.6647418141365051,
0.20330554246902466,
-0.03592532128095627,
0.19049648940563202,
-0.5583691596984863,
0.13930478692054749,
0.0265195295214653,
0.051177702844142914,
-0.014896053820848465,
-0.18111668527126312,
-0.20558863878250122,
-0.7444818615913391,
-0.6167497038841248,
-0.40670982003211975,
0.42600977420806885,
0.22365626692771912,
0.006383860949426889,
0.5519041419029236,
-0.5289462804794312,
4.3266072273254395,
1.167478322982788,
0.4806113839149475,
0.23311254382133484,
0.8133141398429871,
0.9248086214065552,
0.06374331563711166,
-0.3735998272895813,
0.6100777983665466,
-0.2895183861255646,
-0.5756102800369263,
-0.3010158836841583,
0.3260524272918701,
-0.4696517884731293,
-0.4211599826812744,
0.524462878704071,
-0.10853439569473267,
-0.4303394556045532,
-0.3542979061603546,
-0.6784283518791199,
-0.7328270077705383,
0.00046372547512874007,
0.5592842102050781,
0.139591246843338,
0.5233634114265442,
0.2886938750743866,
0.29832974076271057,
-0.8959837555885315,
-0.14212137460708618,
-0.418096661567688,
-0.9662920236587524,
-0.5618455410003662,
-0.3002772331237793,
0.19657272100448608,
-0.6610887050628662,
0.12462808191776276,
0.1568560004234314,
-0.4564878046512604,
0.13522031903266907,
0.06582047045230865,
0.21306297183036804,
-0.3481731414794922,
0.002917266683652997,
-0.35326051712036133,
-0.3256261348724365,
0.9867642521858215,
-0.07724835723638535,
0.39460670948028564,
0.11386048793792725,
-0.11762857437133789,
0.15143319964408875,
0.2589852213859558,
0.6709023118019104,
-0.39494726061820984,
-0.6302306652069092,
0.12459886074066162,
-0.521669864654541,
-0.22320707142353058,
0.29182493686676025,
-0.43654870986938477,
0.16182367503643036,
-0.15062393248081207,
-0.04026922583580017,
0.089737169444561,
-0.6004665493965149,
0.5197996497154236,
0.05316677317023277,
-0.21018241345882416,
-0.43772968649864197,
0.37263479828834534,
-0.05948403850197792,
-0.5009480118751526,
-0.251669704914093,
0.4491276144981384,
-0.020539328455924988,
0.2918627858161926,
0.04596458747982979,
0.17542922496795654,
0.1331101804971695,
0.04407396540045738,
0.13370078802108765,
-0.0375458188354969,
-0.07747271656990051,
-0.06999724358320236,
0.2500888407230377,
0.4356830418109894,
-0.34685859084129333,
-0.23919019103050232,
0.19540920853614807,
0.33596038818359375,
0.394328236579895,
0.35236656665802,
0.4017255902290344,
0.23208777606487274,
-0.5378929972648621
] |
A Study of the $N=2$ Kazakov-Migdal Model
|
We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In contrast to our earlier work on the subject we have chosen here {\it not} to integrate out the gauge fields but to keep them in the Monte Carlo simulation. This allows us to measure observables associated with the gauge fields and thereby address the problem of the local $Z_2$ symmetry present in the model. We confirm our previous result that the model has a line of first order phase transitions terminating in a critical point. The adjoint plaquette has a clear discontinuity across the phase transition, whereas the plaquette in the fundamental representation is always zero in accordance with Elitzur's theorem. The density of small $Z_2$ monopoles shows very little variation and is always large. We also find that the model has extra local U(1) symmetries which do not exist in the case of the standard adjoint theory. As a result, we are able to show that two of the angles parameterizing the gauge field completely decouple from the theory and the continuum limit defined around the critical point can therefore not be `QCD'.
|
Sinya Aoki, Andreas Gocksch and Yue Shen
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208029
|
hep-lat/9208030
|
[
0.01018525194376707,
-0.6205120086669922,
-0.06702986359596252,
0.2650086581707001,
-0.24359476566314697,
-0.6649283170700073,
-0.24935978651046753,
-0.42114338278770447,
-0.06890975683927536,
1.4633135795593262,
0.6549066305160522,
0.1997968852519989,
0.2638580799102783,
-0.7612059116363525,
-0.4909970164299011,
0.23626121878623962,
-0.3232402205467224,
-0.4815484583377838,
-1.7436623573303223,
0.45253539085388184,
0.38760092854499817,
-0.2147776037454605,
-1.4884974956512451,
-0.6488236784934998,
0.16082879900932312,
1.2988225221633911,
0.5202265381813049,
0.017292844131588936,
1.1584819555282593,
0.41859206557273865,
0.13624438643455505,
-0.19222451746463776,
-0.29887422919273376,
-0.2063407152891159,
-0.5107094645500183,
-0.06570355594158173,
0.37350448966026306,
-0.02151753380894661,
0.4958193302154541,
-0.1517193466424942,
0.42688125371932983,
-0.35360002517700195,
-0.027912039309740067,
-0.45159825682640076,
-1.0100078582763672,
-0.12394863367080688,
-0.9129477143287659,
-0.36365237832069397,
0.4557827115058899,
-1.8918185234069824,
0.09295593202114105,
0.2734718322753906,
0.7645586729049683,
-1.0241327285766602,
-0.5800636410713196,
-0.4041885435581207,
-0.2766202986240387,
0.479780912399292,
-0.2541479468345642,
-0.32443833351135254,
1.1797571182250977,
-0.06989650428295135,
0.8221615552902222,
-1.0904490947723389,
0.41256529092788696,
0.2052130252122879,
-0.4637705683708191,
0.773040235042572,
-0.17276817560195923,
-0.21499401330947876,
-0.16290801763534546,
-0.62906414270401,
-1.662211537361145,
-0.3912961781024933,
-0.7848117351531982,
0.14083130657672882,
-0.16596367955207825,
-0.486508309841156,
-1.0809370279312134,
-0.8337628841400146,
-0.09626327455043793,
-0.47315657138824463,
-1.068642020225525,
0.5179306268692017,
-0.719743013381958,
-0.9496340155601501,
-0.006392919458448887,
-0.4977504014968872,
-0.020092904567718506,
0.3594517409801483,
0.58193039894104,
0.9063290357589722,
0.11329523473978043,
0.2741038203239441,
0.5474953055381775,
0.4008583724498749,
-0.18647977709770203,
0.6664435863494873,
-0.03128926083445549,
0.05506386235356331,
0.009255006909370422,
0.22359107434749603,
-1.2084331512451172,
0.3232463598251343,
0.07021845877170563,
0.6605571508407593,
-0.3904431462287903,
-0.5028585195541382,
-0.08542551100254059,
-0.44211244583129883,
0.29785075783729553,
-0.6396276354789734,
0.4537643492221832,
1.0985336303710938,
-0.5705506801605225,
0.7579288482666016,
-0.6196271181106567,
0.06319046020507812,
-0.19248735904693604,
-0.19070732593536377,
0.16205985844135284,
-0.010735204443335533,
0.24915005266666412,
0.12616336345672607,
-0.1109708696603775,
-0.00018346786964684725,
-0.156795933842659,
0.41641953587532043,
-0.47306910157203674,
0.5525255799293518,
-0.07569583505392075,
-0.05409129336476326,
-0.21357546746730804,
0.824771523475647,
-0.7631583213806152,
-0.4596957564353943,
-0.01111407671123743,
0.4173291027545929,
0.021316025406122208,
-0.5880732536315918,
1.0325504541397095,
-1.0496374368667603,
0.07460705935955048,
1.6573266983032227,
0.1039615049958229,
0.7568660378456116,
-0.0591147318482399,
0.290591299533844,
-0.3330768346786499,
0.6268079876899719,
-0.4841358959674835,
0.36124077439308167,
-0.3073568344116211,
0.1581839919090271,
0.37165945768356323,
0.040855132043361664,
-0.38320574164390564,
0.03143449127674103,
-0.4650987386703491,
-0.4521508514881134,
0.6000734567642212,
-0.02050691470503807,
-0.5314001441001892,
0.15404729545116425,
-0.8685062527656555,
-0.1428123414516449,
-0.7010443806648254,
-0.10003196448087692,
0.4031641483306885,
-1.0779311656951904,
-0.8527299761772156,
0.7063261270523071,
-0.1716017723083496,
0.8685292601585388,
0.607254683971405,
0.28625252842903137,
0.25614872574806213,
-0.5739467144012451,
0.17602406442165375,
0.19992820918560028,
0.1759500354528427,
-0.5369957089424133,
-0.8253636360168457,
0.14673136174678802,
-0.004476415459066629,
-0.3867972195148468,
-0.0749417170882225,
-0.35079920291900635,
0.029034676030278206,
0.12553474307060242,
-0.3705916404724121,
0.34438392519950867,
-0.5101103782653809,
0.8472707867622375,
-0.5565184354782104,
-0.16556042432785034,
-0.5830369591712952,
-0.107822485268116,
-0.5273707509040833,
-0.643420398235321,
0.27483758330345154,
0.37163224816322327,
-0.8544228076934814,
0.033856138586997986,
-1.1845946311950684,
0.04535596817731857,
1.0948426723480225,
0.06666558235883713,
-1.0556390285491943,
-0.6567753553390503,
0.13305878639221191,
0.12996433675289154,
0.5544484257698059,
-0.892089307308197,
0.4673374593257904,
0.22681614756584167,
0.9670423269271851,
0.7155551910400391,
0.3201201856136322,
-0.039622712880373,
0.26807987689971924,
0.6334906220436096,
-0.010522827506065369,
0.7701377868652344,
-0.5624232292175293,
-0.5990715026855469,
-0.008642666041851044,
0.16488246619701385,
0.04640255868434906,
0.1492968648672104,
-0.10695356130599976,
0.37513071298599243,
-0.1321011185646057,
0.42302265763282776,
0.24638937413692474,
0.38584622740745544,
0.7908519506454468,
-0.05116177722811699,
0.5076253414154053,
0.585729718208313,
-0.8432188630104065,
-0.02408631145954132,
0.2622697651386261,
-0.07670512050390244,
0.10496488958597183,
0.06651826202869415,
-0.6215253472328186,
-0.062046825885772705,
-0.6677162647247314,
0.14896683394908905,
-0.17151674628257751,
0.9734231233596802,
0.05091380327939987,
0.5398908853530884,
-1.2825007438659668,
0.10842331498861313,
-0.34336161613464355,
0.9856452345848083,
0.39913520216941833,
0.14145968854427338,
0.5879426598548889,
-0.4033036530017853,
-0.009140717796981335,
-1.0241378545761108,
-0.04578985646367073,
1.0751121044158936,
0.18521416187286377,
-0.055315472185611725,
0.5756027102470398,
-0.2615062892436981,
-1.1091771125793457,
0.057445719838142395,
-1.1715539693832397,
0.2465180605649948,
-0.6471657752990723,
-0.19511738419532776,
0.4025288224220276,
-0.6422228217124939,
0.4235185980796814,
-0.10764153301715851,
-0.46105116605758667,
0.415193647146225,
-0.6149078011512756,
0.24773333966732025,
0.6401081681251526,
-0.33830341696739197,
-0.2567945122718811,
0.4227033257484436,
-0.668742835521698,
-0.4872995913028717,
-0.2720238268375397,
0.3733559846878052,
0.6557202339172363,
-0.617944061756134,
0.45023083686828613,
0.03978165611624718,
-0.08281455188989639,
0.2618497908115387,
0.3158825635910034,
-0.3633520007133484,
-0.08808183670043945,
0.5820884704589844,
-0.3025533854961395,
-0.9111048579216003,
-1.1996798515319824,
0.5012556910514832,
0.37744367122650146,
-0.37271416187286377,
-0.08667060732841492,
0.13543246686458588,
-0.426073282957077,
0.9068871736526489,
0.14972122013568878,
-0.4143868088722229,
-0.020742420107126236,
1.6032476425170898,
0.5794195532798767,
0.05997084081172943,
-0.17926985025405884,
-0.12851744890213013,
-0.5247477889060974,
0.1972680389881134,
0.11007452011108398,
-0.42226719856262207,
-0.8191420435905457,
1.0577365159988403,
-0.1364712417125702,
-0.49861034750938416,
0.17833486199378967,
-0.6413877010345459,
-0.6728619337081909,
0.06533073633909225,
-0.37063831090927124,
0.25425276160240173,
0.03744640573859215,
-0.13875697553157806,
-1.101649284362793,
0.1570686548948288,
0.541508138179779,
-0.1645558923482895,
0.4239226281642914,
-0.5454196929931641,
0.31868454813957214,
0.12373694777488708,
0.47982826828956604,
0.03719909116625786,
-0.29180780053138733,
-0.4812934696674347,
-0.6514192819595337,
0.3339625597000122,
-0.7614176869392395,
0.15098312497138977,
-0.34511029720306396,
0.7768003940582275,
0.24306930601596832,
0.38463327288627625,
-0.3381772041320801,
-0.34854501485824585,
-0.5432743430137634,
-0.42528289556503296,
0.782260537147522,
0.7880926132202148,
-0.5134153962135315,
-0.39697080850601196,
-0.8198450207710266,
-0.15267428755760193,
-0.21040336787700653,
-0.27717509865760803,
0.5927317142486572,
-0.910658597946167,
0.613253116607666,
-0.04334859177470207,
-0.7389920949935913,
-0.24014654755592346,
-0.5107756853103638,
0.5422893166542053,
0.2591888904571533,
-0.06735647469758987,
1.0615326166152954,
-0.11715877801179886,
-0.5481254458427429,
0.011478694155812263,
0.6948427557945251,
0.4045863151550293,
0.5064964294433594,
0.03882669657468796,
-0.48876243829727173,
0.23383262753486633,
-0.21654340624809265,
-0.18978354334831238,
-0.3076860010623932,
0.10677409917116165,
0.012626624666154385,
-0.2612217962741852,
0.10439279675483704,
0.7589107751846313,
1.1362894773483276,
-0.44303685426712036,
0.20236489176750183,
0.4313901662826538,
0.29219841957092285,
0.31331947445869446,
0.7400456666946411,
0.49129974842071533,
0.41103851795196533,
0.7596002817153931,
-0.9927203059196472,
0.16102568805217743,
0.34608080983161926,
0.513671875,
-0.4285108745098114,
-0.4298916757106781,
-0.4867621660232544,
-0.7061401605606079,
0.25246351957321167,
0.523106575012207,
-0.8471930623054504,
0.6619409918785095,
0.5958897471427917,
0.445149302482605,
0.018248477950692177,
-0.20192639529705048,
1.0890870094299316,
0.3227839767932892,
0.15012845396995544,
-0.9677438139915466,
0.34519848227500916,
-0.26257815957069397,
-0.305745929479599,
0.4845639765262604,
-0.9440667629241943,
-0.6807740926742554,
-1.3678390979766846,
0.5352913737297058,
-0.725932776927948,
0.3246281147003174,
0.8779922723770142,
-0.07167491316795349,
0.289505273103714,
-0.4156242311000824,
-0.4038865268230438,
0.6134417653083801,
-0.19961699843406677,
-0.4741614758968353,
0.12645037472248077,
0.24385781586170197,
-0.39316725730895996,
1.1877772808074951,
0.3084191381931305,
-0.2786911427974701,
0.07152236998081207,
-0.2744157314300537,
-0.18870128691196442,
-0.45821335911750793,
-0.3572283387184143,
-0.07843691855669022,
-0.2797585129737854,
-0.49030616879463196,
0.4455827474594116,
-0.14397500455379486,
0.06743381917476654,
-0.1057058572769165,
0.2225203514099121,
-0.22159522771835327,
0.10286320000886917,
-0.14094528555870056,
0.13590599596500397,
0.9922773241996765,
0.6181146502494812,
0.42220062017440796,
-0.07299776375293732,
-0.12363830208778381,
0.30359724164009094,
0.19264204800128937,
0.48391905426979065,
0.3002132177352905,
0.16129127144813538,
-0.5694612860679626,
-0.23336786031723022,
-0.5923271775245667,
-0.8432902693748474,
0.36147236824035645,
0.04500795528292656,
0.9689783453941345,
-0.30351758003234863,
-0.4284602999687195,
-0.03566649928689003,
0.1643725037574768,
-0.5443987250328064,
0.36996859312057495,
-0.2687978744506836,
-0.6231480836868286,
0.6432193517684937,
-0.8579385876655579,
0.2754076421260834,
-0.5733217000961304,
-0.15299181640148163,
0.19150520861148834,
0.699238121509552,
0.49953293800354004,
0.18004314601421356,
0.7848323583602905,
-0.8887142539024353,
-0.06756269186735153,
-0.7939168214797974,
0.2532086968421936,
-0.68609619140625,
-0.025583848357200623,
-0.26567041873931885,
-0.6308622360229492,
0.3690333664417267,
-0.16621585190296173,
0.14105278253555298,
-0.04723862558603287,
0.07470615953207016,
-0.09253979474306107,
0.11765807867050171,
0.21973025798797607,
-0.03522024303674698,
0.46617433428764343,
0.12165398895740509,
-0.41095614433288574,
-0.0034286929294466972,
0.8526747226715088,
-0.5695586204528809,
0.17205758392810822,
0.06667715311050415,
-0.6035157442092896,
0.36905884742736816,
-0.18053282797336578,
0.476440966129303,
-0.2912454605102539,
-0.3087364137172699,
-0.1784912496805191,
-0.2778854966163635,
0.9020546674728394,
0.40760645270347595,
0.2347748726606369,
0.15918901562690735,
-0.9396360516548157,
0.0674009621143341,
0.5070169568061829,
-0.37019282579421997,
-0.4834987223148346,
-0.05088626593351364,
-0.401888370513916,
-0.08930566906929016,
0.9706422090530396,
-0.3850715458393097,
0.7773821353912354,
-0.09374204277992249,
-0.018882131204009056,
0.27812570333480835,
0.5256651043891907,
-0.1980327069759369,
0.09302493184804916,
0.2538093030452728,
0.22635197639465332,
0.7427187561988831,
0.287807822227478,
-0.556786060333252,
0.581254780292511,
-0.9630600214004517,
1.2658772468566895,
-1.2716330289840698,
-0.32609739899635315,
-0.18822024762630463,
-0.08110912889242172,
0.918729841709137,
-0.9142597317695618,
0.27441421151161194,
0.5120113492012024,
0.07190978527069092,
0.0015686624683439732,
0.19328786432743073,
-0.19262099266052246,
-0.9556989073753357,
-1.291978359222412,
-0.5183104872703552,
0.1642095148563385,
0.11744971573352814,
-0.1253892481327057,
-0.6095951795578003,
-0.570283830165863,
0.27833905816078186,
0.03507675603032112,
0.7873615026473999,
0.18401755392551422,
0.044913917779922485,
0.0683302953839302,
0.5062772035598755,
-0.4911316931247711,
-0.5398073792457581,
0.41727644205093384,
-0.12319253385066986,
0.17040285468101501,
0.16718578338623047,
0.1751106232404709,
-1.0137938261032104,
-0.5085450410842896,
-0.09500384330749512,
0.10335052758455276,
0.12355415523052216,
-0.5728597044944763,
0.6044532060623169,
-0.24856318533420563,
-0.17546063661575317,
-0.4608159065246582,
0.24109777808189392,
0.008016126230359077,
0.40412044525146484,
0.024022111669182777,
0.41346248984336853,
0.6090219020843506,
0.06600689888000488,
0.6912320256233215,
-0.1288110315799713,
-0.5575388669967651,
0.3806481957435608,
-0.5228151679039001,
-0.31406429409980774,
0.5702498555183411,
-0.039266690611839294,
-0.6449469327926636,
0.2630405128002167,
-0.8271902799606323,
0.15893006324768066,
-0.7793118357658386,
-0.5748639106750488,
-0.0015773442573845387,
-0.7401677966117859,
-0.37011271715164185,
0.9911425709724426,
0.5302641987800598,
-0.28406354784965515,
0.16668067872524261,
0.1676364243030548,
-0.3879898190498352,
-0.1490287333726883,
-0.5507033467292786,
1.4175416231155396,
-0.2677730321884155,
-0.5838213562965393,
0.16714316606521606,
0.4547870457172394,
-0.3656567633152008,
0.34667712450027466,
0.3303048312664032,
-0.361280232667923,
0.5567073822021484,
0.3729132413864136,
0.24049240350723267,
0.7043916583061218,
0.8887511491775513,
0.06749595701694489,
-0.04781753942370415,
-0.17269770801067352,
-0.8584877252578735,
-0.4409155547618866,
-0.2940624952316284,
0.14643295109272003,
0.998356282711029,
0.15491162240505219,
0.4343022406101227,
0.5063107013702393,
-0.5697234272956848,
-0.19463375210762024,
-1.5030163526535034,
0.08523864299058914,
-0.776177704334259,
-0.12175120413303375,
-0.16098926961421967,
-0.49091029167175293,
0.882004976272583,
0.6813346147537231,
-0.003040897659957409,
-0.0944669172167778,
-1.114617943763733,
0.14338061213493347,
0.15656982362270355,
-0.2757577896118164,
-0.29604002833366394,
-0.5881780385971069,
-0.04243297874927521,
-0.5000462532043457,
0.06977348029613495,
0.20689226686954498,
-0.05131951719522476,
-0.21245957911014557,
0.04112057760357857,
0.41199490427970886,
-0.06066923215985298,
0.2961358428001404,
-0.975904643535614,
-1.0652492046356201,
-0.32258543372154236,
-0.0056414371356368065,
-1.5221805572509766,
0.5205039978027344,
0.3974458873271942,
0.7228384613990784,
0.2376670390367508,
0.5700740218162537,
-0.8646497130393982,
0.11947212368249893,
-1.082111120223999,
0.05380244925618172,
0.35296982526779175,
0.3980735242366791,
-0.26832929253578186,
-0.20943406224250793,
-0.6081795692443848,
0.1635526716709137,
-0.6642144918441772,
0.7205499410629272,
-0.30897510051727295,
0.17387568950653076,
-0.39477890729904175,
0.4941279888153076,
0.5235518217086792,
0.19064730405807495,
-0.05508270487189293,
0.9927467107772827,
-0.6310445070266724,
-0.19960562884807587,
0.452998548746109,
0.39839842915534973,
-0.050424329936504364,
0.13622668385505676,
0.11731965839862823,
-0.417630672454834,
0.30062857270240784,
-0.0019051568815484643,
0.059731367975473404,
0.5246935486793518,
0.11660055071115494,
-0.5525304079055786,
-0.4759010076522827,
-0.33100295066833496,
-0.9079933762550354,
0.4521850645542145,
0.337581992149353,
-0.6831930875778198,
-0.04474012553691864,
-0.40363940596580505,
-0.9890364408493042,
0.6000760197639465,
-0.7874096035957336,
-0.3675154745578766,
0.5237950682640076,
-0.5559420585632324,
-0.21885031461715698,
-0.1559303253889084,
-0.19801750779151917,
0.12008033692836761,
0.4449945092201233,
0.15700779855251312,
-0.882859468460083,
0.11313958466053009,
-0.19377487897872925,
-0.0021730600856244564,
-0.48657405376434326,
-0.4089507758617401,
-0.6045321226119995,
0.5871180891990662,
-0.47732242941856384,
-0.7874899506568909,
-0.10179298371076584,
0.6865450143814087,
-0.1029469445347786,
-0.2700030207633972,
-0.14805875718593597,
-0.06546085327863693,
-0.06482356786727905,
-0.2203013151884079,
-0.3965325951576233,
-0.08766837418079376,
-0.5604836940765381,
0.3263797163963318,
0.07137967646121979,
-0.18078204989433289,
0.22189582884311676,
0.4714517891407013,
-0.03668844327330589,
0.21967260539531708,
0.1642378568649292,
1.3755196332931519,
0.22484354674816132,
-0.3863735795021057,
0.7596572041511536,
-0.18465536832809448,
-0.09006177634000778,
-0.05895116552710533,
-1.0134204626083374,
0.013552067801356316,
0.1595919132232666,
0.36786162853240967,
0.7121079564094543,
-0.09917505085468292,
0.2000548541545868,
0.7257415652275085,
0.636227548122406,
0.40789610147476196,
-0.08351556956768036,
0.5297484993934631,
0.3257092237472534,
0.5986196398735046,
-0.00015233817975968122,
-0.15108433365821838,
0.11561497300863266,
-0.3012978136539459,
-0.672724723815918,
-0.15374986827373505,
-0.3994290828704834,
-0.25994953513145447,
0.36026525497436523,
-0.3519667387008667,
-0.45723453164100647,
0.08004244416952133,
-0.33348172903060913,
0.22522728145122528,
0.6391960978507996,
0.47936493158340454,
-0.028772208839654922,
0.23668403923511505,
0.9127643704414368,
0.22483497858047485,
-0.1817384511232376,
0.371265709400177,
0.07839605212211609,
0.943087100982666,
0.9126939177513123,
0.10163389891386032,
0.944352924823761,
0.4790254533290863,
0.711741030216217,
-0.566072404384613,
-0.19103501737117767,
0.5208004713058472,
-1.1634713411331177,
-0.06554674357175827,
-0.7792277932167053,
0.2646090090274811,
-0.3105732202529907,
-0.6900500059127808,
0.6273524165153503,
-0.7679677605628967,
-0.029804622754454613,
0.7075956463813782,
-0.4884994924068451,
0.5716753602027893,
0.7649731636047363,
0.30935606360435486,
-0.18457236886024475,
0.7750070095062256,
0.2301478087902069,
-0.08210135996341705,
1.2073187828063965,
1.4254028797149658,
-0.07739634066820145,
0.36711353063583374,
0.39146727323532104,
-0.30246058106422424,
0.25913944840431213,
0.767436683177948,
-0.6488872170448303,
0.7689493298530579,
-0.5971719026565552,
-0.2575998306274414,
0.43087995052337646,
0.4603000581264496,
-0.12406927347183228,
-0.23440876603126526,
0.032553136348724365,
-0.08583702147006989,
-0.3629629909992218,
-0.476891428232193,
1.9620112180709839,
1.0760571956634521,
-0.6626165509223938,
-0.8267454504966736,
0.013426866382360458,
-0.366763710975647,
-0.23070257902145386,
-0.3948901295661926,
0.41395828127861023,
0.14402180910110474,
-0.005150357726961374,
-0.2283501774072647,
-0.8885598182678223,
-0.7000356316566467,
-0.5676278471946716,
0.27559250593185425,
-0.8131324648857117,
0.32783547043800354,
0.38966864347457886,
0.11782541126012802,
-0.09096351265907288,
-0.7990633249282837,
-0.1890736222267151,
0.08282539248466492,
0.8664210438728333,
0.06951630860567093,
-0.0370488315820694,
0.7360206246376038,
0.8384201526641846,
-0.6509855389595032,
0.6504936814308167,
1.1015292406082153,
-0.6285679936408997,
1.2882044315338135,
-0.25750431418418884,
0.4360334575176239,
1.0407524108886719,
-0.001662644324824214,
0.4555339217185974,
0.09731152653694153,
0.33554911613464355,
0.18758918344974518,
-0.07985362410545349,
-0.7949671149253845,
-0.5265395641326904,
0.7841300964355469,
-0.7257460951805115,
0.7816009521484375,
0.02411934733390808,
0.5941153764724731,
0.40963542461395264,
-0.6632612347602844,
3.9972524642944336,
0.7590538263320923,
0.3223315477371216,
0.33980339765548706,
0.8786277770996094,
0.9870744347572327,
-0.2048218995332718,
-0.7555767893791199,
0.24590499699115753,
-0.5052265524864197,
-0.5810303688049316,
0.3809857666492462,
-0.2300589680671692,
0.39730891585350037,
-0.34757640957832336,
1.26530921459198,
-0.7607623338699341,
-0.4536673426628113,
0.210114985704422,
-0.7972919940948486,
-0.5949621200561523,
0.05191457271575928,
0.6202537417411804,
-0.3001970052719116,
0.35599377751350403,
0.2992987334728241,
-0.02598578669130802,
-0.7628234624862671,
-0.35014456510543823,
-0.805922269821167,
-0.1449243724346161,
-0.8664250373840332,
0.010334332473576069,
-0.2427125871181488,
-1.083348035812378,
0.6289582252502441,
0.07279224693775177,
-0.05654452368617058,
-0.2512107491493225,
-0.24920521676540375,
0.07449901849031448,
-0.16036778688430786,
0.24954745173454285,
-0.4246034026145935,
-0.32958707213401794,
0.8196411728858948,
-0.9685922861099243,
1.1987254619598389,
0.36952531337738037,
-1.0092191696166992,
0.36647364497184753,
-0.1936994045972824,
1.0806447267532349,
-0.16030848026275635,
-0.2777111232280731,
0.36326390504837036,
-0.2293219417333603,
0.10619814693927765,
0.1003962978720665,
0.7848296761512756,
0.08523117005825043,
-0.17728319764137268,
-0.0007744544418528676,
-0.042596202343702316,
0.2551800608634949,
0.06475192308425903,
0.03714098781347275,
0.5799345970153809,
-0.22229769825935364,
0.33018478751182556,
-0.2039724588394165,
-0.6955028772354126,
-0.06458457559347153,
0.42864444851875305,
0.38820701837539673,
-0.06559281796216965,
0.15376333892345428,
0.10355275869369507,
0.5336357355117798,
-0.2547459304332733,
0.2827790081501007,
-0.45507311820983887,
-0.5069271326065063,
0.1292887181043625,
-0.20522001385688782,
0.423045814037323,
-0.3658492863178253,
-0.2242165505886078,
0.05269128829240799,
0.5459079146385193,
0.4292308986186981,
1.1262620687484741,
0.06034070625901222,
0.15606854856014252,
-0.40040189027786255
] |
Lattice Calculation of QCD Vacuum Correlation Functions
|
The first exploratory calculations of QCD vacuum correlation functions on a lattice are reported. Qualitative agreement with phenomenological results is obtained in channels for which experimental data are available, and these correlation functions are shown to be useful in exploring approximations based on sum rules and interacting instantons.
|
M.-C. Chu, J. M. Grandy, S. Huang and J. W. Negele
|
hep-lat
|
August
| 1,992 |
https://arxiv.org/abs/hep-lat/9208030
|
hep-lat/9209001
|
[
0.007556766737252474,
-0.43199843168258667,
0.032059527933597565,
0.5837007164955139,
-0.14402540028095245,
0.011071193031966686,
-0.45528116822242737,
0.08960400521755219,
-1.00094473361969,
1.9124239683151245,
0.6012977361679077,
0.020137591287493706,
-0.2245314121246338,
-0.7693380117416382,
0.03609827905893326,
0.7543053030967712,
0.09825901687145233,
-0.3032718300819397,
-1.1752926111221313,
0.6921420097351074,
0.4676291346549988,
0.43125179409980774,
-1.3786484003067017,
-0.5984897017478943,
-0.03715377300977707,
1.2255007028579712,
0.32624468207359314,
0.42024460434913635,
1.133235216140747,
0.703605055809021,
0.46920761466026306,
-0.07346880435943604,
-0.5969493389129639,
-0.11866133660078049,
-0.5771830677986145,
-0.18870939314365387,
-0.10784640908241272,
0.021059054881334305,
0.8102786540985107,
0.1277039647102356,
0.44061902165412903,
-0.3035436272621155,
-0.2038247138261795,
-0.7961865663528442,
-0.5580486059188843,
0.08924149721860886,
-0.026798615232110023,
0.03882076218724251,
0.24157829582691193,
-1.219480276107788,
0.34615495800971985,
0.034716349095106125,
0.4978712797164917,
-1.4571261405944824,
-0.649333119392395,
-0.6275027394294739,
0.1462845355272293,
-0.021352674812078476,
-1.0693994760513306,
-0.11738564074039459,
0.3085898160934448,
0.22600217163562775,
0.5949018001556396,
-1.1266236305236816,
0.18153777718544006,
1.0371993780136108,
-0.1951359063386917,
0.7716033458709717,
-0.38183388113975525,
-0.3565162122249603,
0.0524524562060833,
-0.4478101134300232,
-0.7432059049606323,
0.719264805316925,
-0.399189293384552,
0.05746649578213692,
-0.3837527930736542,
-0.3211963176727295,
-0.8673251867294312,
-0.32559382915496826,
-0.44707274436950684,
0.1866540163755417,
-0.22723610699176788,
0.5398237109184265,
-0.675844132900238,
-0.2734057903289795,
-0.08693313598632812,
-0.033349741250276566,
-0.07741555571556091,
0.35458487272262573,
0.13581037521362305,
0.5156265497207642,
-0.5545234084129333,
-0.4095182418823242,
0.6511322855949402,
0.531444251537323,
0.14541780948638916,
0.5025864839553833,
0.01959863491356373,
-0.20942658185958862,
0.13407282531261444,
1.019726276397705,
-0.6370221376419067,
-0.044471219182014465,
-0.5576103925704956,
0.4331519305706024,
-0.32959315180778503,
-0.3472394645214081,
-0.7576374411582947,
-0.6859527826309204,
0.19610056281089783,
-0.3156236410140991,
0.6499865055084229,
0.8695148825645447,
0.1322866976261139,
0.6527794599533081,
-0.6014513373374939,
0.12406286597251892,
-0.6666418313980103,
-0.10823047906160355,
0.3631753623485565,
0.4251176714897156,
0.3534804880619049,
0.5803739428520203,
0.12359560281038284,
-0.43121084570884705,
0.45444607734680176,
0.1123175323009491,
-0.7741551995277405,
0.17214803397655487,
0.07525665313005447,
-0.17860889434814453,
-0.5898065567016602,
0.3200130760669708,
-0.09505712985992432,
-0.29856961965560913,
-0.30439674854278564,
0.04364918917417526,
-0.07873040437698364,
-0.37301984429359436,
0.6894014477729797,
-0.9294977188110352,
-0.0769587978720665,
0.8644100427627563,
0.15192227065563202,
0.3983008563518524,
-0.3770766258239746,
0.7508620023727417,
-0.030055735260248184,
0.2410096526145935,
-0.505825936794281,
-0.04590659588575363,
-0.1831834763288498,
0.05000258982181549,
0.09557420760393143,
0.5478048324584961,
-0.9460741877555847,
0.3366513252258301,
-0.49117472767829895,
-0.8427798748016357,
0.39135658740997314,
0.027215823531150818,
-0.541183590888977,
0.7258672118186951,
-0.8127248287200928,
0.1574176549911499,
-0.2701975405216217,
-0.21557049453258514,
0.6059496998786926,
-0.4447779953479767,
-0.11865858733654022,
0.374102383852005,
-0.3057481348514557,
0.5975605249404907,
0.6695899367332458,
0.5873306393623352,
0.6021342873573303,
-0.6087196469306946,
-0.06534908711910248,
0.118289053440094,
-0.03797892853617668,
-0.5453238487243652,
0.3107152283191681,
0.22173844277858734,
-0.75870281457901,
-0.16093097627162933,
0.044928815215826035,
-0.5079414248466492,
0.3697091042995453,
0.6929271221160889,
-0.7091851830482483,
0.1711280196905136,
-0.6940133571624756,
0.9260627031326294,
-0.7283841967582703,
0.2565332353115082,
-0.9865753650665283,
0.24453182518482208,
-0.3555890619754791,
-0.5917114615440369,
0.6378957033157349,
-0.01907939463853836,
-0.9348623156547546,
0.24192336201667786,
-1.1231471300125122,
0.24408012628555298,
0.7835595011711121,
0.1614755392074585,
-0.7236764430999756,
-0.47063422203063965,
0.2795496881008148,
-0.32292938232421875,
0.34210336208343506,
-0.6665676832199097,
0.5532451868057251,
0.33173975348472595,
-0.11921841651201248,
-0.18281055986881256,
0.16790655255317688,
0.30353501439094543,
0.5292530655860901,
0.3528660535812378,
-0.23140276968479156,
0.9827035665512085,
-0.7688993215560913,
-0.7283201813697815,
0.505264163017273,
0.44179800152778625,
0.14051242172718048,
0.441731333732605,
0.5686181783676147,
0.367543488740921,
0.18727406859397888,
0.237941712141037,
0.6803619265556335,
0.09471815824508667,
0.7271231412887573,
0.6086860299110413,
0.4284757971763611,
0.5872987508773804,
0.11829287558794022,
0.025233155116438866,
0.47436225414276123,
-0.7548368573188782,
-0.35543161630630493,
0.43509799242019653,
-0.4858892261981964,
0.39716973900794983,
-0.8623185157775879,
0.4271079897880554,
-0.2320472002029419,
0.41307613253593445,
0.05217191204428673,
0.1344759613275528,
-1.2457231283187866,
0.5868590474128723,
-0.3261254131793976,
0.2038886994123459,
0.03363155573606491,
0.1347300112247467,
0.09641563892364502,
0.22834622859954834,
0.09585119783878326,
-0.6824795007705688,
-0.3489731252193451,
0.6272033452987671,
-0.662625789642334,
-0.04685863107442856,
0.8626952171325684,
-0.3244127035140991,
-1.1223779916763306,
0.25084927678108215,
-0.6123920679092407,
-0.1987271010875702,
-0.4734013080596924,
-0.0937269777059555,
0.6728014945983887,
-0.29612866044044495,
0.5203676223754883,
0.20877809822559357,
0.09008225798606873,
0.30003559589385986,
-0.2175673544406891,
0.054571568965911865,
0.42502880096435547,
-0.10724987089633942,
-0.7410176992416382,
-0.018242310732603073,
-0.8309364318847656,
-0.03551911562681198,
-0.5208635330200195,
0.30922508239746094,
0.9782212972640991,
-0.2204371690750122,
0.6809061169624329,
-0.18232415616512299,
-0.5262746810913086,
-0.027332322672009468,
0.3327324688434601,
-0.6247426867485046,
0.31525126099586487,
0.6226908564567566,
0.5690407156944275,
-0.03634845092892647,
-1.0804630517959595,
0.9076018929481506,
0.6346592307090759,
-0.3445436954498291,
0.5624979138374329,
-0.990460216999054,
-0.6288577914237976,
0.29061731696128845,
0.26342642307281494,
0.2408602237701416,
-0.1282389611005783,
1.1571810245513916,
0.8239526748657227,
-0.23187723755836487,
-0.2720714211463928,
-0.17607223987579346,
-0.2328239530324936,
0.021713705733418465,
0.47099754214286804,
-0.6083803176879883,
0.009306912310421467,
0.5521323084831238,
-0.03953033685684204,
-0.32747572660446167,
0.7453304529190063,
-0.7155225872993469,
-0.5444518327713013,
-0.24290378391742706,
-0.6564158201217651,
0.30768486857414246,
-0.3943924307823181,
0.1848907768726349,
-1.1210768222808838,
-0.17836663126945496,
-0.6717156767845154,
0.2278197556734085,
0.434395432472229,
0.38164904713630676,
0.40042415261268616,
0.5329362154006958,
0.5317733883857727,
-0.43763917684555054,
-0.10389658063650131,
-0.4418886601924896,
-0.2786671221256256,
0.5018577575683594,
-0.414272665977478,
0.049191396683454514,
-0.11045442521572113,
0.2961466908454895,
0.01894400268793106,
0.4018065333366394,
0.09254273027181625,
-0.46934774518013,
-0.9142090082168579,
-0.3435085415840149,
0.012135877273976803,
1.113863229751587,
0.028215888887643814,
-0.6036341786384583,
-0.9154894948005676,
-0.4097349941730499,
-0.20281553268432617,
0.2232111096382141,
0.6998498439788818,
-0.9901537895202637,
-0.13259853422641754,
0.05898013710975647,
-0.3338722288608551,
-0.2306269407272339,
-0.06177745759487152,
0.6587535738945007,
0.4875170886516571,
0.22026753425598145,
0.3139408826828003,
0.2202591747045517,
-0.7541362047195435,
0.285121351480484,
0.8674982786178589,
0.5585213899612427,
0.7697142958641052,
-0.029454289004206657,
-0.20112349092960358,
0.0010471353307366371,
-0.15426616370677948,
-0.284707248210907,
-0.5849462151527405,
-0.40232062339782715,
0.4080847501754761,
0.12382698059082031,
0.31346622109413147,
0.10838980972766876,
0.26256901025772095,
0.49718499183654785,
0.22008980810642242,
0.18755359947681427,
0.027333982288837433,
-0.23552149534225464,
0.7967713475227356,
0.5389409065246582,
0.017805825918912888,
0.7625226974487305,
-0.715588390827179,
0.16368460655212402,
0.3388371467590332,
0.8940521478652954,
0.29781004786491394,
-0.776676595211029,
0.16130544245243073,
-0.5966794490814209,
0.29650312662124634,
0.37482839822769165,
-0.6733683943748474,
0.2973940968513489,
0.15558280050754547,
0.3375176191329956,
-0.2515369653701782,
0.4211564064025879,
0.9623759388923645,
0.3129974603652954,
-0.23187923431396484,
-0.5966121554374695,
-0.2299470603466034,
-0.5208656191825867,
0.23582227528095245,
0.173251211643219,
-1.1938804388046265,
-0.6138393878936768,
-0.6757543087005615,
-0.23305664956569672,
0.12694156169891357,
0.41649311780929565,
0.7451737523078918,
-0.07647654414176941,
-0.07179243117570877,
-0.3879458010196686,
-0.5151996612548828,
0.5915530323982239,
0.06747676432132721,
-0.5469563007354736,
0.5827664732933044,
-0.3373474180698395,
-0.2882613241672516,
0.8034684062004089,
0.15583601593971252,
-0.6731021404266357,
0.13872376084327698,
-0.3021935224533081,
0.07982581108808517,
-0.43308374285697937,
-0.8019347190856934,
-0.06623660027980804,
-0.21293330192565918,
-0.5347392559051514,
0.5766900181770325,
-0.027607545256614685,
0.4502132534980774,
0.05069154128432274,
-0.3351907432079315,
0.05465507134795189,
0.50323086977005,
-0.3844660818576813,
-0.3537011444568634,
0.7443759441375732,
0.6699919700622559,
0.5425878763198853,
0.7122635841369629,
0.4370657801628113,
-0.20111405849456787,
-0.001893710228614509,
0.49830177426338196,
-0.3571694493293762,
-0.15054742991924286,
-0.6549369692802429,
0.19154483079910278,
-1.1786022186279297,
-0.5036583542823792,
0.49824610352516174,
-0.15783809125423431,
0.6088517904281616,
-0.1511421799659729,
-0.6597827672958374,
-0.745274007320404,
-0.9851082563400269,
-0.6451219320297241,
0.6473090648651123,
-0.05644354969263077,
-0.12776851654052734,
0.6528991460800171,
-0.6901896595954895,
0.046005964279174805,
-0.4334865212440491,
0.27038145065307617,
0.0006064633489586413,
-0.17840909957885742,
0.9569116234779358,
0.24695125222206116,
0.4601489305496216,
-1.3286426067352295,
0.4012685716152191,
-0.5505586266517639,
-0.4881274998188019,
-0.629631519317627,
-0.4184553623199463,
0.1639888882637024,
-0.24407966434955597,
0.4843774437904358,
-0.03505997732281685,
-0.06688244640827179,
-0.01108247134834528,
0.21421676874160767,
-0.01158998068422079,
-0.455081045627594,
-0.44493162631988525,
-0.06654059886932373,
0.6241432428359985,
-0.06693384796380997,
-0.1654926985502243,
-0.32176241278648376,
0.5683216452598572,
0.07805164158344269,
0.472874253988266,
0.05149669945240021,
-0.48733630776405334,
0.03909662738442421,
-0.834339439868927,
0.26875460147857666,
-0.8670223951339722,
-0.7528945803642273,
0.0672137588262558,
-0.5436089038848877,
0.5318391919136047,
0.3208296597003937,
-0.3451479375362396,
0.027464520186185837,
-0.6941329836845398,
-0.10847993940114975,
0.3509032726287842,
-0.38404330611228943,
0.34810110926628113,
-0.8393049836158752,
-0.2930062711238861,
0.02298533357679844,
0.8234043121337891,
0.1005658432841301,
0.7459340691566467,
0.005514692515134811,
-0.04857734963297844,
-0.35993221402168274,
0.9708462357521057,
0.6812957525253296,
-0.3978707790374756,
0.39443904161453247,
0.5530276894569397,
-0.08288685232400894,
0.182573139667511,
-0.4473770558834076,
0.7951168417930603,
-0.1903686225414276,
0.9457007646560669,
-0.6447367668151855,
-0.2447604537010193,
0.049718957394361496,
-0.14250554144382477,
0.4693729877471924,
-0.7829403877258301,
0.1926288902759552,
1.3819414377212524,
-0.29724547266960144,
0.2879323363304138,
0.21677249670028687,
-0.7406954169273376,
-0.2837240993976593,
-0.14304913580417633,
-0.19633086025714874,
0.41172611713409424,
0.19592320919036865,
-0.4025239050388336,
-0.7750785946846008,
-0.7592803835868835,
0.07161461561918259,
-0.043291956186294556,
0.39381277561187744,
0.1486709862947464,
-0.2715742886066437,
0.3188190758228302,
-0.1618039608001709,
-0.2695011794567108,
-0.8031911849975586,
0.37107571959495544,
-0.19136816263198853,
-0.30781298875808716,
0.24850131571292877,
-0.31435176730155945,
-0.3818647265434265,
-0.62471604347229,
-0.29946020245552063,
0.317781537771225,
0.1072235181927681,
-0.16170036792755127,
0.5270894169807434,
-0.10255249589681625,
-0.3199293315410614,
-0.35460662841796875,
0.0942055806517601,
0.3128262758255005,
0.11651541292667389,
0.5130650997161865,
0.7140390872955322,
0.26445162296295166,
0.07740788161754608,
0.37698301672935486,
-0.2374376505613327,
-0.09747999906539917,
0.29870179295539856,
-0.7628854513168335,
0.1598297357559204,
0.6031529903411865,
-0.4746735692024231,
-0.8060066103935242,
-0.4238905608654022,
-1.3932114839553833,
-0.36239564418792725,
-0.2722303867340088,
-0.3742421567440033,
-0.3125545084476471,
-0.35846635699272156,
-0.07008958607912064,
0.730965793132782,
0.7859383225440979,
0.146060049533844,
-0.4478453993797302,
0.2046058028936386,
-0.2794268727302551,
-0.2368106096982956,
-0.17730066180229187,
1.4184160232543945,
0.32976093888282776,
-0.9895197749137878,
0.2956647276878357,
0.06568829715251923,
-0.30907273292541504,
-0.1807401478290558,
0.8566114902496338,
-1.0612096786499023,
0.58750319480896,
0.15493227541446686,
0.04933222755789757,
0.6099206209182739,
0.9436182975769043,
0.24598145484924316,
0.15310002863407135,
-0.6781560182571411,
-0.7244776487350464,
-0.02103416994214058,
-0.48579561710357666,
0.37025338411331177,
1.1147221326828003,
0.1169157475233078,
0.3829835057258606,
-0.10982190817594528,
-0.28589048981666565,
0.04235246032476425,
-0.6920023560523987,
0.14037132263183594,
-1.2661972045898438,
-0.22543670237064362,
-0.7265967726707458,
-0.5944058895111084,
0.016173385083675385,
0.7083627581596375,
-0.42589902877807617,
0.2673284411430359,
-0.7007237076759338,
-0.1757017821073532,
0.3564305901527405,
0.4847923815250397,
-0.44054585695266724,
-0.9141102433204651,
-0.5614817142486572,
-0.3147942125797272,
0.2707970440387726,
-0.9472261071205139,
-0.3020806312561035,
-0.25535354018211365,
-0.11713189631700516,
0.6276996731758118,
-0.09357860684394836,
0.6573631167411804,
-0.6141501069068909,
-1.076479434967041,
0.6619223356246948,
0.07198924571275711,
-0.9021589756011963,
0.7391716241836548,
-0.05625584349036217,
1.0274995565414429,
0.5669397711753845,
0.4516127407550812,
-0.6354469656944275,
-0.024470912292599678,
-0.8468083143234253,
0.18543928861618042,
0.7724076509475708,
-0.0032749157398939133,
-0.2493310123682022,
-1.0828382968902588,
-0.011079324409365654,
-0.3520011007785797,
-0.9048213958740234,
0.378050297498703,
-0.5713556408882141,
0.3282938599586487,
-0.6229429244995117,
0.7556830048561096,
0.1418367475271225,
0.22627884149551392,
0.44051119685173035,
0.8872179985046387,
-0.5110659599304199,
0.06141813099384308,
0.1910664290189743,
0.26949089765548706,
-0.11839160323143005,
0.08397433161735535,
0.30839136242866516,
-0.23566758632659912,
0.32858285307884216,
0.2837549149990082,
-0.24493423104286194,
-0.08330332487821579,
-0.24842819571495056,
-0.05043409764766693,
0.1461682915687561,
-0.06111433357000351,
-0.4835677742958069,
0.587863028049469,
0.3765695095062256,
-0.6511589884757996,
-0.23386064171791077,
-0.8028666973114014,
-0.5129517912864685,
0.10930297523736954,
-0.7692520022392273,
-0.5272606611251831,
0.3494698405265808,
0.23751220107078552,
0.15029452741146088,
0.5115059614181519,
-0.29810047149658203,
-0.11712837219238281,
-0.20817311108112335,
0.5590304732322693,
0.5656965970993042,
-0.3280048668384552,
-0.5584567785263062,
0.05489027500152588,
-0.1962842345237732,
-0.5196810960769653,
-0.5409740209579468,
0.7219946980476379,
-0.895442545413971,
-1.2054671049118042,
-0.12330343574285507,
0.09590009599924088,
0.07307947427034378,
-0.18796208500862122,
0.16406728327274323,
-0.693464994430542,
-0.46759748458862305,
0.05159144476056099,
-0.6473249197006226,
0.05077273026108742,
-0.9313505291938782,
0.29851576685905457,
-0.007776170503348112,
-0.564444899559021,
0.1792576014995575,
-0.2129027545452118,
0.6085428595542908,
-0.20309844613075256,
-0.01174527034163475,
1.3064759969711304,
0.0862918496131897,
-0.2725677788257599,
0.336902379989624,
0.0657399594783783,
0.26941120624542236,
0.5571579933166504,
-0.7273896932601929,
0.557608425617218,
0.7500386238098145,
-0.3365978002548218,
0.6778250932693481,
0.2746069133281708,
-0.113068588078022,
0.19116657972335815,
0.34164637327194214,
0.5287328362464905,
-0.056690290570259094,
-0.01904461905360222,
0.9185740947723389,
0.6896836161613464,
0.1424415558576584,
-0.4870476722717285,
0.2549833655357361,
0.04736780747771263,
0.47764453291893005,
-0.1595344841480255,
-0.34345465898513794,
-0.8295607566833496,
0.05972098186612129,
0.3324519395828247,
-0.46239712834358215,
-0.22025595605373383,
0.10435085743665695,
0.3249463140964508,
0.8544420003890991,
0.2363167256116867,
-0.480435848236084,
0.27036169171333313,
0.3885509669780731,
-0.32225438952445984,
-0.06653913855552673,
0.6425572037696838,
0.05131339281797409,
0.8929897546768188,
0.8445253372192383,
0.29498887062072754,
0.32694104313850403,
0.6049311757087708,
0.41556820273399353,
-0.7941914200782776,
0.3695243000984192,
0.5942643880844116,
-0.8939772844314575,
0.30773603916168213,
-0.4793095290660858,
-0.0407247357070446,
-0.5728322863578796,
-0.09553761035203934,
-0.3253314793109894,
-0.525226891040802,
-0.03548883646726608,
0.13679078221321106,
-0.6233280897140503,
0.057366471737623215,
0.47606518864631653,
0.16333600878715515,
0.19523249566555023,
0.4585718810558319,
-0.035682886838912964,
0.40005984902381897,
0.8980869054794312,
1.2540606260299683,
0.35812699794769287,
0.4788215458393097,
-0.3880132734775543,
-0.509634792804718,
0.6627817749977112,
0.8371030688285828,
-0.04457230120897293,
1.1065800189971924,
-0.7209452390670776,
-0.217729851603508,
0.055501896888017654,
-0.17961573600769043,
-0.4357452094554901,
-0.2873914837837219,
0.29512152075767517,
0.010774679481983185,
0.17366120219230652,
-0.4383782148361206,
1.5425286293029785,
0.2987370193004608,
-1.1237614154815674,
-0.2616161108016968,
0.4657251834869385,
-0.6941860914230347,
-0.23941820859909058,
-1.32045578956604,
0.13062253594398499,
-0.47083964943885803,
0.020097821950912476,
-0.1982567012310028,
-0.36984002590179443,
-1.0180288553237915,
-0.7396970391273499,
0.7471812963485718,
-0.8701314926147461,
0.17601780593395233,
0.6923729777336121,
-0.5194202661514282,
0.33088499307632446,
-0.3739824593067169,
-0.1253209114074707,
-0.4011954069137573,
0.7506384253501892,
0.13078562915325165,
-0.47040069103240967,
0.5354927182197571,
0.7518985271453857,
-1.0201746225357056,
0.5324571132659912,
0.6277893781661987,
-0.5635571479797363,
0.7695330381393433,
-0.5168812274932861,
0.340521901845932,
0.779103696346283,
0.3036234974861145,
0.6234077215194702,
-0.029109491035342216,
0.16345076262950897,
0.30136004090309143,
-0.32975533604621887,
-0.047346338629722595,
-0.41140928864479065,
0.10319661349058151,
-0.5764210224151611,
0.398440420627594,
0.47527268528938293,
0.499065637588501,
0.1851506531238556,
-0.732540488243103,
4.176770210266113,
0.31660327315330505,
0.22793996334075928,
0.057686708867549896,
0.726647675037384,
0.9055293798446655,
-0.22063703835010529,
-0.5094701647758484,
0.07622986286878586,
-0.5876458287239075,
-0.05074862763285637,
0.042586758732795715,
0.09540741890668869,
-0.23187123239040375,
0.07617805898189545,
0.549109160900116,
-0.1537502110004425,
-0.7454307675361633,
0.13638189435005188,
-0.513870894908905,
-0.6324205994606018,
0.10117222368717194,
0.1182323470711708,
0.1643379181623459,
0.8588216304779053,
0.22327308356761932,
0.020111816003918648,
-0.405211478471756,
-0.6859694123268127,
-0.6538687944412231,
-0.2468627691268921,
-0.5075805187225342,
0.008617796935141087,
0.0556723028421402,
-1.0300838947296143,
0.30451151728630066,
0.13694864511489868,
-0.5485852360725403,
0.48258817195892334,
0.1531442552804947,
-0.40441370010375977,
-0.45188677310943604,
0.11147017031908035,
-0.11883991211652756,
-0.3516755700111389,
0.9303592443466187,
0.7041810750961304,
0.20433418452739716,
0.591655433177948,
-0.9188954830169678,
0.24077601730823517,
0.3626381754875183,
0.4572297930717468,
-0.872407853603363,
-0.6173927783966064,
-0.25559958815574646,
-0.35212692618370056,
-0.025429796427488327,
0.692915141582489,
-0.004441836848855019,
0.10362415015697479,
-0.3025454580783844,
-0.28820371627807617,
0.5949566960334778,
0.4365706145763397,
0.3174002170562744,
0.3386939465999603,
0.15382994711399078,
-0.21204477548599243,
0.06470265984535217,
-0.3051908612251282,
-0.09109562635421753,
-0.451133131980896,
-0.009336787275969982,
-0.1449781358242035,
0.5860550403594971,
0.46187299489974976,
0.1697232872247696,
0.03521820530295372,
0.24038469791412354,
-0.3325640559196472,
-0.388049453496933,
-0.16114334762096405,
-0.2231827825307846,
-0.04627193138003349,
1.0188320875167847,
-0.1653839498758316,
0.239498570561409,
-0.27675026655197144,
0.5653663873672485,
-0.19888503849506378,
1.2293065786361694,
0.07003436237573624,
-0.003782509593293071,
-1.090407371520996
] |
Asymptotic Freedom and Euclidean Quantum Gravity
|
Pure SU(2) gauge theory is the simplest asymptotically free theory in four dimensions. To investigate Euclidean quantum gravity effects in a fundamental length scenario, we simulate 4$d$ SU(2) lattice gauge theory on a dynamically coupled Regge skeleton. The fluctuations of the skeleton are governed by the standard Regge-Einstein action. From a small $2\cdot 4^3$ lattice we report exploratory numerical results, limited to a region of strong gravity where the Planck mass and hadronic masses take similar orders of magnitude. We find a range of the Planck mass where stable bulk expectation values are obtained which vary smoothly with the gauge coupling, and a remnant of the QCD deconfining phase transition is located. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/krishnan (to go to that directory type: cd pub/krishnan) and is called gravity.ps (to get it type: get gravity.ps). If you have any problems send mail to [email protected].
|
Bernd A. Berg, Balasubramanian Krishnan and Mohammad Katoot
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209001
|
hep-lat/9209002
|
[
0.12124944478273392,
-0.17523398995399475,
0.27327126264572144,
-0.14752830564975739,
0.3115711510181427,
-0.7008342742919922,
0.65992271900177,
-0.46592873334884644,
-1.001983404159546,
1.4584327936172485,
0.2893107533454895,
0.4092068672180176,
0.5582849383354187,
-0.42541319131851196,
0.5676907300949097,
0.6218615770339966,
0.013593065552413464,
-0.7889928221702576,
-1.265005350112915,
0.11615294218063354,
0.3514268100261688,
0.05488444119691849,
-0.5175984501838684,
-0.6177881956100464,
0.007124471012502909,
0.9349128007888794,
0.6377562880516052,
0.6542752385139465,
1.2133640050888062,
0.6710165143013,
0.3372887074947357,
-0.7023011445999146,
-0.04940025880932808,
-0.5646503567695618,
-0.7373346090316772,
-0.3106895089149475,
-0.4815705716609955,
-0.7043678760528564,
0.6774650812149048,
-0.5934773087501526,
0.8191263675689697,
-0.36679184436798096,
0.17316150665283203,
-0.1729314625263214,
-0.217494398355484,
0.38466811180114746,
-0.042384710162878036,
-0.31630513072013855,
0.2282966524362564,
-0.9762057662010193,
0.5468438863754272,
0.3797571063041687,
0.07028955966234207,
-0.02495751716196537,
-0.39112740755081177,
-0.3262399435043335,
0.47205135226249695,
0.41493165493011475,
-0.3136390149593353,
-0.4471827745437622,
0.38297098875045776,
0.30820631980895996,
-0.00047430742415599525,
-1.0470051765441895,
0.09945085644721985,
-0.016887875273823738,
-0.09348863363265991,
0.23286926746368408,
0.3145914077758789,
-0.8293552994728088,
-0.29854318499565125,
0.4886914789676666,
-0.42159655690193176,
-0.29181602597236633,
-1.047725796699524,
0.31036806106567383,
-0.05205243453383446,
-0.5277289152145386,
-0.4000873863697052,
-0.6646204590797424,
-0.27098411321640015,
0.26067742705345154,
-0.41331496834754944,
0.7643776535987854,
-0.6300244927406311,
-0.3011912703514099,
0.13195210695266724,
-0.4657145142555237,
0.022593408823013306,
0.19900111854076385,
0.6398362517356873,
0.9944818615913391,
-0.043521277606487274,
0.24485906958580017,
0.26032930612564087,
0.9196892380714417,
-0.2142668068408966,
0.8107264041900635,
-0.13114415109157562,
-0.16246305406093597,
0.3439176678657532,
0.8472134470939636,
-1.3517683744430542,
0.4692912995815277,
-0.9149261713027954,
0.2450081706047058,
0.11553452908992767,
-0.06493200361728668,
0.4415419399738312,
-0.8726620674133301,
-0.00033356243511661887,
-0.22083845734596252,
0.5463061928749084,
0.6024996638298035,
0.07139158248901367,
0.7975642085075378,
-0.4850535988807678,
0.026895906776189804,
-1.2160444259643555,
-0.28040972352027893,
0.3941228985786438,
-0.4243979752063751,
0.2070809304714203,
0.23573364317417145,
-0.38288524746894836,
-0.5832052230834961,
0.5453217625617981,
0.5806591510772705,
-0.03650723770260811,
0.7427067160606384,
0.26378780603408813,
0.32626739144325256,
-0.07270872592926025,
0.45407265424728394,
-0.19083893299102783,
0.23900969326496124,
-0.4392230212688446,
0.7947429418563843,
0.680252194404602,
-0.3524245619773865,
0.9067405462265015,
-0.8944531083106995,
0.4432266652584076,
1.0621044635772705,
0.7712564468383789,
-0.058144789189100266,
0.39630264043807983,
-0.6476907134056091,
-0.1259363293647766,
0.30347567796707153,
-0.20982812345027924,
-0.011566480621695518,
-0.35411950945854187,
0.5205622315406799,
0.21826548874378204,
0.9226335883140564,
-0.5432887673377991,
0.6040382385253906,
-0.3284273147583008,
-0.3280996084213257,
0.7003475427627563,
-0.03381272777915001,
-0.8018079996109009,
0.03179698437452316,
-0.9247612357139587,
-0.002084434498101473,
-0.2700906991958618,
-0.6981842517852783,
0.35656294226646423,
-0.9168716073036194,
0.025464851409196854,
0.21940553188323975,
-0.5678279995918274,
0.5714966058731079,
0.4055704176425934,
0.25242242217063904,
0.5182072520256042,
-0.06393478810787201,
-0.6713218688964844,
0.12915456295013428,
-0.5172712206840515,
-0.42488881945610046,
0.17908045649528503,
0.04354304075241089,
-0.5493286848068237,
-0.6468481421470642,
0.5162264704704285,
-0.10586661100387573,
-0.04253461956977844,
0.27325326204299927,
-0.21341043710708618,
0.5354719161987305,
-0.15577340126037598,
0.4649403691291809,
-0.5117354989051819,
0.10187499225139618,
-0.6956003904342651,
0.8813501596450806,
-0.5122944712638855,
-0.43808338046073914,
-0.44662126898765564,
0.6020997166633606,
-0.9673529863357544,
0.28747737407684326,
-1.5003114938735962,
0.4436604380607605,
0.8596634864807129,
0.08486773073673248,
-0.21307127177715302,
-0.3874205946922302,
0.2184874415397644,
-0.06880030781030655,
0.38720330595970154,
-0.3210309147834778,
0.4258796274662018,
0.2995828688144684,
0.366772323846817,
0.3779624402523041,
0.9444481730461121,
0.2888897657394409,
1.0882067680358887,
-0.051923368126153946,
-0.32284674048423767,
0.8692693710327148,
-0.42072412371635437,
-0.6244450211524963,
0.17872166633605957,
0.40712398290634155,
0.036403778940439224,
-0.4421531558036804,
0.025115754455327988,
0.26945599913597107,
0.4660433828830719,
0.587231457233429,
0.49170157313346863,
0.6137932538986206,
0.46779683232307434,
0.6306224465370178,
0.2761106491088867,
0.07085127383470535,
0.05800695717334747,
-0.23884107172489166,
0.40175774693489075,
-0.08689604699611664,
0.06188131496310234,
0.5440828204154968,
-0.6741175055503845,
0.23743703961372375,
-0.1433136761188507,
0.6588355302810669,
-0.0683780238032341,
0.28588300943374634,
0.13395220041275024,
0.08538169413805008,
-1.3307464122772217,
-0.3421977460384369,
0.16027800738811493,
0.6120714545249939,
-0.5915495157241821,
-0.549628734588623,
-0.10249309241771698,
0.3818441927433014,
-0.8486759662628174,
-0.43724966049194336,
-0.1545868217945099,
0.846862256526947,
-0.3180623948574066,
0.14837861061096191,
0.5018877983093262,
0.05212267115712166,
-1.0962693691253662,
-0.5821574926376343,
-0.896781325340271,
0.4016374945640564,
-1.3035213947296143,
-0.08367783576250076,
1.1663243770599365,
-1.0179942846298218,
-0.2208826094865799,
-0.5876386165618896,
-0.019921205937862396,
0.12864044308662415,
-0.2718345820903778,
-0.13058800995349884,
0.9956344962120056,
0.7338609099388123,
0.08575551956892014,
0.1292814314365387,
-0.43579909205436707,
0.45453232526779175,
-0.4253925383090973,
0.32216325402259827,
0.8998309373855591,
-0.39318934082984924,
0.4064098596572876,
-0.16451223194599152,
-0.4560038447380066,
-0.19532564282417297,
0.13774758577346802,
-0.7767654657363892,
0.31373918056488037,
0.2858370244503021,
-0.3450542986392975,
-0.3206092119216919,
-1.0456150770187378,
0.3738064169883728,
0.5378640294075012,
-0.48080238699913025,
0.22465912997722626,
0.39654210209846497,
-0.36461877822875977,
0.5509212613105774,
0.41390833258628845,
-0.2601984441280365,
-0.34127873182296753,
0.8226659893989563,
0.7776053547859192,
0.28782325983047485,
0.001555365975946188,
-0.5858364701271057,
-0.5405907034873962,
0.28693363070487976,
0.4883658289909363,
-0.5463348031044006,
-0.20766587555408478,
0.6537312865257263,
0.6386229991912842,
-0.8749150633811951,
-0.004395866766571999,
-1.0695282220840454,
-0.8342586755752563,
0.06150715798139572,
-0.2802678644657135,
0.2534067630767822,
-0.004782848060131073,
0.2689161002635956,
-0.9662739038467407,
-0.4857214391231537,
0.49280306696891785,
0.18617182970046997,
0.8557428121566772,
-0.08072081208229065,
0.308340847492218,
0.027550090104341507,
0.6261781454086304,
-1.0119619369506836,
0.6639128923416138,
-0.42532530426979065,
0.12328758090734482,
0.7584946751594543,
-0.14575769007205963,
0.2817361056804657,
0.22806480526924133,
0.3552378714084625,
-0.16213899850845337,
0.3173927068710327,
-0.49092307686805725,
-0.30288374423980713,
-0.6178076863288879,
-0.43267932534217834,
0.3825156092643738,
0.5435536503791809,
-0.23212900757789612,
-0.38096100091934204,
-0.5716282725334167,
-0.6050206422805786,
-0.5473642945289612,
-0.11123815178871155,
1.0713105201721191,
-0.8788703680038452,
0.48614323139190674,
0.5513671040534973,
-0.06289447844028473,
0.4826696515083313,
-0.5053185820579529,
0.8739597201347351,
1.3112778663635254,
0.6741729378700256,
1.0643768310546875,
-0.49501585960388184,
-0.36715245246887207,
0.5247429013252258,
0.98594731092453,
-0.02233066037297249,
0.7115504145622253,
0.4103306233882904,
0.01286402903497219,
-0.11730430275201797,
0.10767816007137299,
-0.2585015296936035,
-0.6269463300704956,
-0.3419089913368225,
0.21335096657276154,
0.0903424546122551,
0.16718806326389313,
-0.10519572347402573,
0.6744020581245422,
0.3303152024745941,
0.09527304023504257,
-0.3527122735977173,
0.7990370392799377,
0.4209652245044708,
0.43447816371917725,
0.3214190900325775,
-0.3475208580493927,
-0.46983402967453003,
-0.6010327935218811,
0.6765465140342712,
0.22527603805065155,
0.2585114538669586,
-0.4838833510875702,
-0.38654226064682007,
0.03325086832046509,
-0.8995422124862671,
0.5105235576629639,
0.6570377945899963,
-0.9630550742149353,
0.6515341997146606,
0.4838103950023651,
0.8760585784912109,
-0.4386809170246124,
-0.15564188361167908,
0.732243001461029,
0.8294925093650818,
0.5488221049308777,
-0.7794926166534424,
0.17562925815582275,
0.038772452622652054,
0.05117007717490196,
0.15345393121242523,
-0.9801527857780457,
-0.9775062799453735,
-0.7910141944885254,
-0.2234373390674591,
-0.1615387201309204,
-0.16091904044151306,
1.2645255327224731,
0.2729579508304596,
-0.2661554217338562,
-0.1017858013510704,
-0.03576596826314926,
1.1118519306182861,
-0.512974739074707,
-0.3814893066883087,
0.03602749854326248,
0.009034098125994205,
-0.36951231956481934,
0.6812785267829895,
0.11922474205493927,
-0.5041536092758179,
-0.6414591670036316,
0.12621067464351654,
-0.3585851192474365,
-0.17793358862400055,
-0.9586175084114075,
-0.5192680358886719,
-0.18797537684440613,
-0.11685262620449066,
0.42447367310523987,
0.000771339691709727,
-0.39773958921432495,
-0.1890706866979599,
0.39080825448036194,
-0.177454873919487,
-0.4243522882461548,
-0.03589634969830513,
0.7546090483665466,
0.8443336486816406,
0.3801591694355011,
0.4557974338531494,
0.15956644713878632,
0.577877938747406,
-0.3262234032154083,
-0.1006675437092781,
0.3855174481868744,
0.5949735641479492,
-0.48155200481414795,
-1.0479331016540527,
-0.33434996008872986,
-0.671646237373352,
-0.5836259722709656,
0.226972296833992,
0.029844170436263084,
0.7446897625923157,
0.09627719223499298,
-0.7251047492027283,
-0.7583230137825012,
-0.3674542009830475,
-1.4481947422027588,
0.16027839481830597,
0.20292450487613678,
-0.474356085062027,
0.8086504936218262,
-1.0158158540725708,
-0.24934689700603485,
-0.4107058346271515,
0.0035731210373342037,
-0.14195963740348816,
0.5487515926361084,
0.1425158530473709,
0.07838086038827896,
0.5149680972099304,
-0.24451570212841034,
0.6925626993179321,
-1.1674072742462158,
0.5318804979324341,
-0.4563596546649933,
-0.2310178428888321,
-0.2564868927001953,
-0.5786919593811035,
0.3300275504589081,
-0.6658395528793335,
-0.14749352633953094,
-0.04212110862135887,
0.1826891452074051,
-0.12024461477994919,
-0.09059314429759979,
-0.04511614143848419,
-0.3319782018661499,
0.7782231569290161,
-0.19596309959888458,
-0.8004899621009827,
-0.08755184710025787,
0.8685087561607361,
0.3388427495956421,
0.28885921835899353,
-0.24509456753730774,
-0.19350223243236542,
-0.18348200619220734,
0.11256363242864609,
0.26143091917037964,
-0.8902395963668823,
0.22944562137126923,
-0.46156883239746094,
-0.23596681654453278,
0.20791395008563995,
0.7082127332687378,
-0.052155885845422745,
-0.2336256355047226,
-0.2082931250333786,
-0.005227134563028812,
0.6121025681495667,
-0.8481032848358154,
0.15608370304107666,
-1.1971555948257446,
-0.015943843871355057,
-0.707367479801178,
0.5429630875587463,
0.18115435540676117,
0.3711246848106384,
-0.49460482597351074,
-0.3953046500682831,
-0.06824847310781479,
0.6495158672332764,
0.10482167452573776,
0.34412601590156555,
-0.05892707407474518,
0.10147476196289062,
0.260257750749588,
0.12259563058614731,
-0.6576439142227173,
0.039458345621824265,
-0.9559656381607056,
1.1028040647506714,
-0.480313241481781,
-0.28846073150634766,
-0.7940981388092041,
0.451699823141098,
0.9456300735473633,
-0.5352690815925598,
0.2402169108390808,
0.5884681940078735,
-0.1811164915561676,
0.3107474148273468,
0.04593675956130028,
-0.3963613212108612,
-0.24908554553985596,
-0.7420004606246948,
-0.44436559081077576,
0.08600229024887085,
-0.19326837360858917,
-0.021686917170882225,
0.11345948278903961,
-0.9641950726509094,
0.3463646471500397,
0.10119340568780899,
0.036388590931892395,
0.0114296218380332,
-0.10424472391605377,
0.2513886094093323,
0.31713661551475525,
-0.03826156258583069,
-0.18942555785179138,
-0.6250512599945068,
-0.15558965504169464,
-0.33936697244644165,
-0.5300834774971008,
0.25315627455711365,
-0.3631690740585327,
-0.5667240619659424,
-0.4116094410419464,
0.11700596660375595,
0.6235380172729492,
-0.19807370007038116,
0.7154046297073364,
-0.4080754518508911,
-0.9324576258659363,
-0.8347089886665344,
-0.2689778208732605,
-0.18007443845272064,
0.8258744478225708,
0.8035037517547607,
0.13055261969566345,
0.4298762381076813,
0.6425566077232361,
0.12813261151313782,
-0.4480349123477936,
-0.4772106111049652,
0.3986251652240753,
0.15810047090053558,
0.5661693811416626,
1.0928268432617188,
0.3081563413143158,
-0.29740992188453674,
-0.12321748584508896,
-0.6884333491325378,
0.02534428983926773,
-0.5679844617843628,
-0.0593341663479805,
0.09382759779691696,
-0.32586902379989624,
-0.20587725937366486,
0.4512329697608948,
0.6462160348892212,
0.09761016070842743,
0.05599837750196457,
0.4422050714492798,
-0.6771016120910645,
-0.0952657088637352,
-0.4104379713535309,
1.2564308643341064,
-0.31828469038009644,
-0.4970320165157318,
-0.13228170573711395,
0.22220176458358765,
-0.5651640295982361,
0.06011316180229187,
0.12297828495502472,
-0.5475567579269409,
-0.009289445355534554,
0.07662783563137054,
0.10207203030586243,
0.5813164114952087,
0.7455615401268005,
-0.05528220534324646,
-0.1766417771577835,
-0.14690755307674408,
-0.8909621238708496,
-0.1905318647623062,
-0.6840442419052124,
0.3338152766227722,
0.5302940011024475,
-0.0691753625869751,
0.6025334000587463,
-0.38818371295928955,
-0.44854602217674255,
-0.5559638738632202,
-1.3401752710342407,
0.2809618413448334,
-0.8906236290931702,
-0.30397140979766846,
-0.4304627776145935,
-0.6307324171066284,
0.09705715626478195,
1.116237998008728,
-1.03975248336792,
0.40628376603126526,
-0.8357822895050049,
0.11321725696325302,
0.35640600323677063,
-0.5064600706100464,
-0.15107615292072296,
-0.9238975048065186,
-0.6117252111434937,
0.08395294100046158,
-0.8874147534370422,
-0.38919979333877563,
-0.2451716959476471,
-0.16246548295021057,
0.11915265768766403,
0.3026191294193268,
0.3316884934902191,
0.9080750346183777,
-1.0299180746078491,
-1.114622950553894,
-0.19874288141727448,
0.2669541835784912,
-0.29195359349250793,
0.24890628457069397,
0.5011893510818481,
0.41373682022094727,
0.46057480573654175,
-0.037777405232191086,
0.4298819303512573,
0.21588772535324097,
-0.694735586643219,
0.5099846124649048,
-0.07926671952009201,
-0.23271125555038452,
-0.48895263671875,
-0.6910083889961243,
-0.05945678800344467,
-0.11509349942207336,
-0.9839538335800171,
-0.16729024052619934,
-1.1425565481185913,
0.31026843190193176,
-0.834949791431427,
0.4826745092868805,
0.41529789566993713,
0.10171090066432953,
-0.4630134105682373,
0.8200109601020813,
-0.5276960134506226,
0.20114748179912567,
0.21506358683109283,
0.03243745490908623,
-0.6170544624328613,
-0.3336157500743866,
0.5287635326385498,
-0.37758952379226685,
-0.37431788444519043,
0.7032767534255981,
0.10661061853170395,
0.43263959884643555,
0.030357863754034042,
-0.33415716886520386,
-0.32744085788726807,
-0.5810554027557373,
-0.7281466722488403,
0.5320082306861877,
0.8217612504959106,
-0.9124510288238525,
0.030443374067544937,
-0.7812436819076538,
-0.9282076358795166,
-0.1219601258635521,
-0.5988911390304565,
0.1833575963973999,
-0.12592308223247528,
-0.6140828132629395,
-0.17656360566616058,
0.2817799746990204,
0.0696573480963707,
-0.05097440257668495,
-0.4015674293041229,
0.4251973628997803,
0.022775476798415184,
0.33922022581100464,
0.23105071485042572,
-0.24656429886817932,
-1.170731544494629,
-0.1754423826932907,
-0.6999860405921936,
0.6757290363311768,
-0.6620752811431885,
-0.4643350839614868,
-0.6354113817214966,
0.2413187026977539,
-0.3222752511501312,
-0.2494259476661682,
-0.01509958878159523,
-0.4781210422515869,
-0.2920857071876526,
0.3597136437892914,
0.04115846008062363,
-0.44186490774154663,
-0.05514220520853996,
0.6992381811141968,
0.23627129197120667,
-0.687997043132782,
1.057197093963623,
-0.6899538040161133,
-0.6660569906234741,
-0.08091423660516739,
0.36296167969703674,
1.1047272682189941,
-0.03508957102894783,
-0.6325162649154663,
1.2585012912750244,
0.01566549763083458,
-0.173293799161911,
-0.20520557463169098,
-0.47704675793647766,
0.001682173926383257,
0.2889306843280792,
0.6131088733673096,
0.9702545404434204,
0.4523446261882782,
0.5939983129501343,
0.5326516032218933,
-0.0990586057305336,
0.354750394821167,
0.3505888283252716,
-0.06495863199234009,
0.2429208755493164,
0.31056392192840576,
-0.8312609791755676,
0.7323608994483948,
0.38671794533729553,
-0.2857639193534851,
0.12951414287090302,
-0.2864689826965332,
-0.06072013080120087,
-0.23735669255256653,
0.4639081060886383,
0.19964919984340668,
-0.7551299929618835,
-0.22605785727500916,
-0.33627626299858093,
-0.20347818732261658,
0.19646534323692322,
0.3172910809516907,
0.04803381487727165,
0.535855233669281,
0.6438193917274475,
0.0019470592960715294,
0.3802059292793274,
0.8445152044296265,
0.1083609014749527,
-0.11427641659975052,
0.5069241523742676,
-0.21827161312103271,
0.8873429298400879,
0.2325730174779892,
-0.09774065762758255,
-0.697044312953949,
-0.2204117327928543,
0.038765959441661835,
-0.8145037293434143,
0.3065114915370941,
-0.0792040005326271,
-0.40716552734375,
-0.47748738527297974,
-0.5992754101753235,
-0.27949070930480957,
-1.1182082891464233,
0.0684969425201416,
0.7819460034370422,
0.17290954291820526,
0.5364198684692383,
0.5272552371025085,
-0.24689869582653046,
0.1370847076177597,
-0.09048938751220703,
0.010182172991335392,
0.10720324516296387,
0.5945417881011963,
1.8269023895263672,
-0.4194023907184601,
0.8411154747009277,
1.0040807723999023,
-0.5436787605285645,
-0.07185506820678711,
0.4232065677642822,
-0.20406168699264526,
0.19854407012462616,
-0.517806887626648,
-0.30430907011032104,
0.5695317983627319,
0.15790367126464844,
-0.27334854006767273,
0.018423400819301605,
0.5318101644515991,
0.5511407852172852,
-0.3413548171520233,
-0.9395300149917603,
1.1494626998901367,
0.9706348776817322,
-0.01294028665870428,
-0.09012717008590698,
0.3290487229824066,
-0.34135156869888306,
-0.15331953763961792,
-0.712266743183136,
0.21364684402942657,
0.520768404006958,
-0.4305105209350586,
-0.3522414565086365,
-0.7799999117851257,
-0.36753585934638977,
-1.0963066816329956,
0.008464810438454151,
-0.8325062990188599,
0.7227858901023865,
0.23041731119155884,
0.20449011027812958,
0.050076402723789215,
-1.0012876987457275,
-0.49760934710502625,
0.8038780689239502,
0.5303909778594971,
0.05968964472413063,
-0.08257315307855606,
0.41815799474716187,
0.2563157379627228,
-0.5838834643363953,
0.7168042659759521,
0.4708012342453003,
-0.9181509613990784,
0.8737937808036804,
-0.42852795124053955,
0.2480275183916092,
0.06658298522233963,
-0.2356490045785904,
0.21451376378536224,
0.03454291820526123,
0.23637571930885315,
-0.5587428212165833,
0.07548622786998749,
0.01332901418209076,
-0.5264332890510559,
0.006594025529921055,
-1.440933108329773,
0.3028371036052704,
0.015341117978096008,
0.556346595287323,
0.26797738671302795,
-0.5315990447998047,
4.028820991516113,
0.7500201463699341,
0.8797607421875,
0.2917621433734894,
0.34143537282943726,
1.0696038007736206,
-0.21161936223506927,
-0.20617902278900146,
0.6082633137702942,
-1.030975103378296,
-0.7560030817985535,
0.2089102864265442,
-0.014780632220208645,
-0.25312328338623047,
-0.4866763651371002,
0.5046111941337585,
-0.34942904114723206,
0.36402425169944763,
0.031995415687561035,
-0.692120373249054,
-0.9660943746566772,
0.7280932068824768,
0.5128279328346252,
-0.15412858128547668,
0.22084298729896545,
0.5143487453460693,
0.25649529695510864,
-0.9513429403305054,
-0.6032946705818176,
-0.8354960680007935,
-0.12918506562709808,
-1.0676782131195068,
0.4429819881916046,
-0.45614683628082275,
-0.6187937259674072,
0.39301952719688416,
-0.4131487309932709,
0.29384154081344604,
0.700408399105072,
0.48652973771095276,
-0.25529587268829346,
-0.31297048926353455,
0.07128385454416275,
-0.2220057249069214,
-0.4110546410083771,
1.143287181854248,
-0.4967079162597656,
0.7274986505508423,
0.21765238046646118,
-0.20913824439048767,
0.28378480672836304,
0.2928749620914459,
0.17461523413658142,
-0.2718510031700134,
-0.7830179333686829,
0.3668263256549835,
-0.5331560969352722,
-0.07609616965055466,
0.08738136291503906,
-0.37688156962394714,
0.24511820077896118,
-0.102311871945858,
0.07885702699422836,
0.02765052765607834,
-0.0412801057100296,
1.1226921081542969,
0.6611480712890625,
0.35314351320266724,
-0.6836590766906738,
-0.3233691155910492,
-0.0931258276104927,
-0.44131922721862793,
-0.539739727973938,
0.25251340866088867,
0.5281268358230591,
0.19649693369865417,
0.7067807912826538,
0.7676153182983398,
0.07510560005903244,
0.08749793469905853,
-0.4731254279613495,
-0.500650942325592,
-0.09168896824121475,
0.5613394379615784,
-0.16457229852676392,
0.4357873797416687,
-0.46081972122192383,
0.17226363718509674,
0.3960462212562561,
0.8239074945449829,
0.2883021831512451,
1.6042460203170776,
0.12227083742618561,
-0.30522727966308594,
-0.5605010390281677
] |
Critical Momenta of Lattice Chiral Fermions
|
We determine the critical momenta for chiral fermions in the domain wall model recently suggested by Kaplan. For a wide range of domain wall masses $m$ and Wilson couplings $r$ we explicitly exhibit the regions in momentum space where the fermions are chiral. We compare the critical momenta for the infinitely large system with those obtained on a finite lattice.
|
Karl Jansen and Martin Schmaltz
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209002
|
hep-lat/9209003
|
[
-0.5423219799995422,
-0.7672148942947388,
-0.317640095949173,
-0.08804573863744736,
0.42382875084877014,
-0.10822120308876038,
-0.029477624222636223,
-0.7981114983558655,
-1.0109937191009521,
2.007185220718384,
0.06773900240659714,
0.11876441538333893,
0.11270881444215775,
-0.5714995265007019,
0.023278716951608658,
0.4072183072566986,
-0.061621371656656265,
-0.9669628143310547,
-1.134751319885254,
0.3392675518989563,
0.6177366971969604,
0.15679997205734253,
-0.6947991251945496,
-1.0630525350570679,
-0.5473839044570923,
0.879138708114624,
0.4433002471923828,
-0.019818201661109924,
0.8577256798744202,
1.034590482711792,
0.3635629415512085,
-0.7962305545806885,
-0.297892302274704,
-0.5441259741783142,
-0.6094516515731812,
-0.01170163881033659,
-0.4025765359401703,
-0.3607424199581146,
0.5525774359703064,
-0.35206523537635803,
0.5524492263793945,
-0.6860705614089966,
-0.601050078868866,
0.13309326767921448,
0.2888474762439728,
0.23727713525295258,
-0.19603119790554047,
-0.1404949426651001,
0.4398746192455292,
-1.091655969619751,
0.35181036591529846,
-0.22870132327079773,
0.3669307827949524,
-0.5052471160888672,
-0.1375734806060791,
-0.5746051669120789,
0.01951771043241024,
0.3912825882434845,
0.037025969475507736,
-0.38131770491600037,
0.4640183746814728,
0.16814328730106354,
0.28843411803245544,
-1.2597419023513794,
0.08768180012702942,
0.15289607644081116,
0.1929926872253418,
0.8133347034454346,
-0.16477562487125397,
-0.7320067882537842,
-0.39117273688316345,
-0.004196954891085625,
-0.7592766284942627,
0.07280357927083969,
-0.54157555103302,
0.5920014381408691,
-0.0537002757191658,
-1.0981255769729614,
-1.2676624059677124,
-0.9503242373466492,
-0.4789990782737732,
-0.5140092968940735,
-0.21523426473140717,
0.22505681216716766,
-0.2985038757324219,
-0.12040053308010101,
0.043705232441425323,
-0.26172783970832825,
-0.34183090925216675,
0.09041985869407654,
0.831479012966156,
0.8027426600456238,
0.02507603168487549,
-0.24150018393993378,
0.1918378323316574,
0.721757709980011,
-0.08106730133295059,
1.0025666952133179,
-0.09806182980537415,
-0.12475456297397614,
0.23001620173454285,
1.0656789541244507,
-0.7763713598251343,
0.89268559217453,
-0.7017982602119446,
0.3231143653392792,
-0.18467101454734802,
0.28040844202041626,
-0.013203740119934082,
-0.862227737903595,
0.5672290325164795,
-0.6324243545532227,
0.6863177418708801,
0.8937234282493591,
0.44333913922309875,
0.8361155390739441,
-0.17395682632923126,
-0.1365198791027069,
-0.6337981224060059,
-0.44762876629829407,
0.5530509352684021,
-0.2968456447124481,
0.35068532824516296,
-0.029613858088850975,
-0.5344731211662292,
-0.36078301072120667,
0.564837634563446,
0.41131407022476196,
-0.4024244248867035,
0.581396758556366,
0.4682120084762573,
0.29600727558135986,
-0.401449054479599,
0.4246397316455841,
-0.9659713506698608,
-0.04917123168706894,
-1.0094655752182007,
0.5209632515907288,
0.805482804775238,
-0.15736091136932373,
0.7453368306159973,
-0.6743306517601013,
0.23166410624980927,
0.9547085762023926,
-0.17926664650440216,
0.2776091992855072,
0.2640438675880432,
0.1945219486951828,
-0.22844262421131134,
0.23343247175216675,
-0.5358505845069885,
0.284476637840271,
-0.34142637252807617,
0.4659871459007263,
0.20624835789203644,
0.4007568657398224,
-0.44193482398986816,
0.4347207248210907,
-0.8410155773162842,
-0.34101220965385437,
0.4952069818973541,
0.05658428370952606,
-0.6918090581893921,
0.41053491830825806,
-0.9583464860916138,
0.022145744413137436,
-0.6236788034439087,
-1.1663767099380493,
0.2996906638145447,
-0.7317166924476624,
-0.0655970647931099,
-0.05956491827964783,
-0.7091155052185059,
0.7507711052894592,
0.7080913782119751,
0.467782199382782,
0.7535302639007568,
-0.29504674673080444,
-0.21423694491386414,
0.1255139410495758,
-0.5180315375328064,
-0.8175975680351257,
0.5329664349555969,
0.19630280137062073,
-0.6956468224525452,
-0.26998648047447205,
0.3398154675960541,
-0.49674659967422485,
0.2692044675350189,
0.39262527227401733,
-0.072215735912323,
-0.1259685754776001,
0.3451800048351288,
0.2731117904186249,
-0.4748785197734833,
0.9035611152648926,
-1.1975914239883423,
0.04380066320300102,
-0.623134195804596,
-0.2624107897281647,
-0.15765494108200073,
-0.5398243069648743,
-1.5640546083450317,
0.4332341253757477,
-1.1538695096969604,
-0.13157057762145996,
0.7245937585830688,
0.33309993147850037,
-0.16425178945064545,
-0.33925360441207886,
0.15000402927398682,
0.20515727996826172,
0.627640426158905,
-0.1590842455625534,
0.3713166117668152,
0.4099556803703308,
0.4545978903770447,
0.258774071931839,
0.7255098819732666,
0.33108359575271606,
0.7099640369415283,
0.25045597553253174,
0.43075263500213623,
0.5379258394241333,
-0.6774434447288513,
-0.5060135722160339,
0.218313068151474,
0.5617417097091675,
0.6289873123168945,
0.5172393918037415,
-0.3891162574291229,
0.2430085688829422,
-0.2522273659706116,
0.9669481515884399,
0.5754163265228271,
0.38394561409950256,
0.19905953109264374,
0.5359963774681091,
0.752136766910553,
0.11415143311023712,
-0.14918512105941772,
0.4356194734573364,
0.6455630660057068,
-0.2633104920387268,
-0.6437670588493347,
0.4310508966445923,
-0.48592647910118103,
0.5378128886222839,
-0.3824186325073242,
0.5845944285392761,
-0.4835546016693115,
-0.20042410492897034,
0.030701152980327606,
-0.23229466378688812,
-1.0772730112075806,
0.2536650598049164,
0.09145773947238922,
0.36835017800331116,
-0.03805920109152794,
-0.3196214735507965,
0.13600581884384155,
0.14264190196990967,
0.2677723467350006,
-1.002583622932434,
-0.06643947213888168,
1.0070781707763672,
-0.17397993803024292,
0.1904434710741043,
0.4520471692085266,
-0.018331920728087425,
-1.286895990371704,
0.011498206295073032,
-0.8888076543807983,
0.40574583411216736,
-0.9752973318099976,
0.03254813328385353,
0.6119594573974609,
-0.3988012969493866,
0.432853639125824,
-0.6350870728492737,
-0.009240237064659595,
0.466677725315094,
-0.6028938293457031,
0.21826739609241486,
0.6821849346160889,
0.13709335029125214,
-0.6205642223358154,
-0.3441215753555298,
-0.575285017490387,
-0.03870352357625961,
-0.7223281860351562,
0.20422804355621338,
0.7364600300788879,
-0.6682548522949219,
0.7167726755142212,
-0.24581266939640045,
-0.17050471901893616,
-0.3799935281276703,
-0.002212249208241701,
-0.47109776735305786,
0.15165352821350098,
0.27032116055488586,
-0.1494251936674118,
-0.1632881462574005,
-1.5197031497955322,
0.8222830295562744,
0.19783948361873627,
-0.6390007734298706,
0.6874872446060181,
-0.3103385865688324,
-0.8220533728599548,
0.6681891679763794,
0.8774892687797546,
-0.40647801756858826,
-0.2162415087223053,
0.98976069688797,
0.7276298403739929,
0.056532979011535645,
-0.27831077575683594,
-0.07226549088954926,
-0.726456344127655,
0.28364625573158264,
0.6526938080787659,
-0.575683057308197,
-0.292949378490448,
0.5447016954421997,
0.48536425828933716,
-0.4170086085796356,
0.45747074484825134,
-0.7749619483947754,
-0.2918480932712555,
-0.38008856773376465,
-0.19972294569015503,
0.7700902223587036,
0.21135863661766052,
0.12844717502593994,
-0.8925489187240601,
-0.2566099166870117,
0.7959372401237488,
0.3233044445514679,
0.09328626096248627,
-0.3471068739891052,
0.45317044854164124,
-0.15881261229515076,
0.6428461074829102,
-0.860333263874054,
-0.10309575498104095,
-0.3156370222568512,
-0.3949364423751831,
0.42064452171325684,
-0.5525034666061401,
0.3106728494167328,
-0.036482349038124084,
-0.05191738158464432,
-0.09140139818191528,
0.4807843267917633,
-0.5237151980400085,
-0.3517618775367737,
-0.62593013048172,
-0.3035338819026947,
0.15547379851341248,
0.4954480528831482,
-0.37276288866996765,
-0.9023411870002747,
-0.9351297616958618,
-0.5030438303947449,
-0.15891003608703613,
0.4383426308631897,
1.0802927017211914,
-0.631967306137085,
0.6317688822746277,
-0.07332909107208252,
-0.21158650517463684,
0.6801062226295471,
-0.46127912402153015,
0.0960984081029892,
0.21313484013080597,
0.12400386482477188,
1.087417483329773,
-0.5787621140480042,
-0.9831730723381042,
-0.10167886316776276,
1.1185795068740845,
0.6460956335067749,
0.7254541516304016,
0.2598453760147095,
0.017893465235829353,
-0.12215562909841537,
0.21651045978069305,
-0.4933708608150482,
0.23384404182434082,
-0.25269800424575806,
0.05979714170098305,
0.1836249828338623,
0.22369050979614258,
0.08765184879302979,
0.8406420946121216,
0.41721150279045105,
-0.08197236806154251,
0.24054722487926483,
0.9050664305686951,
0.6473627686500549,
1.0003554821014404,
-0.03944946080446243,
-0.5832630395889282,
0.351728230714798,
-1.1110825538635254,
0.226932555437088,
0.42897918820381165,
0.3838748633861542,
-0.5021249055862427,
-0.5990145802497864,
-0.2994920313358307,
-0.49803489446640015,
0.33069708943367004,
0.1737644076347351,
-0.21989060938358307,
0.15851767361164093,
0.6658182740211487,
1.1454274654388428,
-0.05047818273305893,
0.48879218101501465,
1.3541386127471924,
0.5013287663459778,
0.7856785655021667,
-1.0864365100860596,
-0.011594033800065517,
-0.43379461765289307,
0.5381284356117249,
0.4655360281467438,
-0.8614654541015625,
-0.9848816394805908,
-0.22241801023483276,
0.05000357702374458,
-0.5406993627548218,
0.028534086421132088,
0.9850146770477295,
-0.12149692326784134,
0.17892181873321533,
-0.22003445029258728,
-0.2466753125190735,
0.542655348777771,
-0.5557154417037964,
-0.8278560042381287,
0.054936934262514114,
0.11377990990877151,
-0.21903523802757263,
0.5548568964004517,
-0.4592028558254242,
-0.4978359341621399,
-0.5837031602859497,
-0.212201327085495,
-0.026603497564792633,
-0.05057736113667488,
-0.5599889755249023,
0.0565854050219059,
-0.5420070886611938,
-0.08616442233324051,
0.5540070533752441,
-0.21350201964378357,
-0.4492705166339874,
-0.46170496940612793,
0.0026827924884855747,
0.13765740394592285,
-0.13981685042381287,
0.3360249102115631,
0.06329992413520813,
1.7898653745651245,
0.4984014928340912,
0.23496553301811218,
0.40072527527809143,
-0.03301819786429405,
0.2147483080625534,
-0.29388388991355896,
0.2061818391084671,
0.07910841703414917,
-0.36429014801979065,
-1.0816112756729126,
0.00587973278015852,
-0.3482775092124939,
-0.6644104719161987,
0.6827910542488098,
-0.45769253373146057,
0.6124861240386963,
0.1403517872095108,
-0.6037488579750061,
-0.483966201543808,
-0.6042044758796692,
-1.4119595289230347,
0.6534463763237,
0.014570286497473717,
-0.15888284146785736,
0.8243314623832703,
-0.5773841142654419,
0.3860797584056854,
-0.9020344018936157,
-0.3883286416530609,
-0.0021702453959733248,
0.39381903409957886,
0.6929531693458557,
0.028137778863310814,
0.169010728597641,
-0.481538325548172,
0.35800859332084656,
-0.5327220559120178,
0.33974921703338623,
-0.49675798416137695,
0.050472911447286606,
-0.4041503369808197,
-0.39095744490623474,
0.34409379959106445,
-0.733708381652832,
-0.008934291079640388,
0.2268034815788269,
-0.22097362577915192,
0.41033098101615906,
-0.5581968426704407,
0.14107957482337952,
0.05732966959476471,
0.6141267418861389,
0.3057177662849426,
-0.45220282673835754,
0.16159172356128693,
1.522459864616394,
-0.09202614426612854,
0.1358385533094406,
0.18253588676452637,
-0.3312397301197052,
0.6498647332191467,
0.32951289415359497,
1.3362758159637451,
-0.632816731929779,
-0.3642190396785736,
0.16192787885665894,
-0.40538594126701355,
0.9084256291389465,
0.8694339394569397,
-0.3693694472312927,
0.13137564063072205,
-0.38591575622558594,
0.08636804670095444,
0.19144468009471893,
-0.7440195679664612,
0.5818397402763367,
-0.6359990835189819,
-0.6708313226699829,
-0.9596474766731262,
0.34066423773765564,
0.1668621450662613,
0.4108055830001831,
0.35763323307037354,
-0.12070649117231369,
0.2451421320438385,
0.4011884033679962,
0.22778885066509247,
0.127894327044487,
-0.3029495179653168,
0.4202471375465393,
0.02592058852314949,
0.4760461151599884,
-0.4359491765499115,
0.016344204545021057,
-0.6065237522125244,
1.3695499897003174,
-0.3085767328739166,
-0.48321810364723206,
0.05765000730752945,
0.08333240449428558,
0.595832347869873,
-1.1786051988601685,
0.004176767077296972,
0.39472487568855286,
-0.10188035666942596,
-0.11532952636480331,
0.14778731763362885,
-1.1200255155563354,
-0.4121120870113373,
-0.8576143980026245,
-1.0777466297149658,
0.4281584918498993,
-0.2465481162071228,
-0.5763840675354004,
-0.2735397219657898,
-1.032448410987854,
0.47117459774017334,
0.2370583862066269,
0.04024871066212654,
0.5221477150917053,
0.4276100993156433,
-0.1913672536611557,
-0.4502687454223633,
-0.2717176079750061,
-0.5734562873840332,
0.23154954612255096,
0.5521131753921509,
-0.14199043810367584,
0.05130196735262871,
0.317045658826828,
0.275200217962265,
-0.7162441611289978,
-0.2705951929092407,
-0.19762597978115082,
-0.3075360953807831,
-0.5446906089782715,
0.6998640298843384,
-0.049313079565763474,
0.05426228791475296,
-0.5112109780311584,
-0.2961052656173706,
-0.22095994651317596,
0.31988030672073364,
-0.01138762291520834,
0.11745613813400269,
0.7611603140830994,
0.19438835978507996,
0.3200843632221222,
-0.5932981371879578,
-0.30145734548568726,
0.3701859414577484,
-0.4660507142543793,
-0.3767155110836029,
0.5837403535842896,
0.25246983766555786,
-0.484893262386322,
-0.07812868058681488,
-0.6459178328514099,
-0.14066433906555176,
-0.23693525791168213,
-0.17881661653518677,
-0.3279460072517395,
-0.23872052133083344,
0.2628015875816345,
0.28586357831954956,
0.905384361743927,
0.4136699438095093,
0.4939432740211487,
0.3428819179534912,
-0.6675422191619873,
-0.18011751770973206,
0.27735069394111633,
1.3645328283309937,
-0.16523019969463348,
-0.7816879153251648,
0.236649751663208,
0.28868934512138367,
-0.10650111734867096,
0.09774397313594818,
0.8346038460731506,
-0.5262513756752014,
0.8505294322967529,
-0.24980701506137848,
-0.29490938782691956,
0.8548622131347656,
1.0068809986114502,
-0.5413421988487244,
-0.4772239327430725,
0.14834964275360107,
-0.9100419282913208,
-0.3929294943809509,
-0.5904682874679565,
0.25364047288894653,
0.38762834668159485,
-0.16639351844787598,
0.1244845762848854,
0.4281223714351654,
-0.8227623701095581,
-0.7183278799057007,
-1.23944890499115,
-0.5046302676200867,
-1.1074082851409912,
-0.2509911358356476,
-0.38524317741394043,
-0.03283517435193062,
-0.16114258766174316,
0.5597952008247375,
-0.36603230237960815,
0.17045089602470398,
-0.7446478009223938,
-0.018840080127120018,
0.1936829835176468,
-0.10005133599042892,
-0.3952291011810303,
-0.9485516548156738,
-0.6386998295783997,
-0.47517210245132446,
-0.47018155455589294,
-0.10996879637241364,
-0.12486562877893448,
-0.6747537851333618,
0.06132489815354347,
0.1383572220802307,
-0.11982448399066925,
0.2815071940422058,
-0.9346778392791748,
-1.2937570810317993,
-0.16335034370422363,
0.4432014524936676,
-0.5995745062828064,
0.733544111251831,
1.187751054763794,
0.5642918944358826,
0.7237220406532288,
0.5297223925590515,
-0.1964338719844818,
0.29150888323783875,
-1.0623053312301636,
0.26116669178009033,
0.4475768506526947,
-0.11821165680885315,
-0.21882078051567078,
-0.6825705170631409,
0.1118856817483902,
0.16304485499858856,
-0.8436928391456604,
0.3343409597873688,
-0.49987587332725525,
0.2697775363922119,
-0.8171671628952026,
0.6058560609817505,
0.4175111949443817,
0.37484103441238403,
-0.02326899953186512,
0.6646530628204346,
-0.5402799844741821,
0.20164665579795837,
0.17240343987941742,
0.12162952870130539,
-0.6042934060096741,
-0.1593107134103775,
0.29345887899398804,
-0.46846243739128113,
-0.3710857927799225,
0.2884998619556427,
-0.4940928816795349,
0.6412272453308105,
-0.1780625581741333,
-0.1886736899614334,
-0.4209531545639038,
-0.5911185145378113,
-0.485994815826416,
0.26520445942878723,
0.5604276061058044,
-0.9336045980453491,
0.28237661719322205,
-0.5191037058830261,
-1.040381908416748,
-0.0077718463726341724,
-0.631389319896698,
0.029085727408528328,
0.079556405544281,
-0.5504311919212341,
-0.5016899108886719,
-0.11074788123369217,
-0.32361936569213867,
0.2662639021873474,
0.3461703658103943,
0.5525001883506775,
-0.1955791711807251,
-0.017246320843696594,
0.024376392364501953,
0.000374104012735188,
-0.6112666130065918,
0.3543721139431,
-0.8008349537849426,
0.3488514721393585,
-0.44243696331977844,
-0.22678129374980927,
-0.0854620710015297,
0.31210261583328247,
0.0796217992901802,
-0.09161535650491714,
-0.23489542305469513,
-0.4053354561328888,
0.03238590061664581,
-0.10937220603227615,
-0.37885725498199463,
-0.23469899594783783,
-0.8191244006156921,
0.4416165351867676,
0.21967260539531708,
-0.8704409599304199,
0.5050964951515198,
0.2704009413719177,
-0.29238176345825195,
-0.09288439154624939,
0.3895622491836548,
1.4787611961364746,
-0.2716940641403198,
-0.21030302345752716,
0.8763703107833862,
0.26205626130104065,
0.20191600918769836,
-0.233014315366745,
-0.25109055638313293,
0.2227092683315277,
-0.15632279217243195,
0.6288140416145325,
1.2441893815994263,
0.6754214763641357,
0.7099925875663757,
0.260347455739975,
0.17198219895362854,
0.047453463077545166,
0.7461698651313782,
0.11242324113845825,
0.774918258190155,
0.43654975295066833,
-0.47436168789863586,
-0.07261130213737488,
-0.054699212312698364,
-0.05293610319495201,
0.18461138010025024,
-0.2171424925327301,
-0.4295978546142578,
-0.5059675574302673,
0.5435633659362793,
0.16349132359027863,
-0.9962531924247742,
-0.40810254216194153,
-0.03149940446019173,
-0.1372462660074234,
0.727131724357605,
0.14429132640361786,
-0.046234581619501114,
0.5731029510498047,
0.5327985286712646,
-0.06255083531141281,
-0.004319880623370409,
0.6630434393882751,
-0.2732378840446472,
0.6183199882507324,
0.503589928150177,
0.41581109166145325,
1.1431591510772705,
0.8922619223594666,
0.14845961332321167,
-0.9465960264205933,
-0.45536598563194275,
0.6108191013336182,
-1.0081428289413452,
0.3198719322681427,
-0.1863717883825302,
0.01991995796561241,
0.08534505218267441,
-0.5804329514503479,
0.5097837448120117,
-0.545324981212616,
-0.6093534827232361,
0.5225841403007507,
-0.2258453369140625,
0.10739478468894958,
0.3992234766483307,
0.10980639606714249,
0.17049124836921692,
0.3127039968967438,
0.4806259572505951,
0.3405548632144928,
0.6013026833534241,
1.6942274570465088,
-0.4572555124759674,
0.7704963684082031,
0.4550768733024597,
-0.3615778088569641,
0.3141077756881714,
0.6218562126159668,
0.014629809185862541,
0.656446099281311,
-0.6780417561531067,
0.10985936969518661,
0.360534131526947,
0.18780939280986786,
0.11711741983890533,
0.24793387949466705,
0.23686127364635468,
0.2886506915092468,
-0.48781925439834595,
-0.23228289186954498,
1.3871519565582275,
0.5618669986724854,
-0.6275128126144409,
-0.3352557420730591,
0.16695274412631989,
-0.7208268046379089,
-0.0633261576294899,
-0.947272777557373,
0.09729164838790894,
-0.014643507078289986,
-0.05540720000863075,
-0.12437225133180618,
-0.8212310075759888,
-0.3698139190673828,
-0.7009535431861877,
0.5419299006462097,
-0.6007760763168335,
0.6419489979743958,
0.34931135177612305,
-0.32181885838508606,
0.1682523787021637,
-0.504308819770813,
-0.23110610246658325,
0.504881739616394,
1.1126078367233276,
0.37206265330314636,
0.34538230299949646,
0.3181765377521515,
0.3866114616394043,
-0.34305375814437866,
0.6617966890335083,
0.6931291222572327,
-1.1507351398468018,
1.0003514289855957,
-0.8316471576690674,
0.1874971240758896,
0.2631278336048126,
-0.6161500811576843,
0.2385222464799881,
-0.17990419268608093,
0.1616472452878952,
-0.22948375344276428,
-0.2731240391731262,
-0.07170888781547546,
-0.5281287431716919,
0.2330632358789444,
-0.5369071960449219,
0.20707590878009796,
-0.7334402203559875,
0.20159676671028137,
-0.2760280966758728,
-0.6388425230979919,
3.946873664855957,
0.5309943556785583,
0.9610072374343872,
0.609275221824646,
1.0017622709274292,
1.3297401666641235,
-0.41447195410728455,
0.05133789777755737,
-0.12507623434066772,
-1.4227783679962158,
-0.8360348343849182,
0.253719687461853,
0.03863532096147537,
0.11511830985546112,
-0.37617209553718567,
0.9763583540916443,
-0.4114798307418823,
0.37375393509864807,
-0.1991180181503296,
-0.8778783679008484,
-0.2704015374183655,
0.2018086165189743,
0.15317803621292114,
0.001447474816814065,
0.2496359497308731,
0.25405025482177734,
0.4458801746368408,
-1.155186653137207,
-1.0222634077072144,
-0.6935675740242004,
-0.8674753904342651,
-0.9562990665435791,
0.5376259684562683,
-0.5961580872535706,
-1.0100966691970825,
-0.16251525282859802,
-0.18239346146583557,
-0.6000048518180847,
0.14355218410491943,
0.19146300852298737,
-0.19904522597789764,
0.2954658567905426,
0.39377057552337646,
-0.46142062544822693,
-0.028040068224072456,
0.49524417519569397,
-0.7950876355171204,
1.2875090837478638,
0.3947046101093292,
-0.4348171055316925,
0.46345382928848267,
0.016435321420431137,
0.4186558127403259,
-0.39638957381248474,
-0.21100886166095734,
0.42575153708457947,
-0.006857919506728649,
-0.17797468602657318,
0.0830097571015358,
0.15341198444366455,
0.3491942882537842,
-0.08512884378433228,
-0.20887288451194763,
0.022997040301561356,
0.6222535967826843,
0.707612156867981,
0.26539504528045654,
-0.029523178935050964,
0.12106438726186752,
-0.16715815663337708,
0.18072861433029175,
-0.6228126883506775,
-0.2303222417831421,
0.6423102617263794,
0.6278418302536011,
0.2708970904350281,
0.08094580471515656,
0.6133261919021606,
0.513282835483551,
-0.22143451869487762,
-0.5077885389328003,
-0.6243569850921631,
-0.28736111521720886,
0.30082207918167114,
-0.07201788574457169,
0.4946727752685547,
-0.13378803431987762,
-0.2699304521083832,
-0.4035876989364624,
0.30015015602111816,
0.20802080631256104,
1.521570086479187,
0.18560779094696045,
0.10348483175039291,
-0.4881761968135834
] |
Chern-Simons Currents and Chiral Fermions on the Lattice
|
We compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$ dimensional lattice, making use of a topological interpretation of the momentum space fermion propagator as a map from the torus to the sphere, $T^{d}\to S^{d}$. These mappings are shown to fall in different homotopy classes depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the Wilson coupling. As a result, the induced Chern-Simons term changes discontinuously at $d+1$ different values for $m$, unlike in the continuum. This behavior is exactly what is required by the peculiar spectrum found for a recently proposed model of chiral lattice fermions as zeromodes bound to a domain wall.
|
Maarten Golterman, Karl Jansen and David Kaplan
|
hep-lat hep-th
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209003
|
hep-lat/9209004
|
[
0.05458696186542511,
0.05015798285603523,
-0.19557920098304749,
0.65261310338974,
-0.1925383359193802,
0.2659136950969696,
-0.45382562279701233,
-0.6123974323272705,
-0.8301859498023987,
1.3693854808807373,
0.24336421489715576,
-0.010785422287881374,
0.3840801417827606,
-0.8541342616081238,
-0.7445587515830994,
0.6875899434089661,
-0.241975799202919,
-0.8061435222625732,
-1.3230170011520386,
0.2850528657436371,
0.08715362846851349,
-0.28453966975212097,
-1.0988329648971558,
-0.7163267135620117,
-0.5326656699180603,
0.8267804980278015,
-0.11017492413520813,
0.39292997121810913,
0.9158594608306885,
0.5927603840827942,
0.33584168553352356,
-0.4828583002090454,
-0.31126660108566284,
-0.6976659297943115,
-0.46033862233161926,
-0.20793291926383972,
-0.46205803751945496,
-0.14087723195552826,
0.8599907755851746,
-0.4029170572757721,
0.9040345549583435,
-0.007084736134856939,
0.3568333089351654,
-0.30812811851501465,
-0.4904174208641052,
0.3625296354293823,
-0.18602408468723297,
0.04972728714346886,
0.25723639130592346,
-1.4665627479553223,
0.3704281449317932,
0.43358519673347473,
0.4742453694343567,
-0.4715695381164551,
-0.016679197549819946,
-0.24976535141468048,
-0.15978917479515076,
0.12416847795248032,
-1.0926586389541626,
-0.4274483919143677,
0.6680006384849548,
-0.039374422281980515,
0.8688102960586548,
-0.6162707805633545,
0.16365014016628265,
1.2416749000549316,
0.0842658057808876,
0.747301459312439,
0.3384974002838135,
-0.0654626339673996,
-0.7868456244468689,
-0.2954138517379761,
-0.7025417685508728,
0.37951380014419556,
-0.48540544509887695,
0.6374303698539734,
0.07199382781982422,
-0.2790161073207855,
-0.31896674633026123,
-0.20108191668987274,
0.01860434003174305,
0.6377242207527161,
-0.3800866901874542,
0.09178652614355087,
-0.5137119293212891,
-0.3007524013519287,
-0.3605971336364746,
-0.3349156081676483,
-0.22792400419712067,
0.5162673592567444,
0.11734727770090103,
0.5373148918151855,
0.005504019092768431,
0.35056525468826294,
0.43267759680747986,
0.43253910541534424,
-0.33473825454711914,
0.4142031669616699,
0.6218439936637878,
0.1188642680644989,
-0.31435561180114746,
0.4054599404335022,
-0.6036152839660645,
-0.08610614389181137,
-0.8584651350975037,
-0.1691863238811493,
-0.6069079041481018,
0.2973839342594147,
-0.0015054626855999231,
-0.3117426931858063,
0.019188636913895607,
0.19856441020965576,
0.6215360164642334,
0.4637130796909332,
0.7345478534698486,
0.6276074051856995,
-0.6099212169647217,
-0.33475461602211,
-1.2930852174758911,
-0.17077675461769104,
-0.015690045431256294,
0.4280846416950226,
-0.02715638279914856,
0.604538083076477,
0.2546859681606293,
0.001509787398390472,
0.7071083784103394,
0.5966347455978394,
-0.3560856580734253,
0.6507644653320312,
-0.3402266204357147,
-0.2703301012516022,
-0.46586453914642334,
0.6783532500267029,
-0.37201371788978577,
0.2843531668186188,
-0.44381579756736755,
0.4051225781440735,
0.5061432123184204,
-0.5958390831947327,
0.8876355886459351,
-0.6240395307540894,
0.1692298948764801,
0.8161332011222839,
0.01487165130674839,
-0.45495346188545227,
0.2481095939874649,
-0.16902662813663483,
-0.5402736067771912,
0.2374029904603958,
-0.5113595724105835,
0.16798800230026245,
0.4970862865447998,
0.05079396814107895,
0.08589410781860352,
0.4859744906425476,
-0.5252456068992615,
0.35757455229759216,
-0.4532356262207031,
-0.8100254535675049,
-0.05974957346916199,
0.20159128308296204,
-0.283269464969635,
0.4509918987751007,
-0.14816153049468994,
0.07229892164468765,
-0.25693127512931824,
0.09856365621089935,
0.004893510136753321,
-1.2086873054504395,
0.13250046968460083,
0.5472195148468018,
-0.25976356863975525,
0.5432491898536682,
0.25516432523727417,
-0.1600678712129593,
0.9595028758049011,
-0.9466665387153625,
-0.3391776978969574,
0.47342854738235474,
-0.28034645318984985,
-0.2855209410190582,
0.7555621266365051,
0.3003227710723877,
-0.06511206179857254,
-0.1291205883026123,
-0.40058451890945435,
-0.45263993740081787,
0.4483383297920227,
0.2864801287651062,
-0.4108770489692688,
0.347114622592926,
-0.6071287393569946,
0.6663357019424438,
-0.5468589663505554,
-0.25396043062210083,
-0.9586977958679199,
0.34877079725265503,
-0.4620687663555145,
-0.477775901556015,
-0.2072526216506958,
0.4906308352947235,
-0.7303929924964905,
0.5420399904251099,
-1.0881648063659668,
-0.15974031388759613,
0.20709848403930664,
-0.545443594455719,
-0.6646602153778076,
0.3004942238330841,
0.5887423157691956,
-0.6487659811973572,
0.12443266808986664,
-0.701077938079834,
-0.38189777731895447,
0.47281578183174133,
-0.21558821201324463,
0.27934300899505615,
-0.055167004466056824,
0.44415757060050964,
0.9819890856742859,
0.0478287972509861,
-0.1598319709300995,
0.9286414980888367,
-0.21954351663589478,
-0.785749077796936,
0.23033656179904938,
0.4597996175289154,
0.3008098900318146,
-0.7323452234268188,
0.22887888550758362,
0.966227650642395,
0.44604161381721497,
0.35981613397598267,
0.8065878748893738,
0.5414219498634338,
-0.10006784647703171,
0.701373279094696,
0.2044161707162857,
0.26309385895729065,
0.12427760660648346,
-0.4790184497833252,
0.5746509432792664,
0.09712301939725876,
-0.3518499732017517,
-0.030545281246304512,
-0.39400121569633484,
0.2859024405479431,
-0.9582319855690002,
0.5894930958747864,
0.30032724142074585,
0.18179088830947876,
0.6089451313018799,
0.5008229613304138,
-1.2403371334075928,
-0.027325233444571495,
-0.05320269614458084,
-0.020910849794745445,
-0.2388046532869339,
-0.41154393553733826,
-0.5473437309265137,
0.03718514367938042,
0.05401424691081047,
-0.44197604060173035,
-0.40286752581596375,
1.0863529443740845,
0.07069392502307892,
0.2700880467891693,
0.4288313090801239,
-0.8547484278678894,
-1.074216365814209,
0.08684828132390976,
-0.6256967186927795,
-0.14640028774738312,
-0.14650095999240875,
0.7134374380111694,
0.775361180305481,
-1.0080041885375977,
0.5600576400756836,
0.507466733455658,
0.0069601754657924175,
0.38663747906684875,
-0.2868764102458954,
0.11308305710554123,
0.6665551662445068,
0.3770047426223755,
-1.0023552179336548,
0.07960306107997894,
-0.125376358628273,
-0.011175212450325489,
-0.12445354461669922,
-0.459223210811615,
0.6749990582466125,
-0.25393837690353394,
0.09915187954902649,
0.44144299626350403,
-0.7572698593139648,
0.18253393471240997,
0.04380146786570549,
-0.40449059009552,
0.562739372253418,
0.34168606996536255,
-0.3488447070121765,
0.20078404247760773,
-0.7611886262893677,
0.45236945152282715,
-0.20045289397239685,
-0.05953655391931534,
0.5530636310577393,
0.6004364490509033,
-0.29358506202697754,
0.3134518265724182,
-0.9957225322723389,
0.2889972925186157,
0.0675213485956192,
0.4503285884857178,
0.2942776381969452,
0.2558635473251343,
-0.344295471906662,
-0.49529001116752625,
-0.8564465641975403,
-0.0272712092846632,
-0.19065961241722107,
-0.44285959005355835,
0.14444485306739807,
0.18290291726589203,
0.2852534055709839,
-0.5357660055160522,
0.9110102653503418,
-1.0982969999313354,
-0.8941718339920044,
-0.14534831047058105,
-1.0796607732772827,
0.49642443656921387,
-0.007280380465090275,
0.03611624613404274,
-0.2820364236831665,
0.24375736713409424,
0.022115901112556458,
0.3469592034816742,
0.772371768951416,
-0.187649205327034,
1.135270118713379,
0.42819949984550476,
0.19697213172912598,
-0.29143330454826355,
0.9200045466423035,
0.020845558494329453,
-0.7731353640556335,
-0.08392456918954849,
-0.9977013468742371,
0.5326928496360779,
0.15250703692436218,
0.17081908881664276,
-0.4051438570022583,
0.3832007050514221,
-0.16805417835712433,
-0.6415225863456726,
-0.5675867199897766,
-0.8403481245040894,
0.2885269522666931,
0.4440697431564331,
-0.5375055074691772,
-0.04676087945699692,
-0.40558984875679016,
-0.20099224150180817,
0.8800987601280212,
0.5911862850189209,
0.05003352463245392,
-0.4999675452709198,
-0.16838057339191437,
0.10405256599187851,
-0.6577265858650208,
0.2912083566188812,
-0.10215362906455994,
0.2021014243364334,
0.3842516243457794,
0.4351189136505127,
0.4814057946205139,
-0.25882431864738464,
-0.7624165415763855,
-0.34963205456733704,
0.8166974186897278,
0.9383596181869507,
0.06329528987407684,
0.7981069087982178,
-0.028833074495196342,
0.6226068735122681,
-1.047200322151184,
-0.8043918013572693,
0.023402074351906776,
-0.3730164170265198,
0.5698331594467163,
-0.7629178762435913,
-0.23504124581813812,
-0.1310252845287323,
-0.1082940623164177,
0.6535870432853699,
-0.11433948576450348,
-0.21740438044071198,
0.8101731538772583,
-0.02945083938539028,
0.1432110220193863,
1.0419663190841675,
0.11719308793544769,
-0.07561560720205307,
-0.49240246415138245,
0.46554142236709595,
-0.04077734425663948,
-0.12595246732234955,
-0.09525547176599503,
-0.9442601203918457,
-0.45753586292266846,
-0.540673553943634,
0.6408711075782776,
0.20833416283130646,
-0.05039241537451744,
0.8125928044319153,
-0.2504388689994812,
0.43273764848709106,
-0.4226551353931427,
0.2960294187068939,
0.1884283870458603,
0.3040253818035126,
0.08125703036785126,
-0.69922935962677,
0.3939194679260254,
-0.2727304697036743,
0.21654890477657318,
0.5861808657646179,
-0.14883184432983398,
-1.2199897766113281,
-0.5189758539199829,
0.31408360600471497,
-0.08296526968479156,
-0.0029869070276618004,
0.9087735414505005,
0.18081291019916534,
-0.03521469607949257,
-0.6319299340248108,
-0.09642522037029266,
1.2058727741241455,
-0.5350989699363708,
-0.5246467590332031,
0.17279160022735596,
-0.0867307260632515,
0.23014375567436218,
0.8245896100997925,
-0.494651198387146,
-1.0072910785675049,
0.03898484259843826,
-0.8204145431518555,
0.36561334133148193,
-0.5944697856903076,
-0.8646209239959717,
-0.48904889822006226,
-0.059822481125593185,
-0.3581129014492035,
0.5362133383750916,
-0.23988096415996552,
-0.6997591257095337,
0.27412334084510803,
0.03702735900878906,
-0.5357850790023804,
-0.2782655358314514,
0.04387553036212921,
0.2744366526603699,
1.208031177520752,
0.9559142589569092,
0.6991050243377686,
-0.3740389347076416,
0.5362222194671631,
0.06267498433589935,
0.0143074756488204,
-0.17496687173843384,
-0.3046683669090271,
-0.2531616985797882,
-0.30492934584617615,
-0.06307274848222733,
-0.6022481918334961,
-0.22398988902568817,
0.24694345891475677,
-0.10372459888458252,
0.7914528846740723,
0.46435123682022095,
-0.8456488847732544,
-0.2976575493812561,
-0.22084759175777435,
-0.4676915109157562,
0.23302492499351501,
-0.4660443365573883,
-0.5695536136627197,
-0.03127839416265488,
0.37415722012519836,
-0.13107722997665405,
-0.35210689902305603,
-0.04822066053748131,
-0.4044078588485718,
-0.01842428930103779,
0.6883777379989624,
0.43915078043937683,
0.7589982151985168,
-0.8102341890335083,
0.9945765733718872,
-0.4162370264530182,
0.2524332106113434,
-0.3044588565826416,
-0.63886559009552,
-0.5958064198493958,
-0.2880561351776123,
0.5661490559577942,
-0.08517267554998398,
-0.1500774770975113,
-0.3350690007209778,
0.10165418684482574,
0.22999148070812225,
0.038905441761016846,
-0.30828964710235596,
-0.2263580560684204,
0.10944073647260666,
-0.05600446090102196,
-0.5800113677978516,
-0.47976183891296387,
0.5399530529975891,
0.2502075731754303,
0.015500434674322605,
-0.12586212158203125,
-0.3488788306713104,
0.43777981400489807,
-0.5107475519180298,
0.2248256951570511,
-0.714103639125824,
-0.17348305881023407,
0.14380529522895813,
-0.4134388267993927,
0.475087970495224,
0.5738593339920044,
0.04659982770681381,
0.022178834304213524,
-0.39914435148239136,
-0.4723612368106842,
-0.14695851504802704,
-0.7769460678100586,
-0.6804412603378296,
-0.5064002275466919,
-0.40170228481292725,
-0.4123280942440033,
1.0929923057556152,
-0.860873818397522,
0.648757815361023,
0.5188741683959961,
0.05798305571079254,
-0.2997252941131592,
0.3577076196670532,
0.5622535943984985,
0.15094240009784698,
0.512136697769165,
0.4825379550457001,
-0.12721127271652222,
0.7940448522567749,
-0.35179561376571655,
0.21249204874038696,
-0.2903371751308441,
0.9530118107795715,
-1.0173839330673218,
-0.004401430021971464,
-0.12946061789989471,
0.9436087608337402,
0.6295732855796814,
-1.0244817733764648,
0.7331030964851379,
0.35495293140411377,
0.06422469019889832,
0.8536718487739563,
0.7288221120834351,
-0.404506653547287,
-0.5915457606315613,
-0.40303823351860046,
-1.1146275997161865,
0.8938072323799133,
-0.10799945145845413,
-0.1937067210674286,
-0.38443079590797424,
-0.6090924739837646,
-0.7009848952293396,
-0.10232622921466827,
-0.07036101818084717,
0.1026812344789505,
0.608695924282074,
-0.07914192974567413,
-0.10638613253831863,
0.6871625781059265,
-0.3682476282119751,
-0.13580864667892456,
-0.8668739199638367,
-0.17200970649719238,
-0.8773288130760193,
0.26804283261299133,
-0.5232006907463074,
-0.7274589538574219,
-0.261116623878479,
0.36092573404312134,
0.037577416747808456,
0.13052873313426971,
1.4177970886230469,
-0.3495810925960541,
-0.8031466603279114,
-0.11211973428726196,
-0.390214741230011,
0.5801606178283691,
-0.4105563759803772,
0.7494675517082214,
0.1910090446472168,
-0.28604480624198914,
0.4143385887145996,
0.06139984726905823,
0.18174317479133606,
-0.7629046440124512,
0.5516547560691833,
-0.2432282567024231,
-0.5405985713005066,
0.4702298045158386,
-0.16681472957134247,
-0.7926380038261414,
-0.5204886794090271,
-1.5410270690917969,
-0.020717106759548187,
-0.2074749916791916,
0.025748785585165024,
0.0675060972571373,
-0.06177753955125809,
-0.06791423261165619,
0.5607025027275085,
0.8321477770805359,
0.20334956049919128,
-0.17871777713298798,
0.2506747543811798,
-0.039074309170246124,
-1.105806589126587,
0.17499865591526031,
1.2164567708969116,
-0.027026383206248283,
-1.2384207248687744,
-0.07372420281171799,
-0.0908769965171814,
-0.4113321602344513,
-0.29117846488952637,
0.5014010071754456,
-1.001454472541809,
0.6662402749061584,
-0.042700301855802536,
0.04146367311477661,
0.04938529059290886,
0.45099884271621704,
0.1426456719636917,
0.07753263413906097,
0.1639912724494934,
-0.6059158444404602,
-0.4822964072227478,
-0.4770255386829376,
-0.15704558789730072,
0.2710900902748108,
0.4971083402633667,
0.7722498178482056,
-0.1796838641166687,
-0.2288997620344162,
-0.11547993123531342,
-0.48193782567977905,
-0.11313169449567795,
-0.8142311573028564,
-0.07184090465307236,
-0.11283083260059357,
0.3241819441318512,
-0.3350086212158203,
0.3591245114803314,
-0.07531613111495972,
0.11284225434064865,
-0.25095468759536743,
-0.19980838894844055,
0.2525698244571686,
0.42004749178886414,
-0.29733872413635254,
-1.4065500497817993,
-0.09839697182178497,
0.1891985535621643,
-0.20598329603672028,
-0.7680972218513489,
-0.2496180683374405,
0.8054986596107483,
-0.2759140431880951,
0.5495081543922424,
-0.41101282835006714,
0.6345548033714294,
-0.9325960278511047,
-0.2939767837524414,
0.062368590384721756,
-0.0022319573909044266,
-0.46760839223861694,
0.2710341215133667,
0.12269215285778046,
0.6133066415786743,
0.45834776759147644,
-0.20939290523529053,
0.11254086345434189,
-0.4375123679637909,
-0.8801330327987671,
-0.5002709627151489,
-0.43056386709213257,
0.640509307384491,
0.1529948115348816,
-0.7664916515350342,
-0.08284933865070343,
0.5435226559638977,
-1.2953510284423828,
0.37300726771354675,
-0.2340133786201477,
0.04019201546907425,
-0.06351518630981445,
0.23505204916000366,
0.20466288924217224,
0.11266853660345078,
-0.0071211885660886765,
1.3127726316452026,
-0.20015926659107208,
-0.06453650444746017,
0.5471353530883789,
0.6989102959632874,
-0.5574225187301636,
0.3386855721473694,
0.5804798603057861,
-0.3918784260749817,
0.029816865921020508,
0.7339516282081604,
-0.23406881093978882,
0.08324560523033142,
-0.05448736622929573,
-0.22546802461147308,
-0.0974920392036438,
0.1390571892261505,
-0.2998049259185791,
0.642098069190979,
0.6185609698295593,
-0.839252233505249,
-0.5153487920761108,
-0.5470641851425171,
-0.6789499521255493,
0.19060039520263672,
-0.5127439498901367,
-0.06886248290538788,
-0.6267531514167786,
-0.25405287742614746,
-0.2964462339878082,
-0.0008635406848043203,
-0.07976865023374557,
0.4093085527420044,
0.3514098823070526,
0.2509694993495941,
-0.17648938298225403,
-0.35769644379615784,
-0.3791521191596985,
0.09254136681556702,
-1.2138413190841675,
-0.6658655405044556,
-0.30548956990242004,
1.022803783416748,
-0.35444051027297974,
-0.6933623552322388,
-0.15498679876327515,
0.0903015285730362,
-0.35237830877304077,
0.14832048118114471,
0.26157820224761963,
-0.20088998973369598,
-0.0435350127518177,
-0.02788958139717579,
-0.41121912002563477,
0.024609040468931198,
-0.15503062307834625,
0.5250912308692932,
-0.3393707275390625,
-0.3844517171382904,
0.45605987310409546,
-0.2682337462902069,
0.11489064246416092,
-0.144163578748703,
0.04331202432513237,
0.6314056515693665,
0.19826486706733704,
-0.2120477259159088,
0.7684195041656494,
-0.027969155460596085,
0.7291008234024048,
0.3557020127773285,
-0.2710738778114319,
0.056890640407800674,
0.7634511590003967,
0.2313498556613922,
0.44106337428092957,
0.12031790614128113,
0.0811481848359108,
0.2953886389732361,
-0.05611332878470421,
0.20635056495666504,
0.19245384633541107,
0.48369717597961426,
0.20160779356956482,
0.8455971479415894,
0.19439542293548584,
0.006662845611572266,
0.08450821787118912,
0.4960825443267822,
0.5215230584144592,
-0.2657293975353241,
-0.17052863538265228,
-0.15055915713310242,
-0.18347124755382538,
0.5680524706840515,
-1.114012598991394,
-0.4266294240951538,
-0.43127983808517456,
-0.22029873728752136,
0.37078434228897095,
0.22416003048419952,
0.06882011145353317,
0.8607537150382996,
0.29987502098083496,
0.4373294711112976,
0.003401604713872075,
0.5365307927131653,
-0.15806585550308228,
0.9413357973098755,
0.2382628321647644,
0.11391115188598633,
0.6351796984672546,
-0.00115714140702039,
0.2754509747028351,
-1.0144269466400146,
0.6830143332481384,
0.49523642659187317,
-1.2767930030822754,
0.1048361137509346,
-0.18880243599414825,
0.0249908696860075,
-0.7378884553909302,
-0.6449651718139648,
0.40399181842803955,
-0.12997981905937195,
0.12776312232017517,
0.7807478308677673,
-0.6146813035011292,
0.6818325519561768,
0.5542778968811035,
0.06764057278633118,
0.34627142548561096,
0.6769366264343262,
0.5616801381111145,
-0.5679348111152649,
0.6119104027748108,
1.0653700828552246,
-0.153428852558136,
0.2399722933769226,
0.11367657035589218,
-0.8488479852676392,
0.6740725636482239,
1.1214537620544434,
-0.16191144287586212,
0.4502135217189789,
-0.27499720454216003,
-0.4759122133255005,
-0.05424689128994942,
-0.3647850453853607,
-0.3550025224685669,
-0.48642241954803467,
0.06628797203302383,
0.14199784398078918,
0.14861570298671722,
-0.3922249376773834,
1.0179089307785034,
0.365145206451416,
-0.5863568186759949,
-0.5118382573127747,
-0.048266876488924026,
-0.4516027271747589,
-0.0616193488240242,
-0.5687066912651062,
0.5210890769958496,
-0.39383235573768616,
0.02259214222431183,
-0.1715182363986969,
-0.4874766170978546,
-0.776695191860199,
-1.2489678859710693,
0.131296306848526,
-0.35374385118484497,
0.024055026471614838,
0.2613963186740875,
0.32125476002693176,
0.6451259851455688,
-0.5551392436027527,
0.5798571705818176,
0.09055106341838837,
1.5301438570022583,
-0.001976231811568141,
-0.18209382891654968,
0.800706148147583,
0.29685863852500916,
-0.9827861785888672,
0.4014414846897125,
0.9309743642807007,
-0.07419943809509277,
0.5153012275695801,
-0.4922080338001251,
0.12483029812574387,
0.5907195210456848,
0.03889175131917,
0.34263187646865845,
-0.019670652225613594,
-0.020632749423384666,
-0.13204723596572876,
0.09965649992227554,
-0.4904705882072449,
-0.7115745544433594,
0.23144355416297913,
-0.43569663166999817,
0.2230137288570404,
0.2889193594455719,
0.41718441247940063,
0.7784515023231506,
-0.7326593399047852,
4.1970295906066895,
1.1429492235183716,
0.4083992838859558,
0.26990747451782227,
0.5522813200950623,
1.2630126476287842,
-0.2164291888475418,
0.0825735405087471,
0.1614963263273239,
-0.723160445690155,
-0.06819701194763184,
0.4430304765701294,
-0.09995395690202713,
0.30123797059059143,
-0.7386590838432312,
0.3871285617351532,
-0.19579489529132843,
0.36946046352386475,
0.30933770537376404,
-0.821549654006958,
-0.4235321879386902,
0.4012177586555481,
0.24748556315898895,
-0.01580764353275299,
0.2960793375968933,
0.31638458371162415,
0.355352520942688,
-0.27555331587791443,
-0.5493000745773315,
-0.6317330002784729,
-1.1580331325531006,
-1.264760136604309,
-0.30182912945747375,
0.2942708134651184,
-0.8264544606208801,
0.5847299695014954,
-0.18961136043071747,
-0.4675610661506653,
0.37352481484413147,
0.15578773617744446,
-0.3123607039451599,
-0.2020297795534134,
0.19144205749034882,
-0.2160170078277588,
-0.3788160979747772,
0.39943042397499084,
0.11767745018005371,
0.8171394467353821,
0.46130192279815674,
-0.28546273708343506,
0.7384231686592102,
-0.05608915165066719,
0.5554559230804443,
-0.23698417842388153,
-0.8402593731880188,
0.3873152434825897,
-0.6360862255096436,
-0.19757485389709473,
-0.19074885547161102,
-0.38403797149658203,
0.3944002687931061,
-0.17869515717029572,
-0.7753639817237854,
0.3451378047466278,
-0.5073559880256653,
0.8660091757774353,
0.10690129548311234,
0.5218815803527832,
-0.7916112542152405,
0.006173512898385525,
-0.058453671634197235,
-0.028847206383943558,
-0.09498640894889832,
-0.1793500781059265,
0.08285345882177353,
-0.22564467787742615,
-0.6534540057182312,
0.2959398925304413,
-0.3848678767681122,
0.2863979935646057,
0.334179162979126,
-0.11345119774341583,
-0.14185553789138794,
0.13469155132770538,
0.19965068995952606,
0.8847341537475586,
-0.41681215167045593,
-0.19261278212070465,
-0.04078918322920799,
0.8150192499160767,
0.18340474367141724,
1.1653525829315186,
0.4183475077152252,
0.7932848334312439,
-1.0255985260009766
] |
The Finite Temperature Phase Diagram of a U(1) Higgs-Yukawa Model
|
The finite temperature phase diagram of a U(1) Higgs-Yukawa model at a finite value of the scalar self coupling $\lambda$ is investigated by means of a large-$N_f$ calculation and numerical simulations. The phase diagram is similar to the one at zero temperature and shows a ferromagnetic, two symmetric and an antiferromagnetic phase. However, the phase transition lines are shifted to larger values of the Yukawa coupling demonstrating the occurence of the finite temperature symmetry restoration.
|
Karl Jansen
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209004
|
hep-lat/9209005
|
[
0.8753969073295593,
-0.4451080858707428,
-0.2904447615146637,
-0.07399453967809677,
0.6128167510032654,
-0.36989879608154297,
-0.20674008131027222,
-0.8579679727554321,
-0.6749534010887146,
1.1297599077224731,
0.9029374718666077,
-0.15094740688800812,
0.7754810452461243,
-1.120639443397522,
-0.18755599856376648,
0.5421443581581116,
-0.35528355836868286,
-1.2497584819793701,
-0.8699188828468323,
0.4819483458995819,
-0.08769510686397552,
-0.33399903774261475,
-1.5297932624816895,
-0.6111537218093872,
0.1380118429660797,
0.8083526492118835,
0.23202431201934814,
0.03086843155324459,
1.569562554359436,
0.636913001537323,
0.314098596572876,
-0.34704041481018066,
-0.4962370991706848,
-0.4045106768608093,
-0.47333550453186035,
-0.6542559862136841,
0.05393659323453903,
0.0017144029261544347,
0.28327322006225586,
-0.2559988498687744,
0.2250639647245407,
-0.43084412813186646,
0.11690716445446014,
-0.5256159901618958,
-1.2169309854507446,
0.14670388400554657,
-0.20802222192287445,
-0.06796509027481079,
0.35337182879447937,
-1.1092209815979004,
0.21713852882385254,
-0.21194782853126526,
0.01404271274805069,
-0.6478107571601868,
-0.35877957940101624,
-0.22711685299873352,
0.1598319709300995,
0.33057883381843567,
-0.688447117805481,
-0.7845542430877686,
1.4664292335510254,
0.4930669069290161,
0.49679994583129883,
-0.7137881517410278,
0.7268970608711243,
0.9290629625320435,
-0.7006940841674805,
0.44248414039611816,
0.06560523062944412,
-0.3874812722206116,
-0.08048657327890396,
-0.6182888150215149,
-0.7604743838310242,
0.24452325701713562,
-0.5965132117271423,
0.4546257257461548,
0.4203931391239166,
-0.5148028135299683,
-1.5097334384918213,
-0.6805915236473083,
0.0373787060379982,
-0.444460391998291,
-0.704598605632782,
0.6894780397415161,
-0.5147692561149597,
-0.43518179655075073,
0.5104214549064636,
-0.08166014403104782,
0.17919503152370453,
0.42719876766204834,
0.2803019881248474,
0.4818864166736603,
0.3110347092151642,
-0.43052053451538086,
0.3519594073295593,
0.6117008924484253,
0.26906299591064453,
1.016614317893982,
0.27811142802238464,
0.5585283637046814,
-0.290068656206131,
1.4233871698379517,
-1.295589566230774,
0.36120718717575073,
-0.5878854990005493,
0.229910746216774,
-0.12378109991550446,
-0.42221418023109436,
0.22800882160663605,
-0.8842982053756714,
-0.20118574798107147,
-0.8012747168540955,
0.11893156915903091,
0.8670746088027954,
-0.22770807147026062,
1.3670037984848022,
0.12717553973197937,
0.3202088177204132,
-0.6395151615142822,
-0.05714377388358116,
0.12535086274147034,
0.06470698863267899,
0.5545173287391663,
0.2831554412841797,
0.014454437419772148,
-0.3305152654647827,
0.027785692363977432,
0.7470036745071411,
-1.3493789434432983,
0.07952014356851578,
-0.30697736144065857,
-0.3398538827896118,
-0.6324021816253662,
0.9588766098022461,
-0.03393569588661194,
0.049307774752378464,
-0.08679643273353577,
0.8262516856193542,
-0.19053910672664642,
-0.4169425666332245,
0.7373453974723816,
-0.6344200968742371,
0.11438027769327164,
1.4356915950775146,
0.01493873167783022,
0.245564803481102,
0.2594188153743744,
-0.5843389630317688,
-0.0604911744594574,
1.0188729763031006,
-0.9416068196296692,
-0.17586658895015717,
-0.5205490589141846,
0.8643521666526794,
0.27211880683898926,
0.18047519028186798,
-0.7321635484695435,
0.6276193261146545,
-0.549736738204956,
-0.5848397016525269,
0.20418278872966766,
-0.1398186981678009,
-0.689831554889679,
0.5594425201416016,
-0.3462563455104828,
0.07270805537700653,
-0.567912757396698,
0.18046104907989502,
0.28522300720214844,
-0.7223792672157288,
-0.38462328910827637,
-0.12414444237947464,
0.10366159677505493,
0.987921953201294,
0.109085313975811,
0.6795798540115356,
0.24965141713619232,
-0.8061917424201965,
0.16226306557655334,
0.32884320616722107,
-0.6236053705215454,
-0.09424439072608948,
0.3063948452472687,
-0.33116260170936584,
-0.014645065180957317,
-0.36557430028915405,
-0.2724531888961792,
-0.32986387610435486,
0.2578294575214386,
0.6282593607902527,
-0.15422369539737701,
0.8491258025169373,
-0.37467160820961,
1.1100544929504395,
0.027950579300522804,
-0.3803150951862335,
-0.23804299533367157,
-0.1340555101633072,
-0.8290343880653381,
-0.6855767965316772,
-0.0628654807806015,
0.5954368114471436,
-0.16787581145763397,
0.3118985891342163,
-1.4415396451950073,
0.3172130584716797,
0.8652006983757019,
0.10203398019075394,
-0.5678555369377136,
-0.07198379188776016,
0.4769497215747833,
-0.2155141681432724,
0.49959078431129456,
-0.9088144302368164,
0.1755424290895462,
0.018378328531980515,
-0.154349684715271,
0.25279197096824646,
0.6707638502120972,
-0.21269983053207397,
0.83207768201828,
0.4471657872200012,
-0.035654712468385696,
0.7043853402137756,
-0.4459574222564697,
-0.6347944736480713,
-0.15949398279190063,
0.5708758234977722,
0.3062168061733246,
0.1372438669204712,
-0.3071058988571167,
0.46803930401802063,
-0.2513401508331299,
0.2777714729309082,
0.7545158267021179,
0.44209545850753784,
0.7162514925003052,
0.572927713394165,
0.19112350046634674,
0.4885317087173462,
0.06020217761397362,
0.23359128832817078,
0.43150976300239563,
0.6401380896568298,
0.25395670533180237,
0.5616130828857422,
-0.3241560757160187,
-0.31279250979423523,
-0.30459949374198914,
0.1097651869058609,
-0.5322639346122742,
1.064832091331482,
-0.23549884557724,
0.1371125727891922,
-0.883274257183075,
0.3325621783733368,
0.034153033047914505,
0.6373025178909302,
-0.38383692502975464,
-0.5116013288497925,
0.0715557411313057,
0.245303675532341,
-0.08670869469642639,
-0.21127434074878693,
-0.4049467444419861,
1.4260601997375488,
-0.24121341109275818,
0.5096560120582581,
1.2895450592041016,
-0.607538104057312,
-1.1476231813430786,
-0.3729611039161682,
-0.6423613429069519,
-0.1380402147769928,
0.035682328045368195,
-0.31867697834968567,
0.6012179851531982,
-0.5224115252494812,
0.36371496319770813,
0.09897230565547943,
-0.22794072329998016,
0.7435815930366516,
0.05957687273621559,
0.7213659882545471,
0.5836246609687805,
0.01347894873470068,
-0.4177047908306122,
0.1992415487766266,
-0.6696949005126953,
-0.3550639748573303,
-0.17663729190826416,
0.20018461346626282,
0.6331188082695007,
-0.1723511964082718,
0.5777543783187866,
-0.10752991586923599,
-0.6070863604545593,
0.040841780602931976,
-0.18051373958587646,
-0.634181022644043,
0.35739296674728394,
0.6605265736579895,
-0.10684344917535782,
-0.35837113857269287,
-0.7292550802230835,
0.33259519934654236,
0.3507364094257355,
-0.2241283506155014,
0.5429126024246216,
0.2595464885234833,
-0.9222185015678406,
0.2088179886341095,
-0.1587752252817154,
0.08203817903995514,
0.05755191296339035,
0.8291457891464233,
1.008926272392273,
-0.2824254631996155,
0.26081016659736633,
-0.41047102212905884,
-0.07167533785104752,
-0.0024585514329373837,
-0.0709199532866478,
-0.3805760443210602,
-0.3772895634174347,
1.3713974952697754,
-0.37259578704833984,
-0.8028417825698853,
0.6451559066772461,
-0.7403903007507324,
-1.0056911706924438,
0.13763603568077087,
-0.5472826957702637,
0.34030967950820923,
0.08165017515420914,
-0.09689798951148987,
-0.8225495219230652,
0.339095801115036,
0.33004316687583923,
0.3318941593170166,
0.40182673931121826,
-0.6171793341636658,
0.9747677445411682,
0.3077647387981415,
0.3585442006587982,
-0.3366352915763855,
0.43441349267959595,
-0.40877285599708557,
-0.054871246218681335,
0.8286267518997192,
-0.3015422224998474,
0.41477277874946594,
-0.0734771341085434,
0.5919495820999146,
-0.5003248453140259,
-0.12549972534179688,
-0.6374821066856384,
-0.16893523931503296,
-0.21140624582767487,
-0.12516511976718903,
1.0324296951293945,
0.8724586963653564,
0.016038604080677032,
0.5157751441001892,
-0.456451416015625,
-0.036229267716407776,
0.5109148025512695,
-0.3537329435348511,
1.3126527070999146,
-1.2436586618423462,
1.0454610586166382,
0.026207130402326584,
-0.8871291279792786,
0.09502167254686356,
0.03849067911505699,
0.4058437645435333,
0.20206983387470245,
0.20506462454795837,
1.2072349786758423,
-0.2837187647819519,
-0.8359128832817078,
-0.2818506956100464,
1.1936067342758179,
0.6129140853881836,
0.7936739325523376,
0.16072651743888855,
0.012888391502201557,
-0.36463862657546997,
-0.24320363998413086,
0.07688097655773163,
-0.3525753915309906,
-0.07165266573429108,
-0.46332013607025146,
-0.46538493037223816,
0.2681178152561188,
-0.353698194026947,
1.0050280094146729,
0.3948826789855957,
0.5467542409896851,
0.09517759084701538,
0.8391245603561401,
-0.18178072571754456,
0.9717803597450256,
0.9275487065315247,
0.842748761177063,
0.17984633147716522,
-1.1902804374694824,
0.28982439637184143,
0.4593445360660553,
-0.047960780560970306,
-0.03310028836131096,
-0.21642324328422546,
0.08913557231426239,
-0.5785757303237915,
0.255636602640152,
0.14561618864536285,
-0.9324464201927185,
0.36773911118507385,
-0.46071940660476685,
0.7492828965187073,
-0.5359160304069519,
0.06653295457363129,
1.1089420318603516,
0.7009180188179016,
-0.290537565946579,
-1.3140971660614014,
-0.22413787245750427,
-0.737924337387085,
0.24340827763080597,
0.36683759093284607,
-0.3948981761932373,
-0.5506315231323242,
-1.0924315452575684,
-0.8469621539115906,
-0.7099767923355103,
0.25182265043258667,
1.1680951118469238,
-0.25837865471839905,
-0.24069525301456451,
-0.945357084274292,
-0.5605432391166687,
0.5062394738197327,
-0.12918144464492798,
-0.28361406922340393,
0.33510664105415344,
0.07733189314603806,
-0.5172428488731384,
0.6321346759796143,
0.12980429828166962,
-0.17682772874832153,
0.17870628833770752,
-0.050074271857738495,
0.19504374265670776,
-0.4207586348056793,
-0.5655866265296936,
-0.5310032367706299,
-0.45196259021759033,
-0.5642048716545105,
0.6427040696144104,
-0.13277630507946014,
0.04591812938451767,
-0.22646716237068176,
0.6256584525108337,
-0.7139999866485596,
0.013900628313422203,
0.06713391840457916,
-0.045441608875989914,
-0.10690126568078995,
0.7026233077049255,
0.7024694681167603,
0.4870961010456085,
0.24734583497047424,
0.007422941271215677,
0.656371533870697,
0.5348621606826782,
0.2200053632259369,
0.21341319382190704,
-0.3838735818862915,
-0.08651406317949295,
-0.9002882242202759,
-1.0699152946472168,
-0.3595982491970062,
-0.13875839114189148,
0.8560923337936401,
-0.04614899307489395,
-0.5199589729309082,
-0.22076435387134552,
-0.22314758598804474,
-0.28988274931907654,
0.364158570766449,
-0.3337574005126953,
-0.6028148531913757,
0.5313949584960938,
-0.5235870480537415,
0.009115288034081459,
0.3918832540512085,
0.04443088918924332,
-0.3702554702758789,
0.5661007165908813,
0.8780606389045715,
-0.27158597111701965,
0.539404034614563,
-1.0336600542068481,
0.19904330372810364,
-0.7013643383979797,
-0.26289865374565125,
-0.1640338897705078,
-0.6931559443473816,
-0.3496014177799225,
0.1541479378938675,
-0.09827211499214172,
-0.8091578483581543,
0.07842355966567993,
0.12349332123994827,
0.5576489567756653,
-0.34709325432777405,
-0.37889933586120605,
-0.21144776046276093,
-0.9364787340164185,
0.9515429735183716,
-0.07492775470018387,
-1.0613006353378296,
-0.18997548520565033,
0.649065375328064,
-0.6156476140022278,
0.07310428470373154,
0.0782291442155838,
-0.7838323712348938,
0.4832899570465088,
-0.32606151700019836,
0.2523123323917389,
-1.0174270868301392,
-0.41764530539512634,
-0.32232218980789185,
-1.4217479228973389,
0.08768027275800705,
0.5411657691001892,
0.6792251467704773,
-0.18961013853549957,
-0.5936862826347351,
-0.51606285572052,
0.5630531311035156,
-0.29486340284347534,
-0.44391167163848877,
-0.4350145757198334,
-0.03226368874311447,
-0.032969921827316284,
0.7630287408828735,
0.04790068045258522,
0.2621246576309204,
-0.04357099160552025,
0.11215493083000183,
0.322212815284729,
0.7003583312034607,
-0.2830163538455963,
-0.3040311336517334,
-0.03823968395590782,
0.14696209132671356,
0.21755407750606537,
0.5373141765594482,
-0.5950726270675659,
0.4785657525062561,
-1.0915565490722656,
1.190409541130066,
-0.9399796724319458,
-0.1439586579799652,
-0.04259198531508446,
0.04683583229780197,
0.5011535882949829,
-0.91903156042099,
0.7464356422424316,
0.5973851084709167,
0.3088102638721466,
0.6934544444084167,
0.39391908049583435,
-0.24030104279518127,
-0.1728915572166443,
-0.3528166115283966,
-0.8699394464492798,
1.0972858667373657,
-0.41806843876838684,
-0.34218883514404297,
-1.0558762550354004,
-0.2048804610967636,
0.9091594815254211,
-0.05944707244634628,
0.47987067699432373,
0.7297341823577881,
0.11266925185918808,
0.03647192567586899,
0.3544349670410156,
-0.6768507957458496,
0.0143472570925951,
-0.12526389956474304,
0.7813414931297302,
-0.5924177169799805,
-0.11450466513633728,
-0.12708741426467896,
-0.8592612743377686,
-0.7010076642036438,
-0.4790525436401367,
0.5086884498596191,
-0.0421115942299366,
-0.5524085164070129,
0.5141741037368774,
-0.3447326123714447,
-0.45454058051109314,
-0.46857312321662903,
-0.33790165185928345,
-0.2791815996170044,
0.4539068639278412,
0.7292892932891846,
0.6490339636802673,
0.6670017242431641,
-0.12468037009239197,
0.47767969965934753,
-0.25579315423965454,
0.0018608634127303958,
0.8042718768119812,
-0.22760647535324097,
-0.5038936138153076,
0.06299171596765518,
0.12994606792926788,
-1.106696605682373,
-0.45135927200317383,
-0.32834717631340027,
0.41905704140663147,
-0.1644584834575653,
-0.76666259765625,
-0.3710767328739166,
-0.28554660081863403,
-0.06476999819278717,
0.6842623949050903,
1.1346603631973267,
-0.9628158807754517,
0.07299242168664932,
0.4783031642436981,
-0.13982972502708435,
-0.5139101147651672,
-0.08470714092254639,
1.1771352291107178,
-0.17122064530849457,
-0.36240261793136597,
-0.09064196795225143,
-0.54759681224823,
-0.1788037121295929,
-0.13596174120903015,
-0.005018197000026703,
-0.46980318427085876,
0.2856615483760834,
0.6475120782852173,
0.3711990714073181,
0.6462038159370422,
0.7051910161972046,
0.811730146408081,
-0.2861614525318146,
-0.5226851105690002,
-1.0066747665405273,
-1.0366684198379517,
-0.17343632876873016,
-0.004224554169923067,
1.2989213466644287,
0.1624976247549057,
0.13627834618091583,
0.11690046638250351,
-0.9490150809288025,
0.2921169102191925,
-1.3047659397125244,
-0.05500658601522446,
-1.199941635131836,
-0.5807816982269287,
-0.673122227191925,
-0.38386547565460205,
0.1065315380692482,
0.6533294320106506,
0.2414289116859436,
0.10942750424146652,
-0.4333268105983734,
-0.403978168964386,
-0.0516815222799778,
-0.5956167578697205,
0.21283477544784546,
-0.3525315821170807,
-0.896891176700592,
-0.5087281465530396,
-0.10199697315692902,
-0.2252013385295868,
-0.12834082543849945,
-0.1290794461965561,
0.49664753675460815,
0.9956182837486267,
-0.625278651714325,
0.6094768047332764,
-1.0757839679718018,
-0.9933486580848694,
0.011295177973806858,
-0.16851161420345306,
-0.6365990042686462,
0.21019795536994934,
-0.31736287474632263,
0.5139623880386353,
0.3218107223510742,
-0.1478881686925888,
-0.43812087178230286,
0.08524398505687714,
-1.1242319345474243,
-0.028987552970647812,
0.3346274197101593,
0.500236451625824,
-0.45613929629325867,
-1.3176796436309814,
0.40215590596199036,
0.26903849840164185,
-1.1312311887741089,
0.6646348237991333,
0.06596433371305466,
0.027197975665330887,
-0.6974180936813354,
0.4539547562599182,
0.23532052338123322,
0.5738810300827026,
-0.04403330385684967,
1.0488516092300415,
-0.15184222161769867,
0.04344043880701065,
-0.5490227937698364,
0.06509269773960114,
-0.19789822399616241,
0.5533400177955627,
-0.2751976251602173,
-0.9130128026008606,
-0.0795629695057869,
0.18866309523582458,
-0.28936412930488586,
-0.13242457807064056,
-0.06307990849018097,
-0.253404438495636,
-0.6158927083015442,
-0.4771770238876343,
-0.48593810200691223,
0.5674126148223877,
0.2168661206960678,
-0.6409879326820374,
-0.3569585382938385,
-0.5927419662475586,
-0.20294006168842316,
0.24158383905887604,
-1.0581289529800415,
-0.2918928861618042,
-0.16491812467575073,
-0.520560085773468,
0.18760442733764648,
0.28211116790771484,
-0.08163294941186905,
0.5042058825492859,
-0.2172635793685913,
-0.027757974341511726,
-0.8576722145080566,
0.27788153290748596,
-0.25480639934539795,
0.34633520245552063,
-1.2278412580490112,
-0.6593196392059326,
-0.19916905462741852,
0.24356956779956818,
-0.5386199355125427,
-0.8393746018409729,
-0.11986950784921646,
0.6284494400024414,
0.2480160892009735,
-0.20933078229427338,
-0.3220805823802948,
-0.1311526894569397,
0.14160291850566864,
0.0578145794570446,
-0.4187367558479309,
0.10119030624628067,
-0.030130630359053612,
0.5163258910179138,
0.3167749345302582,
-0.6226237416267395,
0.10905133187770844,
0.43484193086624146,
0.22736001014709473,
0.14061841368675232,
-0.3803545832633972,
0.9322595596313477,
-0.3415835499763489,
-1.022639274597168,
1.2143619060516357,
-0.1129872053861618,
1.0053737163543701,
0.09386236220598221,
-0.018146371468901634,
0.4521280825138092,
0.09107358008623123,
0.39855003356933594,
0.5598465800285339,
0.3434874415397644,
-0.05054634064435959,
0.6076495051383972,
0.5651074051856995,
-0.02247587777674198,
0.09275585412979126,
0.6914517283439636,
0.09893810003995895,
-0.034988097846508026,
0.08420487493276596,
-0.12900984287261963,
-0.5879801511764526,
-0.2522459328174591,
0.04197031259536743,
-0.33916088938713074,
-0.09425082802772522,
-0.7201485633850098,
-0.044571418315172195,
0.6190824508666992,
-0.8103827834129333,
-0.16668403148651123,
-0.40474361181259155,
0.4693855047225952,
0.23262402415275574,
0.1752685308456421,
-0.14990264177322388,
0.16140945255756378,
0.8789178729057312,
0.31601789593696594,
-0.15351422131061554,
0.6084619164466858,
0.5222753286361694,
0.41554000973701477,
0.9734496474266052,
1.1748595237731934,
0.8516672253608704,
0.5447306632995605,
0.29088783264160156,
-0.7651905417442322,
-0.2125244438648224,
0.5261886715888977,
-1.7729066610336304,
-0.13909359276294708,
-0.49426841735839844,
-0.1416185051202774,
-0.40038034319877625,
-0.8984552621841431,
0.2580890953540802,
-0.6383492350578308,
-0.049448370933532715,
1.3332027196884155,
0.12755608558654785,
-0.15574908256530762,
0.6134453415870667,
0.10424147546291351,
1.0351378917694092,
0.8112468719482422,
-0.3354944884777069,
-0.12010911852121353,
1.3446555137634277,
1.2003490924835205,
0.07622338831424713,
0.29435160756111145,
0.2661587595939636,
-0.2944968640804291,
0.3837015628814697,
0.7390099763870239,
0.046961553394794464,
0.9370361566543579,
-0.32716450095176697,
-0.7814055681228638,
-0.1215817928314209,
0.4056883156299591,
-0.5693070292472839,
0.10769988596439362,
-0.1713012009859085,
0.6269971132278442,
-0.540944516658783,
-0.8671303987503052,
1.5103259086608887,
0.33555951714515686,
-0.4710020124912262,
-0.18820515275001526,
-0.024555454030632973,
-0.5225439071655273,
-0.37601202726364136,
-1.2212541103363037,
0.6216201186180115,
-0.04335141181945801,
0.16796651482582092,
-0.4198475182056427,
-0.8929935693740845,
-0.5559858679771423,
-0.8848521113395691,
-0.060731515288352966,
-0.4119497239589691,
0.8703567385673523,
0.5927335023880005,
0.32588040828704834,
0.34803542494773865,
-0.6504619121551514,
0.25595393776893616,
0.18009716272354126,
0.7109491229057312,
-0.22768253087997437,
0.2788584530353546,
1.025202989578247,
1.2029579877853394,
-0.6744116544723511,
0.840571403503418,
0.5302072167396545,
-0.6809977293014526,
0.5400857329368591,
-0.13158085942268372,
0.16138263046741486,
-0.12534750998020172,
-0.1896057426929474,
0.06463640183210373,
0.3519194424152374,
0.4750778079032898,
-0.3865610361099243,
-0.25172531604766846,
-0.08832408487796783,
-0.7922906875610352,
0.3443073332309723,
-1.0746207237243652,
0.26217490434646606,
0.22206437587738037,
0.6882132887840271,
-0.0643332228064537,
-0.09935977309942245,
3.77154278755188,
0.7264443039894104,
1.3022722005844116,
-0.173340305685997,
1.2356170415878296,
0.8261302709579468,
-0.19987913966178894,
-0.6288397908210754,
0.39827069640159607,
-0.5604641437530518,
0.08943259716033936,
0.366936057806015,
0.4270021617412567,
0.1690315306186676,
-0.3204476237297058,
0.5640794634819031,
-0.2804279327392578,
-0.045822396874427795,
-0.0012435902608558536,
-0.6513917446136475,
-0.608205258846283,
0.32110393047332764,
0.05879228934645653,
-0.2361784279346466,
0.23647263646125793,
0.10692580789327621,
0.2866479456424713,
-1.1484748125076294,
-0.3453417718410492,
-0.354293555021286,
-0.37862658500671387,
-0.9511532187461853,
-0.16059067845344543,
0.05999963730573654,
-0.9820187091827393,
0.9601732492446899,
0.2942999005317688,
-0.4706980288028717,
0.21011972427368164,
0.4913769066333771,
-0.12298689037561417,
-0.6076865792274475,
-0.5122928023338318,
-0.19308796525001526,
-0.6710684299468994,
1.2043362855911255,
-0.547717273235321,
0.5977274775505066,
0.27667132019996643,
-0.7177289724349976,
0.6329218149185181,
-0.14494889974594116,
0.9384152889251709,
0.05027632787823677,
-1.2207413911819458,
-0.08252404630184174,
-0.33085986971855164,
-0.7617329359054565,
-0.041461821645498276,
0.2745083272457123,
0.6640350818634033,
-0.46799585223197937,
-0.059773702174425125,
0.45507678389549255,
-0.14392825961112976,
0.2616631090641022,
0.2791033387184143,
-0.36551907658576965,
-0.5919036865234375,
-0.027912046760320663,
-0.28039073944091797,
-0.2534530460834503,
-0.33695435523986816,
0.6998476386070251,
-0.6923078298568726,
-0.18710610270500183,
0.34449803829193115,
0.5264109373092651,
-0.2954002916812897,
0.230043426156044,
-0.05636589974164963,
-0.3354142904281616,
-0.24757561087608337,
-0.02995206043124199,
-0.029851198196411133,
0.8525840640068054,
-0.34760329127311707,
0.1260491907596588,
-0.20295943319797516,
0.6112778782844543,
0.41064760088920593,
1.3084383010864258,
0.255469411611557,
-0.20618031919002533,
-0.2533760070800781
] |
High Precision Simulation Techniques for Lattice Field Theory
|
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these tools one is able to probe much closer than before the universal continuum behavior of field theories on the lattice.
|
Ulli Wolff (CERN)
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209005
|
hep-lat/9209006
|
[
-0.0967302992939949,
0.3955431282520294,
0.6567461490631104,
0.3803861439228058,
0.18464615941047668,
0.07518050819635391,
-0.04709608480334282,
-0.39781010150909424,
-0.8424191474914551,
1.203950047492981,
0.5328414440155029,
-0.31397390365600586,
0.31442880630493164,
-0.793311357498169,
0.020560860633850098,
0.6257637739181519,
-0.31180912256240845,
-0.5503718256950378,
-0.9838423728942871,
-0.1916915476322174,
-0.00828094594180584,
-0.5334941148757935,
-0.9568359851837158,
-0.7923204302787781,
-0.20245017111301422,
0.662605881690979,
-0.17179587483406067,
0.22491544485092163,
1.5683374404907227,
0.35493502020835876,
0.04241325333714485,
-0.37631386518478394,
-0.18885937333106995,
-0.7044245600700378,
0.09884922951459885,
-0.3869878649711609,
0.4689394235610962,
-0.041231270879507065,
0.7509549260139465,
-0.41699525713920593,
0.8348085284233093,
-0.05480977147817612,
0.4436223804950714,
-0.19890250265598297,
-0.5786066651344299,
-0.03127911686897278,
-0.33150091767311096,
-0.12449187785387039,
-0.41484886407852173,
-1.0169316530227661,
0.02463751845061779,
-0.24767529964447021,
0.896233081817627,
-0.9333574175834656,
-0.26662781834602356,
0.15689827501773834,
0.02552013285458088,
-0.015380511060357094,
-0.7682771682739258,
-0.43325138092041016,
0.6476885080337524,
-0.20248311758041382,
0.680498480796814,
-0.6732694506645203,
0.2899858355522156,
0.5757174491882324,
-0.08104901760816574,
0.5573796629905701,
0.18364998698234558,
-0.449667751789093,
-0.8466123938560486,
-0.5141334533691406,
-0.011717903427779675,
-0.2963218688964844,
-0.8160340785980225,
0.325632244348526,
0.21015523374080658,
-0.003729918971657753,
-0.6398243308067322,
-0.47643178701400757,
-0.12910953164100647,
-0.37236496806144714,
-0.6333758234977722,
0.5432699918746948,
-0.25021347403526306,
-0.016939427703619003,
-0.16834653913974762,
-0.3313404619693756,
-0.1334831863641739,
0.0638931542634964,
-0.08622469007968903,
1.065205693244934,
-0.1306481808423996,
-0.050238415598869324,
0.11774792522192001,
0.4916069507598877,
0.13066767156124115,
0.49025335907936096,
-0.09979424625635147,
0.46523812413215637,
0.006056223530322313,
1.062639594078064,
-0.9712182879447937,
0.4412073791027069,
-0.3436734974384308,
0.21233052015304565,
-0.3228602409362793,
0.0863710343837738,
-0.6064533591270447,
-0.09432203322649002,
-0.28912869095802307,
-0.18066759407520294,
0.5708194375038147,
1.01804518699646,
-0.07278365641832352,
0.23525050282478333,
0.05029303580522537,
-0.20545583963394165,
-0.7771437168121338,
-0.2911912500858307,
-0.23020516335964203,
0.43910765647888184,
0.26954859495162964,
0.3409021496772766,
-0.51956707239151,
-0.7218942642211914,
0.13266734778881073,
0.8151473999023438,
-0.4833102524280548,
-0.167379230260849,
-0.26215529441833496,
0.12182614207267761,
-0.29194414615631104,
0.6101873517036438,
0.17359106242656708,
0.44123342633247375,
0.013272523880004883,
0.16002081334590912,
0.6075887084007263,
0.07501829415559769,
0.24779972434043884,
-0.4592262804508209,
0.7741943597793579,
0.8291863203048706,
0.18026670813560486,
-0.1612124890089035,
0.8556268215179443,
-0.39756086468696594,
0.3137793242931366,
0.22109191119670868,
-1.1531155109405518,
0.31665492057800293,
0.21086013317108154,
-0.12197402864694595,
0.14747223258018494,
0.10222128033638,
-1.019632339477539,
1.2437560558319092,
-0.7599757313728333,
-0.913639485836029,
0.14057953655719757,
-0.6053244471549988,
-0.6966280937194824,
-0.24504593014717102,
-0.7187119126319885,
-0.0991382896900177,
-0.06473678350448608,
-0.42908990383148193,
0.2716822028160095,
-0.3750816285610199,
-0.053194619715213776,
0.24709554016590118,
0.03899817913770676,
0.6223745942115784,
-0.03362341597676277,
0.3140740394592285,
0.49437662959098816,
0.2633224129676819,
0.15112994611263275,
0.377429336309433,
-0.25482213497161865,
-0.626356840133667,
1.071429967880249,
0.11831015348434448,
-0.4225853383541107,
0.5529789328575134,
-0.3443599045276642,
-0.16768255829811096,
-0.11366733908653259,
0.3640717566013336,
-0.007980852387845516,
0.2969154417514801,
-0.33749228715896606,
0.2673100233078003,
-0.6211237907409668,
-0.13736318051815033,
-0.6103329062461853,
0.7201526165008545,
-0.5481860637664795,
-0.4938025176525116,
-0.6213412880897522,
0.5116140246391296,
-1.0469943284988403,
0.1295979619026184,
-1.8621524572372437,
0.10835482180118561,
0.48951128125190735,
-0.14097897708415985,
-0.8104237914085388,
-0.5583726167678833,
1.010903000831604,
0.14560553431510925,
0.3540707230567932,
-0.24353696405887604,
-0.18044650554656982,
0.0972806066274643,
-0.4274934232234955,
0.013810033909976482,
0.4694802165031433,
-0.13436897099018097,
0.10302406549453735,
-0.03921150043606758,
-0.7771340608596802,
1.0380113124847412,
-0.19207759201526642,
-0.4256232678890228,
0.5081568956375122,
0.38157594203948975,
0.2307727038860321,
-0.22928723692893982,
0.5157533288002014,
0.9156126379966736,
0.17895057797431946,
0.4160967171192169,
1.533578634262085,
0.84867262840271,
0.6548743844032288,
0.6985105276107788,
0.37807825207710266,
-0.18133613467216492,
-0.18219538033008575,
-0.021480262279510498,
0.165304496884346,
0.3818482458591461,
0.1390296220779419,
-0.14688104391098022,
-0.8200818300247192,
-0.14026297628879547,
-0.37532293796539307,
0.07231605052947998,
-0.7005482316017151,
1.2868549823760986,
0.23854351043701172,
0.4512568712234497,
-1.3017147779464722,
-0.28758955001831055,
0.2597850263118744,
0.22916114330291748,
-0.5892331004142761,
-0.6433156728744507,
-0.030479123815894127,
0.6756309270858765,
0.03789566084742546,
0.01415924821048975,
-0.6101596355438232,
0.8672740459442139,
0.27996665239334106,
0.0562896765768528,
-0.2374095618724823,
-0.4185808002948761,
-1.207700252532959,
-0.19323256611824036,
-0.6175717711448669,
0.05625731125473976,
-0.3419736623764038,
0.35136088728904724,
1.0518137216567993,
-0.8893189430236816,
1.0215238332748413,
0.3376990258693695,
-0.6382301449775696,
0.5504453182220459,
-0.5712045431137085,
0.43333205580711365,
0.35081031918525696,
-0.1135578453540802,
-0.9767768383026123,
0.0594983845949173,
-0.2207975834608078,
0.4984823763370514,
0.1976344734430313,
0.061563096940517426,
0.601361095905304,
-0.5043498873710632,
0.3092060387134552,
-0.2359059602022171,
-0.7466476559638977,
-0.34454166889190674,
0.1312796175479889,
-0.1971595138311386,
0.01993422582745552,
-0.10286100953817368,
-0.4201628267765045,
-0.16561271250247955,
-0.56818687915802,
1.3428035974502563,
-0.11313240230083466,
-0.22884254157543182,
0.9969881176948547,
0.2027374655008316,
-0.28049737215042114,
0.588610053062439,
-0.4510912597179413,
0.04931352660059929,
-0.2349308282136917,
0.7944813966751099,
0.8919606804847717,
-0.01728791929781437,
0.3441956043243408,
-0.43084970116615295,
-0.3360152542591095,
0.23250888288021088,
-0.09380331635475159,
-0.5271076560020447,
-0.22385625541210175,
1.0032011270523071,
0.379789799451828,
-0.7182340025901794,
0.30932125449180603,
-1.2081016302108765,
-0.3797415792942047,
-0.053794391453266144,
-0.5525622367858887,
0.4215073585510254,
-0.13919663429260254,
-0.32239121198654175,
-0.7452608942985535,
0.4317759573459625,
-0.0575610026717186,
0.39906567335128784,
0.11418511718511581,
-0.9431763887405396,
0.7944061160087585,
0.3023642599582672,
0.25533947348594666,
-0.38664087653160095,
0.5674100518226624,
-0.5449080467224121,
-0.05592334270477295,
0.8354933857917786,
-0.8254126310348511,
0.19537952542304993,
0.35132482647895813,
0.628756582736969,
-0.28809821605682373,
0.14318032562732697,
-0.4884883463382721,
-0.678007960319519,
-0.7843199968338013,
-0.53699791431427,
0.3995918333530426,
0.35081395506858826,
-0.3216761350631714,
0.7329461574554443,
-1.306033730506897,
-0.6482791304588318,
0.07954898476600647,
0.150006502866745,
1.1245249509811401,
-0.5902230739593506,
0.3167804479598999,
0.5921405553817749,
-0.30558398365974426,
-0.10802590847015381,
-0.16172271966934204,
0.20070905983448029,
0.5820322632789612,
0.47289636731147766,
1.0027705430984497,
-1.2551965713500977,
-0.34119585156440735,
0.29348522424697876,
1.298525333404541,
1.2709120512008667,
0.9558584690093994,
0.9102956652641296,
-0.5605477094650269,
0.3392067849636078,
-0.37209585309028625,
-1.0340276956558228,
0.14189067482948303,
0.02656576596200466,
-0.6545506119728088,
-0.8064368963241577,
-0.38104453682899475,
-0.2561967372894287,
0.5346201658248901,
0.6463563442230225,
0.08898109942674637,
0.28937584161758423,
0.7294986844062805,
-0.03843533992767334,
0.7396581172943115,
0.6016556620597839,
-0.17072701454162598,
-0.5368984937667847,
-0.7718607187271118,
0.4042280316352844,
-0.193563312292099,
-0.15872114896774292,
0.0029977355152368546,
-0.544804573059082,
-0.8498035669326782,
-0.548310399055481,
0.6796186566352844,
0.5806334614753723,
-0.1540929228067398,
0.7611430883407593,
-0.3724920451641083,
0.3180903196334839,
-0.34874793887138367,
-0.5938307046890259,
0.3031712770462036,
0.3391490876674652,
0.23826009035110474,
-0.9088213443756104,
0.5067156553268433,
-0.2068900465965271,
0.3259200155735016,
0.4045989215373993,
-0.31064730882644653,
-1.2145534753799438,
-0.07953722774982452,
0.28642791509628296,
-1.4669109582901,
0.3193606436252594,
0.4200979769229889,
-0.3204967677593231,
-0.09328610450029373,
-0.5383605360984802,
-0.3341219127178192,
0.3968442976474762,
-0.4528048038482666,
-0.004894210956990719,
0.07253028452396393,
0.2939181923866272,
-0.5591428875923157,
0.5944819450378418,
0.33240458369255066,
-0.37409767508506775,
-0.12419287115335464,
-0.049557410180568695,
-0.1970696598291397,
-0.14918826520442963,
-0.7295387387275696,
-0.015568166971206665,
-0.4233355224132538,
-0.5165354013442993,
0.8023911118507385,
-0.41507261991500854,
0.44312286376953125,
0.7024993896484375,
0.030557259917259216,
-0.3155501186847687,
-0.8929162621498108,
0.1067073866724968,
0.4844713807106018,
0.29293301701545715,
0.5870895981788635,
0.8151484727859497,
0.009341241791844368,
0.030086763203144073,
0.024399591609835625,
0.4389175474643707,
0.2179810255765915,
0.07353124022483826,
0.08383212238550186,
-0.8559068441390991,
-0.3951359689235687,
-0.6693642735481262,
-1.3095440864562988,
0.38814881443977356,
-0.42797279357910156,
1.1516656875610352,
-0.1116165965795517,
-0.3256652355194092,
-0.17812378704547882,
-0.9762253165245056,
-0.8863952159881592,
0.39621463418006897,
0.024062249809503555,
-0.5702788829803467,
0.23279424011707306,
-0.6990557312965393,
0.3477768003940582,
-0.07821106165647507,
0.25753316283226013,
-0.563034176826477,
0.11145460605621338,
0.35363417863845825,
-0.6387446522712708,
0.5229297876358032,
-0.09354786574840546,
0.8015949130058289,
-0.06776418536901474,
0.20967061817646027,
-0.2408304512500763,
-0.38142144680023193,
-0.03544539213180542,
-0.28542855381965637,
0.10407081246376038,
-0.47768402099609375,
0.007141760550439358,
-0.07787802070379257,
0.7581865191459656,
0.47366899251937866,
-0.3659267723560333,
0.20019063353538513,
-0.5701656341552734,
0.6716551184654236,
-0.1480688601732254,
-0.0946679413318634,
-0.2980009913444519,
1.271705150604248,
0.3688742220401764,
-0.045434873551130295,
-0.33835458755493164,
-0.34722578525543213,
0.19777259230613708,
0.3546496033668518,
0.44345200061798096,
-0.5358118414878845,
-0.28528568148612976,
-0.4532415270805359,
-0.059267982840538025,
0.34841853380203247,
0.5679139494895935,
-0.05087708681821823,
0.170629620552063,
0.2726084291934967,
-0.8663479089736938,
0.5551939010620117,
0.11460758745670319,
-0.4949445128440857,
-0.14415818452835083,
0.049813687801361084,
-0.8583848476409912,
0.9989014267921448,
0.010148831643164158,
-0.2866228520870209,
0.7114456295967102,
-0.17593131959438324,
-0.08151624351739883,
0.80450040102005,
-0.12586762011051178,
-0.1929696649312973,
0.06645109504461288,
0.5386659502983093,
0.7742319107055664,
0.3306267559528351,
-0.437019407749176,
0.560992419719696,
-1.1636090278625488,
1.0860333442687988,
0.017716431990265846,
0.34287142753601074,
0.22189074754714966,
-0.7005828619003296,
0.7216324210166931,
-0.8037757277488708,
0.00013639123062603176,
0.4523662030696869,
0.0014952655183151364,
1.0875390768051147,
0.642356276512146,
-0.6256469488143921,
-0.2935333251953125,
-0.8175073862075806,
-0.7268644571304321,
0.26680150628089905,
-0.08840697258710861,
-0.3148888945579529,
-0.8122521638870239,
-0.8767126202583313,
0.09878639876842499,
0.07981026917695999,
1.0962508916854858,
0.5594719052314758,
0.09827429801225662,
-0.2577950656414032,
0.18550442159175873,
0.0200558640062809,
0.2214815467596054,
-0.5102522373199463,
0.3122484087944031,
-0.3306156396865845,
-0.7224044799804688,
0.3670540452003479,
-0.6872659921646118,
-1.417956829071045,
-0.4088987112045288,
0.3783009350299835,
0.1535576730966568,
-0.12221521139144897,
0.6065343022346497,
-0.19779208302497864,
-0.43952468037605286,
-0.4403781592845917,
-0.02593870647251606,
-0.14977213740348816,
0.45654743909835815,
0.40735310316085815,
-0.037132151424884796,
-0.43747591972351074,
-0.0317353829741478,
0.03505764156579971,
-0.3279639184474945,
-0.21621960401535034,
0.604129433631897,
-0.19203691184520721,
-0.8118178248405457,
0.1461741328239441,
0.11488356441259384,
-0.5512731075286865,
-0.8917819261550903,
-0.8211073875427246,
0.020816246047616005,
-0.35899755358695984,
-1.1883528232574463,
0.048260681331157684,
-0.3757832646369934,
-0.6145493388175964,
0.7336671948432922,
0.4778532087802887,
-0.40735724568367004,
0.008190955966711044,
0.09731946885585785,
-0.7493563294410706,
-0.46356162428855896,
0.3929378390312195,
0.8885513544082642,
-0.3275751769542694,
-0.08127284795045853,
-0.136693075299263,
-0.464343786239624,
-0.577899694442749,
0.33578765392303467,
0.23116745054721832,
-0.014290550723671913,
0.3307669162750244,
0.3656895160675049,
0.6168864965438843,
0.2978925108909607,
0.5147731304168701,
0.6187121868133545,
-0.6245644092559814,
0.3569592833518982,
-0.8017358779907227,
-0.3244282305240631,
-0.20221856236457825,
0.345640629529953,
0.6450762748718262,
-0.5453020930290222,
0.41758397221565247,
-0.6547946929931641,
0.01006817352026701,
-0.36111682653427124,
-1.0482419729232788,
0.2483639121055603,
-1.2333219051361084,
-0.207204207777977,
-0.7111911177635193,
-0.43569058179855347,
-0.10225854068994522,
0.286044180393219,
0.16178445518016815,
0.18257443606853485,
-0.757429838180542,
-0.20714740455150604,
0.4839608073234558,
0.16720931231975555,
0.38877782225608826,
-0.28120502829551697,
-0.4824010729789734,
-0.4736843705177307,
-0.4920864701271057,
0.1605166494846344,
0.0700228288769722,
-0.11612917482852936,
-0.4519703686237335,
0.27067017555236816,
-0.6427134871482849,
0.8686589598655701,
-0.7463631629943848,
-0.494953989982605,
0.7078279852867126,
0.24655233323574066,
-0.19307419657707214,
-0.2775907516479492,
-0.4811856746673584,
0.4950356185436249,
0.14803411066532135,
0.3359416425228119,
-0.17941005527973175,
0.5054469108581543,
-0.9498212337493896,
-0.11002905666828156,
-0.06553728133440018,
0.33014750480651855,
-0.11929057538509369,
-0.30182120203971863,
0.5052605867385864,
-0.16431552171707153,
-0.7587637901306152,
0.44122958183288574,
-0.3149896264076233,
-0.23893018066883087,
-0.23047670722007751,
-0.13568232953548431,
0.11655015498399734,
0.53439861536026,
-0.3013320863246918,
0.4030645191669464,
-0.21506784856319427,
-0.5583016872406006,
0.09405505657196045,
-0.024195406585931778,
-0.8928969502449036,
0.27185484766960144,
0.7301527261734009,
-1.0930626392364502,
0.12368569523096085,
0.8088269829750061,
-0.5287429690361023,
0.5758824348449707,
-0.3609977066516876,
-0.2657028138637543,
-0.044582270085811615,
-0.4610787034034729,
-0.16449713706970215,
1.048056960105896,
0.27938321232795715,
-0.8734563589096069,
-0.06819669157266617,
-0.4276306927204132,
-0.23140949010849,
0.16010838747024536,
-0.6368197202682495,
0.07318399101495743,
-0.2804794907569885,
0.27025192975997925,
-0.2779007852077484,
-0.3354361653327942,
0.04110174626111984,
0.44526588916778564,
0.14126358926296234,
-0.148835226893425,
-0.10562838613986969,
0.010689462535083294,
0.5064409375190735,
-0.21963094174861908,
-0.7206630706787109,
0.021473567932844162,
0.14001473784446716,
0.7467349767684937,
-0.781728208065033,
-0.679664671421051,
0.08713127672672272,
0.49462106823921204,
0.024966860190033913,
0.19417186081409454,
-0.4606853127479553,
0.2831704616546631,
0.3212242126464844,
0.29356637597084045,
0.1131599098443985,
-0.3627636730670929,
-0.00001901805808302015,
0.67115718126297,
-0.035895656794309616,
-0.8696238398551941,
0.009513234719634056,
0.17109347879886627,
0.25337114930152893,
-0.16069325804710388,
-0.44187477231025696,
0.7818930149078369,
0.39214688539505005,
-0.4631495773792267,
1.0269094705581665,
-0.10694097727537155,
0.7235579490661621,
-0.30219265818595886,
-0.06709354370832443,
0.28827470541000366,
0.09489665180444717,
1.0983020067214966,
0.34185513854026794,
0.22588607668876648,
0.2740073502063751,
0.9572693705558777,
0.2616661787033081,
0.21048451960086823,
0.42762479186058044,
0.3164476156234741,
0.2212894707918167,
0.3419746160507202,
-0.27400436997413635,
0.6202464699745178,
0.41944369673728943,
0.03408673033118248,
-0.4962445795536041,
0.07250907272100449,
-0.714790940284729,
0.19270974397659302,
0.3443220853805542,
0.26577654480934143,
-0.5503976345062256,
-0.13342931866645813,
-0.02203129045665264,
0.12212461233139038,
0.2928937077522278,
0.5256587266921997,
-0.12196230888366699,
0.5529062747955322,
0.53018718957901,
0.2919127345085144,
0.18094101548194885,
0.2907644212245941,
0.63260418176651,
0.19934096932411194,
0.10354115813970566,
1.1703166961669922,
1.2523196935653687,
0.43592190742492676,
0.6263633370399475,
-0.644313395023346,
-0.6204861998558044,
0.356947660446167,
-1.801230549812317,
0.08088674396276474,
-0.6876967549324036,
-0.3124848008155823,
-0.6576886177062988,
-0.9999118447303772,
0.3974519670009613,
-0.5343294143676758,
0.2886977195739746,
0.6151695251464844,
0.222858726978302,
0.39186057448387146,
0.48760148882865906,
-0.18937347829341888,
0.6886240243911743,
0.386903315782547,
0.009157263673841953,
-0.18036487698554993,
0.36819934844970703,
1.256221055984497,
0.2585255205631256,
0.10082223266363144,
0.26033660769462585,
-0.7079538106918335,
-0.043671831488609314,
-0.1662936508655548,
-0.01208669226616621,
1.176201343536377,
-0.9853289723396301,
-0.08111594617366791,
0.18040969967842102,
0.3692944049835205,
-0.37319791316986084,
0.19575904309749603,
-0.18018211424350739,
0.39098021388053894,
-0.7151601910591125,
-0.5609442591667175,
1.0200449228286743,
0.4629756212234497,
-0.14708183705806732,
-0.20557497441768646,
-0.4366968870162964,
-0.009331818670034409,
-0.12437663972377777,
-0.5723257660865784,
0.48948290944099426,
0.7245116233825684,
0.018572937697172165,
-0.2873494029045105,
-0.6660580635070801,
-0.2197515219449997,
-0.6388826966285706,
-0.18381503224372864,
-1.0797557830810547,
0.6670544743537903,
-0.1327233761548996,
0.7523068785667419,
-0.25469839572906494,
-0.7110506892204285,
0.35572412610054016,
1.1022117137908936,
0.7874593734741211,
0.45164206624031067,
0.3952588140964508,
0.6889371275901794,
0.012695095501840115,
-0.15454356372356415,
0.6334834098815918,
0.6608355641365051,
-0.578635573387146,
0.3955518901348114,
-0.1899709552526474,
-0.10938332974910736,
-0.19678081572055817,
-0.08693233877420425,
0.651252806186676,
-0.33074498176574707,
0.45704367756843567,
-0.6628043055534363,
-0.36249250173568726,
-0.4205099940299988,
-0.7338020205497742,
0.24684979021549225,
-0.6795655488967896,
0.2705584764480591,
0.4007073938846588,
0.5321603417396545,
-0.049374163150787354,
-0.37644174695014954,
4.050374984741211,
1.022398829460144,
0.7401058673858643,
-0.5289866924285889,
0.6878520250320435,
0.7277421355247498,
-0.3320085406303406,
-0.2158517837524414,
0.40608373284339905,
-0.5692908763885498,
0.03368215262889862,
0.29648303985595703,
0.6710249185562134,
-0.8539788126945496,
0.35635507106781006,
0.2548765540122986,
0.5244906544685364,
0.29468634724617004,
0.4875843822956085,
-0.9436798691749573,
-0.8853569626808167,
0.39467447996139526,
0.7143597602844238,
0.2274373173713684,
0.2659796476364136,
0.048001304268836975,
0.48440036177635193,
-0.7773964405059814,
-0.8725447058677673,
-0.27956172823905945,
-0.5188162922859192,
-0.9215173721313477,
0.1616283357143402,
-0.8564169406890869,
-0.670463502407074,
0.7880118489265442,
0.5498964786529541,
-0.6976788640022278,
0.19707301259040833,
0.30973953008651733,
-0.5071101188659668,
0.328555166721344,
0.14973613619804382,
0.13603147864341736,
-0.6840777397155762,
1.328598976135254,
0.06024984270334244,
1.150745153427124,
0.17469753324985504,
-0.5360506176948547,
0.18397386372089386,
-0.050575513392686844,
0.42758089303970337,
-0.43932032585144043,
-1.3545587062835693,
0.16287486255168915,
-0.8272971510887146,
-0.6005493402481079,
0.12327705323696136,
-0.23716215789318085,
0.9349880218505859,
0.28909429907798767,
-0.3378812372684479,
0.3434178829193115,
0.023805083706974983,
0.4768836796283722,
0.6215647459030151,
0.07667332142591476,
-0.30386242270469666,
-0.008044766262173653,
-0.47431138157844543,
-0.5186823606491089,
-0.6509461998939514,
-0.07515121251344681,
0.3634364604949951,
-0.32943981885910034,
-0.757106363773346,
0.5279780626296997,
0.7504519820213318,
-0.15471811592578888,
-0.3504737615585327,
-0.13582216203212738,
-0.5124844908714294,
-0.01389994751662016,
-0.34667420387268066,
0.11889899522066116,
-0.5649487972259521,
-0.3194037973880768,
-0.1649467796087265,
0.338309645652771,
0.15574833750724792,
1.5023833513259888,
0.3505139648914337,
-0.6903408765792847,
-0.7741916179656982
] |
Capillary Waves in Binder's Approach to the Interface Tension
|
In Binder's approach the reduced interface tension sigma of the Ising model in the broken phase is determined from the finite volume effects of the partition function Z(M) at fixed total magnetization M. For small |M| the partition function of a system of size L^d with periodic boundary conditions is dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential behavior allows an improved fit of numerical data, and a determination of the interface stiffness.
|
U.-J. Wiese
|
hep-lat cond-mat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209006
|
hep-lat/9209007
|
[
0.1443605124950409,
-0.10310756415128708,
0.0024493131786584854,
0.3996656835079193,
-0.643365740776062,
-0.32874739170074463,
-0.10863479226827621,
-0.15584713220596313,
-0.7234576344490051,
1.2194386720657349,
0.5710094571113586,
0.13561485707759857,
-0.167992502450943,
-0.9179953336715698,
0.17665007710456848,
0.5235346555709839,
-0.01638413593173027,
-0.23672263324260712,
-1.402476191520691,
0.39160317182540894,
0.25791773200035095,
0.1453053206205368,
-1.2022100687026978,
-0.21373631060123444,
0.20028850436210632,
0.7098203301429749,
0.11324246972799301,
0.34792232513427734,
1.0009881258010864,
0.6873112320899963,
0.3640654981136322,
-0.4717613160610199,
-0.497311532497406,
-0.03835419565439224,
-0.38211333751678467,
-0.3707740008831024,
0.19276592135429382,
0.0027650566771626472,
0.9273921251296997,
-0.4422702491283417,
0.4037412106990814,
0.07150240242481232,
-0.12030862271785736,
-0.27251559495925903,
-0.48469483852386475,
0.24431726336479187,
-0.06304053962230682,
-0.587043821811676,
0.15657883882522583,
-1.2459814548492432,
0.16129812598228455,
0.67775559425354,
0.7746614813804626,
-0.8042486310005188,
-0.4749767780303955,
-0.17266696691513062,
-0.16316743195056915,
-0.14771202206611633,
-0.8957313299179077,
-0.13050730526447296,
0.39168500900268555,
-0.34355950355529785,
0.9587051868438721,
-0.4952965974807739,
0.08249788731336594,
0.6273170113563538,
-0.33463916182518005,
0.302378386259079,
-0.2039216309785843,
0.036881618201732635,
0.2718676030635834,
0.06762421876192093,
-0.9313623905181885,
0.4904540181159973,
-0.75645911693573,
-0.019247666001319885,
-0.11471730470657349,
-0.15624432265758514,
-0.49079930782318115,
0.2924644351005554,
0.23713909089565277,
0.2579038441181183,
-0.22944466769695282,
0.3116002678871155,
-0.3948843479156494,
-0.07408496737480164,
-0.0395234078168869,
-0.3039341866970062,
0.07157617062330246,
0.5994203090667725,
0.3006686866283417,
0.7111081480979919,
-0.45375362038612366,
-0.10112958401441574,
0.3639991283416748,
0.32204070687294006,
0.05092640593647957,
0.26797425746917725,
0.3607005178928375,
0.12821465730667114,
0.22217446565628052,
1.0270837545394897,
-0.882642388343811,
0.013019712641835213,
-0.7794298529624939,
0.479491263628006,
0.083387590944767,
-0.6068456172943115,
-0.17728938162326813,
-0.8024381399154663,
0.31527337431907654,
-0.22508546710014343,
0.20021460950374603,
0.803268313407898,
0.44566503167152405,
0.7754982709884644,
-0.18184642493724823,
0.1862541288137436,
-0.1773906648159027,
-0.18223677575588226,
0.21737730503082275,
0.16276107728481293,
0.15807537734508514,
0.2606240212917328,
-0.038779858499765396,
-0.1288117915391922,
0.191987544298172,
-0.06751316040754318,
-0.40542706847190857,
0.07112254947423935,
0.03386559337377548,
-0.13920775055885315,
-0.22482939064502716,
0.5437911748886108,
-0.47445350885391235,
-0.36821481585502625,
-0.30194827914237976,
0.22144900262355804,
0.3395746350288391,
-0.2537914216518402,
0.6652034521102905,
-0.613389253616333,
-0.0813971534371376,
1.1347826719284058,
0.053587693721055984,
0.10253040492534637,
-0.17245563864707947,
0.4250434637069702,
-0.2667820453643799,
0.04573649913072586,
-0.7327983975410461,
-0.09131674468517303,
-0.288820743560791,
0.042019471526145935,
0.1605074405670166,
0.5293859839439392,
-0.3623911142349243,
0.20293638110160828,
-0.5789886713027954,
-0.6536502838134766,
0.21929194033145905,
0.217645063996315,
-0.5964400768280029,
0.050300706177949905,
-0.3979761004447937,
-0.3895798325538635,
-0.48111557960510254,
-1.0113763809204102,
0.6431563496589661,
-0.5871226787567139,
-0.03788858652114868,
0.8070700168609619,
-0.3778148889541626,
1.3131548166275024,
0.3024314343929291,
0.47400203347206116,
0.2999362051486969,
-0.22838778793811798,
-0.30776354670524597,
0.32879865169525146,
-0.22065074741840363,
-0.24185945093631744,
0.29985311627388,
0.15717849135398865,
-0.48752111196517944,
-0.1854737251996994,
-0.0066934251226484776,
-0.46292969584465027,
0.015904977917671204,
0.15306909382343292,
-0.1535128504037857,
0.3894628882408142,
-0.29164183139801025,
0.3244396448135376,
-0.589631199836731,
-0.11736047267913818,
-0.776143491268158,
0.5466250777244568,
-0.6186676621437073,
-0.46213579177856445,
0.348266065120697,
0.02249293215572834,
-0.3550117611885071,
0.1610904335975647,
-1.414911150932312,
0.0422082394361496,
1.177061915397644,
0.0037730515468865633,
-0.8493561744689941,
-0.33577340841293335,
0.17950937151908875,
-0.10568565875291824,
0.4042918086051941,
0.11866743117570877,
0.3332703113555908,
0.1887206882238388,
0.1151178851723671,
0.18814153969287872,
0.8507850170135498,
0.3244268000125885,
0.3931695520877838,
0.16673743724822998,
0.017491627484560013,
0.7551743984222412,
-0.7601000666618347,
-0.8035218119621277,
-0.08631528913974762,
0.7723750472068787,
0.3772916793823242,
-0.2933911979198456,
-0.37020233273506165,
0.6694914698600769,
-0.4520511329174042,
0.2548045516014099,
0.5002091526985168,
-0.11346805840730667,
0.7353034019470215,
0.173991397023201,
0.5004689693450928,
0.46723464131355286,
-0.005600916221737862,
0.08692461997270584,
0.3708648979663849,
0.15516333281993866,
-0.27068158984184265,
-0.05594879761338234,
-0.5708566904067993,
0.11414998024702072,
-1.0766465663909912,
0.4617159962654114,
-0.16520103812217712,
0.6262840628623962,
0.16914038360118866,
0.24666893482208252,
-1.1017016172409058,
-0.14122909307479858,
-0.30792805552482605,
0.27442315220832825,
0.09475550800561905,
-0.2165633589029312,
0.4071446657180786,
-0.12833434343338013,
-0.32969197630882263,
-0.46177107095718384,
-0.04418421909213066,
0.9155774116516113,
-0.5322476029396057,
0.4620710015296936,
0.6186867356300354,
-0.39885950088500977,
-0.8370376825332642,
0.3103097677230835,
-1.1019437313079834,
-0.22337916493415833,
-0.6545323729515076,
0.16303254663944244,
1.0374497175216675,
-0.6377592086791992,
0.6211504340171814,
-0.2456766963005066,
-0.275321900844574,
0.4085136950016022,
-1.2261191606521606,
0.038051098585128784,
0.5186409950256348,
0.015299836173653603,
-0.925013542175293,
0.09296412765979767,
-0.400533527135849,
-0.26149076223373413,
-0.5866289734840393,
0.48775383830070496,
0.9505698084831238,
-0.7378197312355042,
-0.02407718263566494,
0.04031025990843773,
-0.36971670389175415,
0.3224577009677887,
0.3409724533557892,
-0.5191887021064758,
0.17228342592716217,
0.6111689209938049,
-0.12243440747261047,
-0.31176161766052246,
-1.0255749225616455,
0.3800179362297058,
0.4794117510318756,
-0.00842738151550293,
0.5012882351875305,
0.12943707406520844,
-0.24300464987754822,
0.6842360496520996,
-0.025281865149736404,
0.2559416592121124,
-0.013995200395584106,
1.1856005191802979,
0.21156486868858337,
0.19891764223575592,
-0.11208926886320114,
-0.2824946641921997,
-0.4924733638763428,
0.11650107800960541,
-0.7219709753990173,
-0.4361744523048401,
-0.46959248185157776,
0.869825541973114,
-0.2965794503688812,
-0.2769244313240051,
0.6839210987091064,
-0.8662835955619812,
-0.3447730243206024,
0.5111414790153503,
-0.3463082015514374,
0.27564316987991333,
-0.30903151631355286,
-0.34080514311790466,
-1.1575448513031006,
0.39477866888046265,
0.14243176579475403,
-0.24877530336380005,
0.9162995219230652,
-0.003871153574436903,
0.17407231032848358,
0.6009106636047363,
0.188291996717453,
-0.46911054849624634,
-0.5131729245185852,
-0.2765769064426422,
-0.32297906279563904,
0.4093979299068451,
-1.1833362579345703,
0.05023862048983574,
-0.1059538871049881,
0.9144889116287231,
0.0035085214767605066,
0.4040642976760864,
-0.3084240257740021,
-0.5305078029632568,
-0.3207978904247284,
-0.7279620170593262,
-0.28033995628356934,
1.048425555229187,
0.0003912158135790378,
-0.15860265493392944,
-0.9224347472190857,
-0.5764921307563782,
0.11756203323602676,
0.07860331237316132,
-0.14903846383094788,
-0.9670798778533936,
0.028784174472093582,
0.23676612973213196,
-0.062210261821746826,
-0.21618233621120453,
0.1728978157043457,
0.5407978296279907,
0.22871169447898865,
-0.07828833907842636,
0.8657912611961365,
-0.2636503279209137,
-0.23364928364753723,
0.6760977506637573,
0.7373166084289551,
0.9207453727722168,
0.8294011950492859,
0.2835487425327301,
-0.11962628364562988,
0.24209736287593842,
-0.23119568824768066,
-0.397816926240921,
-0.7069458961486816,
0.00038773802225477993,
0.17893271148204803,
0.3221893310546875,
0.5515967607498169,
-0.0234859399497509,
0.35689565539360046,
-0.2503220736980438,
0.21876160800457,
-0.12627503275871277,
0.37893274426460266,
0.07354840636253357,
0.3736072778701782,
0.6838985085487366,
0.09817439317703247,
0.2726658284664154,
-0.6966714262962341,
0.08033518493175507,
0.009652139618992805,
0.5036873817443848,
-0.1779792457818985,
-0.5934432744979858,
-0.06611945480108261,
-0.6230356097221375,
0.7418684959411621,
-0.17376455664634705,
-0.9960570931434631,
0.32679107785224915,
-0.4768601357936859,
0.4530358612537384,
0.08758582919836044,
0.1768297553062439,
0.50154048204422,
0.11050160974264145,
0.18860064446926117,
-0.69081050157547,
0.9628459811210632,
-0.6466246247291565,
0.8071933388710022,
0.3267342746257782,
-1.2741304636001587,
-0.23456603288650513,
-1.091163158416748,
-0.419992059469223,
-0.16838796436786652,
0.41238921880722046,
1.2081905603408813,
0.17696593701839447,
0.046668387949466705,
-0.7089065909385681,
-0.40950343012809753,
0.46272656321525574,
-0.43152284622192383,
-0.6477469801902771,
0.60816890001297,
-0.15510843694210052,
-0.1744256466627121,
0.7966040372848511,
-0.2487727254629135,
-0.6253222823143005,
0.40263631939888,
-0.6357495784759521,
0.018071860074996948,
-0.059640467166900635,
-0.5639093518257141,
-0.3121773600578308,
-0.3850799798965454,
-0.5212260484695435,
0.773187518119812,
0.20735713839530945,
0.012858017347753048,
-0.04851073771715164,
-0.1393677145242691,
-0.02826252579689026,
0.31973719596862793,
0.14693962037563324,
-0.26723232865333557,
0.8599032759666443,
0.893695056438446,
-0.0075716846622526646,
0.45454680919647217,
0.12645277380943298,
-0.0899074450135231,
-0.020105399191379547,
0.5483306646347046,
-0.059914376586675644,
-0.29933401942253113,
-0.752773642539978,
0.2629886567592621,
-0.7798325419425964,
-0.8009486794471741,
0.44257161021232605,
-0.17108333110809326,
0.8140993118286133,
-0.18508784472942352,
-0.26363518834114075,
-0.2996133267879486,
-0.5520331263542175,
-0.40424084663391113,
0.7466548085212708,
0.1150156706571579,
-0.3644986152648926,
0.6576364636421204,
-0.26137465238571167,
0.09184881299734116,
-0.5877906680107117,
-0.06497801840305328,
-0.48076778650283813,
0.4531596899032593,
0.45146578550338745,
0.3889370858669281,
0.1932574063539505,
-0.9802538752555847,
0.5420361161231995,
-0.27598869800567627,
-0.35585734248161316,
-0.5557878017425537,
-0.09902888536453247,
0.260932594537735,
-0.6030604839324951,
0.4191027581691742,
-0.00737548153847456,
-0.21235647797584534,
0.0996197760105133,
-0.4331246316432953,
-0.16298897564411163,
0.14154112339019775,
-0.33843931555747986,
0.032521117478609085,
0.5046853423118591,
-0.11326590925455093,
-0.5294843316078186,
0.2839149534702301,
0.4832741618156433,
-0.0164650846272707,
-0.08571241050958633,
-0.016876015812158585,
-0.6606128811836243,
0.16783635318279266,
-0.04810090363025665,
0.31743285059928894,
-0.40433457493782043,
-0.27692344784736633,
0.08287639915943146,
-0.7944827675819397,
0.18413439393043518,
0.4556424021720886,
-0.11168482154607773,
-0.11936883628368378,
-0.808459997177124,
-0.5829483270645142,
0.27712202072143555,
0.045841414481401443,
0.06799653172492981,
-0.6848204731941223,
-0.16995365917682648,
0.05816589295864105,
0.4606674313545227,
-0.5177280902862549,
0.8802596926689148,
0.20907346904277802,
-0.13413602113723755,
0.055459409952163696,
0.41158658266067505,
0.5266583561897278,
-0.20883417129516602,
0.38529250025749207,
0.561252772808075,
-0.07773999124765396,
0.31968721747398376,
-0.37711408734321594,
0.4523763060569763,
-0.6351637840270996,
0.8470133543014526,
-0.8613371253013611,
-0.2697084844112396,
0.11501608788967133,
0.006862790789455175,
0.573499321937561,
-0.5555975437164307,
0.5006211996078491,
0.6719151139259338,
-0.03520091623067856,
0.48855167627334595,
0.6428017616271973,
-0.7137080430984497,
-0.6404548287391663,
-0.8415718674659729,
-0.2857964038848877,
0.3771454095840454,
0.11840460449457169,
-0.5023530721664429,
-0.9404881000518799,
-0.6976374983787537,
0.14820215106010437,
-0.24941620230674744,
0.3666796386241913,
0.12290111929178238,
-0.3126804232597351,
0.4887695908546448,
-0.004033666104078293,
-0.4877297878265381,
-0.4188616871833801,
0.5279791951179504,
0.13755661249160767,
-0.4249844253063202,
0.345907598733902,
-0.14292120933532715,
-0.5249264240264893,
-0.5471600890159607,
-0.23707225918769836,
0.2682456374168396,
0.10308347642421722,
-0.4715217351913452,
0.9221687316894531,
-0.09417416900396347,
-0.607963502407074,
-0.5459895730018616,
0.5651164650917053,
0.8049121499061584,
0.35665372014045715,
0.14996150135993958,
0.26318731904029846,
0.3542540371417999,
-0.18770037591457367,
0.5928537249565125,
-0.113731250166893,
-0.1963450312614441,
0.19502615928649902,
-0.7148173451423645,
-0.1898893564939499,
0.33605581521987915,
-0.058668434619903564,
-0.929273784160614,
-0.2655982971191406,
-0.9409535527229309,
0.27787965536117554,
-0.5029820203781128,
-0.1712895631790161,
-0.4059803783893585,
-0.46195387840270996,
0.1505599170923233,
0.21036793291568756,
0.7690222859382629,
0.08801160007715225,
-0.4161703586578369,
-0.32590451836586,
-0.09720515459775925,
-0.17257913947105408,
-0.5761247873306274,
1.4725302457809448,
0.29803094267845154,
-0.6563012003898621,
-0.3694877028465271,
-0.1839424967765808,
-0.5043280124664307,
0.20859579741954803,
0.9689688086509705,
-0.5904499888420105,
0.6662914752960205,
0.34557241201400757,
0.0007306435145437717,
0.2606890797615051,
1.2344259023666382,
0.5108121633529663,
0.5905711650848389,
-0.2779656648635864,
-0.8567590117454529,
-0.03142324835062027,
-0.3345504403114319,
0.07285140454769135,
0.6972583532333374,
0.5819066762924194,
0.2358904927968979,
-0.3176848888397217,
-0.07601238042116165,
0.16105720400810242,
-0.7999189496040344,
0.1734502911567688,
-0.7940978407859802,
-0.1430921107530594,
-0.28171855211257935,
-0.4124934673309326,
0.2842195928096771,
0.45734646916389465,
-0.45505157113075256,
-0.5289463996887207,
-0.8513472676277161,
0.11586548388004303,
0.3590562343597412,
0.5229496359825134,
-0.33753958344459534,
-0.8839161396026611,
0.11512577533721924,
-0.4044971466064453,
0.07141350209712982,
-0.04932481050491333,
0.12861566245555878,
-0.24902287125587463,
-0.24341584742069244,
0.24369284510612488,
-0.008377284742891788,
0.6677228212356567,
-0.8781331181526184,
-0.5108230113983154,
0.3227275609970093,
-0.27279606461524963,
-0.9621037840843201,
0.48714134097099304,
-0.14719992876052856,
0.856104850769043,
0.25768256187438965,
-0.3033810555934906,
-0.7916708588600159,
0.293189138174057,
-0.3341807425022125,
-0.022283688187599182,
0.5201796889305115,
0.4978921711444855,
-0.32410526275634766,
-0.32894784212112427,
-0.4177907705307007,
-0.3547540009021759,
-0.7561017274856567,
0.37833768129348755,
-0.7257030606269836,
-0.3751400411128998,
-0.2531993091106415,
0.26052001118659973,
0.3585084080696106,
0.16672423481941223,
0.20424041152000427,
0.92534339427948,
-0.37853556871414185,
-0.020619820803403854,
0.460744708776474,
0.3317123055458069,
-0.5147480368614197,
0.18062010407447815,
0.07698667794466019,
-0.05232914537191391,
-0.16090552508831024,
0.8439581990242004,
-0.05759122222661972,
-0.05905395373702049,
-0.5029321312904358,
-0.29766780138015747,
0.1943303644657135,
-0.5581907629966736,
-0.7142965793609619,
0.4089888334274292,
0.5737541317939758,
-0.6601331830024719,
-0.5414665341377258,
-0.6508944630622864,
-0.45448777079582214,
0.4582107663154602,
-1.0541560649871826,
-0.556660532951355,
0.24321120977401733,
0.4727875888347626,
-0.14752894639968872,
0.47648581862449646,
-0.2859126031398773,
0.18025262653827667,
-0.03536936268210411,
0.01089166197925806,
-0.13757573068141937,
-0.006367702502757311,
-0.14086569845676422,
0.058460380882024765,
0.1285964399576187,
-0.5935552716255188,
-0.24617183208465576,
0.8140140771865845,
-1.1751505136489868,
-0.8865340352058411,
-0.5256235003471375,
0.5982035994529724,
0.4341314435005188,
0.017051227390766144,
-0.3728087842464447,
-0.6084151864051819,
-0.3883530795574188,
-0.18771369755268097,
-0.9569501876831055,
-0.4960780143737793,
-0.4082687199115753,
0.08772934228181839,
-0.24918030202388763,
-0.5759143829345703,
0.5734440088272095,
0.06516676396131516,
0.30502191185951233,
-0.16217252612113953,
-0.34249621629714966,
0.6744753122329712,
0.4812963008880615,
0.09001283347606659,
0.6237177848815918,
-0.21734654903411865,
0.2638776898384094,
0.3012700080871582,
-0.7324458956718445,
0.1452539712190628,
0.4554058015346527,
0.1972811073064804,
0.7351416945457458,
0.2599693238735199,
0.22358977794647217,
0.2829313576221466,
0.3647910952568054,
-0.02722681500017643,
-0.41681167483329773,
-0.0070337713696062565,
0.1993398219347,
0.6272508502006531,
-0.00009393857908435166,
-0.24428856372833252,
0.5903794765472412,
-0.3479253947734833,
-0.27486616373062134,
-0.3293493092060089,
-0.751387894153595,
-0.39682137966156006,
-0.1705886721611023,
-0.1842295229434967,
-0.45266667008399963,
0.0815463587641716,
0.25161483883857727,
-0.046035196632146835,
0.1879027783870697,
0.05099782347679138,
-0.1458217352628708,
0.5822254419326782,
0.5069626569747925,
0.0701567679643631,
0.10277701914310455,
0.5011158585548401,
0.19515563547611237,
1.3162037134170532,
0.8327880501747131,
0.568515419960022,
0.0025374512188136578,
0.5566999316215515,
0.6589093208312988,
-0.8948495984077454,
0.6425415873527527,
0.11274515092372894,
-0.4828619360923767,
0.6798601746559143,
-0.5018532872200012,
-0.03198767080903053,
-0.4345465898513794,
-0.23012101650238037,
0.05955446511507034,
-0.7541171312332153,
0.18414299190044403,
0.4540116488933563,
-0.5515477061271667,
0.333479106426239,
0.7603650689125061,
-0.11730387061834335,
0.07696143537759781,
0.6435108184814453,
-0.11726647615432739,
0.7101185917854309,
1.3508837223052979,
1.4192490577697754,
0.3661024272441864,
-0.1440495252609253,
0.47475582361221313,
-0.42368584871292114,
0.3446499705314636,
0.41021376848220825,
-0.5054662227630615,
0.8898491859436035,
-0.4929879605770111,
-0.2977552115917206,
-0.06714649498462677,
0.38398289680480957,
-0.1407022625207901,
-0.6570978164672852,
0.45125728845596313,
-0.19827455282211304,
-0.7806221842765808,
-0.5886034965515137,
1.4505077600479126,
0.5649641752243042,
-0.3219224214553833,
-0.7430979013442993,
0.458740234375,
0.017004234716296196,
-0.20199070870876312,
-0.5007238388061523,
0.2977028489112854,
-0.4311498999595642,
-0.25306031107902527,
0.004346536006778479,
-0.4047441780567169,
-0.9615931510925293,
-0.48549938201904297,
0.4694660007953644,
-0.8072766661643982,
0.5197227597236633,
0.19337263703346252,
0.2439926266670227,
0.2149774581193924,
-0.9092144966125488,
-0.19747509062290192,
-0.16954652965068817,
1.034098744392395,
0.3061579167842865,
0.3036305606365204,
0.8936414122581482,
-0.02843375876545906,
-1.092241883277893,
0.2210455685853958,
0.3563055992126465,
-0.678429901599884,
0.5692977905273438,
0.015137985348701477,
0.8335994482040405,
0.7573294639587402,
-0.050631001591682434,
0.5315897464752197,
-0.10121165215969086,
0.3258999288082123,
0.4848562180995941,
-0.22047768533229828,
-0.23121961951255798,
-0.9992637038230896,
-0.2950848937034607,
-0.21678802371025085,
0.3345402479171753,
-0.03701376914978027,
0.21771688759326935,
0.2784927189350128,
-0.914738118648529,
4.409927845001221,
0.22587159276008606,
0.2578624486923218,
0.20488585531711578,
0.5636839270591736,
0.48392245173454285,
-0.32241109013557434,
-0.9321826100349426,
0.04458638280630112,
-0.24835434556007385,
-0.2521103024482727,
-0.24814026057720184,
-0.014690385200083256,
-0.1618751734495163,
0.287103533744812,
0.7510066628456116,
-0.3592572808265686,
-0.6384810209274292,
0.2722049951553345,
-0.9504505395889282,
-0.546462893486023,
0.01583356410264969,
0.029133951291441917,
0.19555704295635223,
0.19334687292575836,
0.2459104210138321,
-0.2515658438205719,
-0.25264817476272583,
-0.14451667666435242,
-0.24264903366565704,
-0.44440028071403503,
-0.4394455552101135,
0.12673898041248322,
0.10175421833992004,
-0.3040435314178467,
0.1314152181148529,
0.34601858258247375,
-0.2284107357263565,
0.16096027195453644,
0.4609372019767761,
-0.3887840807437897,
-0.2885591685771942,
0.3412446975708008,
-0.3365989029407501,
-0.4298573136329651,
0.8229221105575562,
-0.12967699766159058,
0.4810307025909424,
0.26554882526397705,
-0.7684276700019836,
0.5579063296318054,
-0.06824178248643875,
0.757188618183136,
-0.4778060019016266,
-1.0122796297073364,
0.3806835412979126,
-0.5618468523025513,
0.10609975457191467,
0.2864406704902649,
0.30671852827072144,
0.3736231327056885,
-0.328512042760849,
-0.38131651282310486,
0.04013456404209137,
-0.1389886885881424,
0.6598712205886841,
0.08823025226593018,
0.6652231812477112,
-0.23762613534927368,
0.4872250556945801,
-0.31733810901641846,
-0.6220670342445374,
-0.235444113612175,
0.12748664617538452,
-0.012144853360950947,
0.13364122807979584,
0.08348534256219864,
0.4353950321674347,
0.21202491223812103,
0.06935002654790878,
0.6468007564544678,
-0.19917240738868713,
-0.42608869075775146,
-0.04598665609955788,
0.395169734954834,
1.0273230075836182,
-0.06051359325647354,
0.002997863804921508,
-0.5206508636474609,
0.5180545449256897,
-0.07371632754802704,
0.9203863143920898,
0.3065040111541748,
-0.368825227022171,
-0.7141768336296082
] |
SU(2) Potentials from Large Lattices
|
We measure accurate values of the inter-quark potentials on a $48^{3}56$ lattice with SU(2) pure gauge theory at $ \beta =2.85$. The scale is set by extracting the string tension - we obtain ${\sqrt K}a=0.063(3)$ at $\beta =2.85.$ From a careful study of the small-$R$ potentials in the region 2 GeV $< R^{-1} < 5$ GeV, we extract a running coupling constant and estimate the scale $\Lambda _{\msbar} = 272(24)$ MeV.
|
The UKQCD Collaboration: S.P. Booth, A. Hulsebos, A.C. Irving, A. McKerrell, C. Michael, P.S. Spencer, P.W. Stephenson
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209007
|
hep-lat/9209008
|
[
0.4714071452617645,
0.14626054465770721,
0.10994051396846771,
0.5778222680091858,
-0.07031068205833435,
0.06547337025403976,
0.016389809548854828,
-0.16221652925014496,
-0.8523892164230347,
0.9830273389816284,
0.3565974831581116,
0.20190349221229553,
-0.3406161069869995,
-0.8450566530227661,
0.21377356350421906,
0.21554678678512573,
-0.01145937293767929,
0.054277244955301285,
-0.9236870408058167,
0.8058735728263855,
0.37481188774108887,
0.15361081063747406,
-1.0111892223358154,
-0.17784340679645538,
-0.02836695685982704,
0.6484293341636658,
0.37293174862861633,
-0.04790344089269638,
0.9137474298477173,
0.7104597091674805,
0.3704535961151123,
-0.7585766315460205,
-0.5902842879295349,
-0.024236729368567467,
-0.4197991192340851,
-0.23209796845912933,
-0.1978413462638855,
-0.20383521914482117,
0.4485992193222046,
-0.584563136100769,
0.40196144580841064,
-0.14908292889595032,
-0.09639551490545273,
-0.21916723251342773,
-0.41077932715415955,
0.4856506586074829,
-0.22513680160045624,
-0.4091154634952545,
-0.08661847561597824,
-1.2850364446640015,
0.1743524819612503,
0.283426970243454,
0.5997017025947571,
-0.6643504500389099,
-0.4238930940628052,
0.14445431530475616,
0.06478782743215561,
0.12211885303258896,
-1.0715601444244385,
0.20043131709098816,
0.49941420555114746,
-0.5926094651222229,
0.8495630025863647,
-0.7687171697616577,
0.21000482141971588,
0.7858482003211975,
-0.33907970786094666,
0.4708917737007141,
-0.07965347915887833,
-0.02232569269835949,
0.19178450107574463,
0.1695900708436966,
-1.285013198852539,
0.4217371344566345,
-0.5186863541603088,
-0.010803316719830036,
-0.0600326769053936,
-0.026811737567186356,
-0.2502450942993164,
0.2932417690753937,
0.21081411838531494,
0.7593808174133301,
-0.30986183881759644,
0.4678553640842438,
-0.5396948456764221,
0.03209861367940903,
-0.5980437994003296,
-0.49740779399871826,
-0.025366665795445442,
0.6865602135658264,
0.2053091675043106,
0.608351469039917,
0.44847196340560913,
-0.337616503238678,
0.5102568864822388,
0.1677083820104599,
-0.1719541698694229,
0.375973641872406,
0.5114618539810181,
0.09069804102182388,
0.4499562978744507,
0.7595876455307007,
-0.35740575194358826,
-0.2810578942298889,
-0.681869626045227,
0.9327965974807739,
-0.23995016515254974,
-0.19261154532432556,
0.07500869035720825,
-0.6877289414405823,
0.4096732437610626,
-0.5908721685409546,
0.27397292852401733,
0.5977579355239868,
0.13146790862083435,
0.35153159499168396,
-0.3198627829551697,
-0.19460353255271912,
-0.7030432224273682,
-0.09083010256290436,
0.3576694130897522,
0.17162860929965973,
0.47043338418006897,
0.7675411105155945,
0.08244352787733078,
0.4013970196247101,
-0.1422371119260788,
0.20683859288692474,
-0.5509850978851318,
0.2711777985095978,
-0.4335346519947052,
-0.30090293288230896,
-0.17173659801483154,
0.2872931957244873,
-0.4054408669471741,
-0.2253311723470688,
-0.34389445185661316,
0.11337592452764511,
-0.2133132964372635,
-0.550244152545929,
0.4278493821620941,
-0.3687835931777954,
-0.04924730211496353,
1.572137475013733,
-0.1492125391960144,
0.21066203713417053,
0.19599509239196777,
0.3906331956386566,
0.06778400391340256,
0.262882798910141,
-0.48348602652549744,
0.21376314759254456,
-0.0152702946215868,
-0.331045925617218,
0.22710469365119934,
0.1862005591392517,
-0.6286477446556091,
0.107304647564888,
-0.35124868154525757,
-0.47891297936439514,
0.398621141910553,
0.11807955801486969,
-0.623776376247406,
0.6582547426223755,
-0.5336084961891174,
-0.08598248660564423,
-0.5416821241378784,
-0.8834395408630371,
0.37768492102622986,
-1.009062647819519,
0.0730690062046051,
0.782357931137085,
-0.04788248613476753,
1.1407474279403687,
0.6299733519554138,
0.5049055814743042,
0.08709307014942169,
-0.30333444476127625,
-0.14740072190761566,
0.6741194128990173,
-0.07957977801561356,
-0.5012776255607605,
0.2559519410133362,
0.28213179111480713,
-0.5468264222145081,
-0.5627675652503967,
0.36971113085746765,
-0.48518437147140503,
-0.1073233112692833,
0.24048300087451935,
-0.37331464886665344,
0.26016080379486084,
-0.28823474049568176,
0.20546528697013855,
-0.6477271914482117,
-0.2588731646537781,
-0.3751298785209656,
0.3274212181568146,
-0.6552384495735168,
-0.3645747900009155,
-0.06128202751278877,
0.41452494263648987,
-0.9284194111824036,
0.5474849343299866,
-1.6867989301681519,
-0.22777552902698517,
0.6294481754302979,
0.1824159473180771,
-0.555380642414093,
-0.31516048312187195,
0.5836722254753113,
-0.15252017974853516,
0.27253443002700806,
-0.7763886451721191,
0.21035011112689972,
0.2051750123500824,
-0.012885365635156631,
0.3594101369380951,
0.25662869215011597,
0.20092973113059998,
0.5274749994277954,
0.25118696689605713,
0.02232728898525238,
0.778548002243042,
-0.4122981131076813,
-1.491791009902954,
0.01900210790336132,
0.8330878615379333,
0.2808934450149536,
-0.11250939220190048,
0.04873372241854668,
0.9311872124671936,
-0.11469635367393494,
0.44438597559928894,
0.19035333395004272,
0.18513387441635132,
0.7562448382377625,
0.11962105333805084,
0.6404284834861755,
0.5436775088310242,
-0.01201061625033617,
0.26383867859840393,
0.6711273789405823,
0.06576710194349289,
-0.21304814517498016,
-0.008613411337137222,
-0.26560917496681213,
0.15827126801013947,
-1.1277809143066406,
0.4299851655960083,
0.21949781477451324,
0.4002203345298767,
0.14782334864139557,
0.6734924912452698,
-1.2412575483322144,
-0.07345019280910492,
-0.4205552935600281,
0.1784382462501526,
-0.0718279555439949,
-0.19001898169517517,
-0.1448373943567276,
-0.04645262286067009,
-0.16580401360988617,
-0.6555054783821106,
0.044668570160865784,
0.6100527048110962,
-0.5442119240760803,
0.5860294699668884,
0.7223358154296875,
-0.5803442001342773,
-0.9728434085845947,
0.4396655857563019,
-0.9041261672973633,
-0.22609153389930725,
-1.143998384475708,
0.174830362200737,
0.94324791431427,
-0.3162846863269806,
0.3309269845485687,
0.1634892076253891,
-0.2502862215042114,
0.45155611634254456,
-0.42589929699897766,
0.6342805624008179,
0.7847391963005066,
0.12081906944513321,
-0.586175262928009,
0.10688072443008423,
-0.40997761487960815,
-0.6618414521217346,
-0.35582783818244934,
0.12354548275470734,
0.9062802791595459,
-0.69804847240448,
0.2604787051677704,
0.0678635761141777,
-0.26218265295028687,
0.6639201045036316,
-0.10617689043283463,
-0.4702107608318329,
0.2950904071331024,
0.05523665249347687,
-0.09507882595062256,
-0.48590779304504395,
-1.0944315195083618,
0.3929416537284851,
-0.07242204993963242,
-0.23778794705867767,
0.3184497654438019,
0.2278328686952591,
-0.7253581285476685,
0.88019198179245,
0.1005716621875763,
0.3547065556049347,
-0.19567297399044037,
1.2007657289505005,
0.19499461352825165,
0.0007933776942081749,
0.029867231845855713,
-0.2649390697479248,
-0.3665391504764557,
0.16264913976192474,
-0.13888582587242126,
-0.6459341049194336,
-0.4879835844039917,
0.6898937225341797,
0.5261350870132446,
-0.43293890357017517,
0.8308258056640625,
-1.2025965452194214,
-0.47621262073516846,
0.10508329421281815,
-0.6411399245262146,
0.13484680652618408,
0.02086593769490719,
-0.320611834526062,
-0.9645958542823792,
0.22890397906303406,
0.2746652662754059,
-0.1439988762140274,
0.6677806377410889,
-0.20138977468013763,
0.32300034165382385,
0.4941564202308655,
0.6781988143920898,
-0.3974430561065674,
-0.44486239552497864,
-0.11838037520647049,
-0.603466272354126,
0.12244568020105362,
-1.3957546949386597,
-0.16849036514759064,
-0.12308517098426819,
0.7979653477668762,
-0.07016292214393616,
0.03377185016870499,
-0.36062029004096985,
-0.3142109513282776,
-0.40804511308670044,
-0.6044237017631531,
-0.18528996407985687,
0.8971949219703674,
0.2527787983417511,
-0.24826449155807495,
-1.1828515529632568,
-0.21531163156032562,
-0.14944903552532196,
0.1627325862646103,
0.5241400003433228,
-0.7258856892585754,
0.44001758098602295,
0.11336805671453476,
-0.10488861799240112,
0.01970028690993786,
0.2002420872449875,
0.5831077694892883,
0.5943259000778198,
0.3131521940231323,
0.4301866590976715,
-0.8787375688552856,
-0.5682490468025208,
0.014351606369018555,
0.8903378844261169,
0.7695379257202148,
0.8022633790969849,
0.27409714460372925,
-0.2935296297073364,
-0.24388989806175232,
-0.35369783639907837,
-0.747066080570221,
-0.7492992281913757,
-0.11435581743717194,
0.33239856362342834,
0.45425933599472046,
0.22099894285202026,
-0.08455876260995865,
0.33552995324134827,
0.13694016635417938,
0.5321252346038818,
-0.13411706686019897,
0.635732889175415,
-0.2717841565608978,
0.48688140511512756,
0.8103197813034058,
0.3808172643184662,
0.46021002531051636,
-0.44240516424179077,
0.5297225117683411,
0.16834478080272675,
0.18038353323936462,
-0.20737840235233307,
-0.2915922701358795,
-0.1345783770084381,
-0.7199618816375732,
0.9814548492431641,
-0.17058323323726654,
-1.0606021881103516,
0.05157085508108139,
-0.06671920418739319,
-0.06917817890644073,
0.1052694171667099,
0.12324082851409912,
0.755075991153717,
0.07499819993972778,
0.570620059967041,
-0.5427022576332092,
0.9322530031204224,
-0.48021408915519714,
0.6452764868736267,
0.4062114655971527,
-0.7268187403678894,
-0.7895200252532959,
-0.9129488468170166,
-0.12693308293819427,
-0.4304889440536499,
0.592276930809021,
1.4772953987121582,
0.6355451941490173,
-0.33143019676208496,
-0.7652276754379272,
-0.4189763367176056,
0.7605141401290894,
-0.31535816192626953,
-0.019059238955378532,
0.398388147354126,
0.27960509061813354,
-0.7033414840698242,
0.7531759142875671,
0.20308175683021545,
-0.8513613939285278,
0.5438104271888733,
-0.47147074341773987,
0.308421790599823,
-0.12473611533641815,
-0.6056079268455505,
-0.5862450003623962,
-0.22155410051345825,
-0.1892155557870865,
0.3286961615085602,
-0.13398727774620056,
-0.19186946749687195,
-0.1419721394777298,
0.016145596280694008,
-0.2550261616706848,
0.33819928765296936,
0.30625757575035095,
-0.2049935907125473,
1.0485084056854248,
1.033769130706787,
0.2989296615123749,
0.09468156099319458,
0.09506560862064362,
0.10859109461307526,
0.3599330186843872,
0.5620641112327576,
-0.4268983006477356,
-0.21125240623950958,
-0.6481862664222717,
0.29845163226127625,
-0.5395536422729492,
-0.9093486666679382,
0.4261263608932495,
-0.31072473526000977,
0.7725168466567993,
-0.11328185349702835,
-0.2540856897830963,
-0.5435498952865601,
-1.0618809461593628,
-0.4356720447540283,
0.8400921821594238,
-0.1900530755519867,
-0.3697873651981354,
0.5460178852081299,
-0.2543906569480896,
0.41960760951042175,
-0.8794720768928528,
-0.2296331375837326,
-0.07854760438203812,
0.21422791481018066,
0.8213139176368713,
0.3917924165725708,
0.15456362068653107,
-0.745059072971344,
0.3727918267250061,
-0.633230984210968,
-0.1112857460975647,
-0.40921473503112793,
-0.10871846228837967,
0.47723662853240967,
-0.8755903840065002,
0.8269332051277161,
0.07867824286222458,
-0.004226332530379295,
0.4032939672470093,
-0.3658195734024048,
-0.09572557359933853,
0.18762396275997162,
-0.4253128468990326,
0.021202484145760536,
0.45691829919815063,
0.16607649624347687,
-0.7203829288482666,
0.33410975337028503,
0.4193614423274994,
0.13751959800720215,
0.2639145255088806,
-0.16616053879261017,
-0.5531747937202454,
0.24783091247081757,
-0.5767791271209717,
0.4030987024307251,
-0.33805522322654724,
-0.4373164474964142,
-0.08682893216609955,
-0.782450258731842,
0.610780656337738,
0.4416716992855072,
0.01553104817867279,
-0.11037027090787888,
-0.947888970375061,
-0.8160009384155273,
0.7684991359710693,
-0.1854265183210373,
0.08382970839738846,
-0.6041393280029297,
-0.4418221712112427,
0.6025696396827698,
0.6689577102661133,
-0.12731830775737762,
0.48162853717803955,
-0.021042820066213608,
0.007171248085796833,
0.07653327286243439,
0.2575274407863617,
0.4803221523761749,
-0.28562861680984497,
0.257934033870697,
0.13897433876991272,
-0.39290621876716614,
0.22733299434185028,
-0.20257030427455902,
0.5374388694763184,
-0.3636758327484131,
1.0657066106796265,
-0.9256092309951782,
-0.07229050993919373,
-0.007314085494726896,
-0.00673883780837059,
0.22028523683547974,
-0.21138767898082733,
0.30334097146987915,
0.6069620251655579,
0.07643716037273407,
0.3002208173274994,
0.1380300521850586,
-1.0410051345825195,
-0.4970379173755646,
-0.7538125514984131,
-0.6696211695671082,
0.6400101184844971,
0.43355613946914673,
-0.6611224412918091,
-0.7668319940567017,
-0.9227336049079895,
0.21924367547035217,
0.20117035508155823,
0.6596368551254272,
-0.07555009424686432,
0.17865343391895294,
0.5387510657310486,
-0.15266932547092438,
-0.16431225836277008,
-0.22236105799674988,
0.4049573838710785,
-0.030509503558278084,
-0.6487075090408325,
0.6902047991752625,
-0.05989573895931244,
-0.44065356254577637,
-0.5487051010131836,
-0.016740569844841957,
0.695112407207489,
0.06982080638408661,
-0.2801012694835663,
0.9992628693580627,
0.09916093945503235,
-0.8563041687011719,
-0.24571512639522552,
0.1997203528881073,
0.4853515028953552,
0.39462539553642273,
0.242486834526062,
0.04733531177043915,
0.4392092227935791,
0.07440599054098129,
0.4744049608707428,
-0.16951708495616913,
-0.19579915702342987,
0.5499531626701355,
-0.7475689649581909,
-0.7640053629875183,
0.20402269065380096,
-0.35231298208236694,
-1.1041538715362549,
-0.08794742822647095,
-1.1239960193634033,
0.7252554297447205,
-0.39102602005004883,
-0.310031920671463,
0.04150121286511421,
-0.14906667172908783,
0.579403817653656,
0.2808351218700409,
0.5694570541381836,
-0.04346863925457001,
-0.24306580424308777,
-0.16277174651622772,
-0.27652111649513245,
-0.4599359631538391,
-0.16521777212619781,
1.182773232460022,
0.3340010941028595,
-0.6065464019775391,
-0.14593011140823364,
-0.26133090257644653,
-0.40884339809417725,
-0.09898959845304489,
1.0689407587051392,
-1.1305691003799438,
0.3312000632286072,
0.48554736375808716,
-0.12202632427215576,
-0.16143563389778137,
0.8553562164306641,
0.6232790350914001,
0.437669962644577,
0.06149498000741005,
-0.7099683284759521,
-0.013038274832069874,
-0.08127515017986298,
0.41212600469589233,
0.453768253326416,
0.23056164383888245,
0.285549521446228,
-0.0860220417380333,
-0.20817796885967255,
0.46314358711242676,
-0.9325176477432251,
0.04762185737490654,
-0.7077889442443848,
-0.4766659438610077,
-0.46054863929748535,
-0.14400997757911682,
0.14582668244838715,
0.4859028458595276,
-0.3212873041629791,
-0.6008230447769165,
-0.6739261746406555,
0.12803272902965546,
0.3790646493434906,
0.27982285618782043,
-0.4422523081302643,
-0.8872438669204712,
0.12083633244037628,
-0.5692224502563477,
0.016147803515195847,
-0.265933096408844,
-0.14009472727775574,
0.02237253077328205,
-0.4085853099822998,
0.454793244600296,
0.1848887950181961,
0.2744646370410919,
-1.0548239946365356,
-0.6381278038024902,
0.5410732626914978,
-0.185111403465271,
-0.9089399576187134,
1.2479742765426636,
-0.3554101288318634,
1.2455673217773438,
0.22785872220993042,
0.05468939244747162,
-0.9176677465438843,
0.09144830703735352,
-0.43134841322898865,
0.07149669528007507,
0.25248342752456665,
0.7939026951789856,
0.011682509444653988,
-0.12990963459014893,
-0.559373140335083,
-0.745147705078125,
-0.6794902086257935,
0.4333353340625763,
-0.7668793201446533,
-0.3776346445083618,
-0.41457587480545044,
0.5586957931518555,
0.6110863089561462,
-0.30079272389411926,
0.42987558245658875,
0.6656973361968994,
-0.3855224847793579,
-0.12987913191318512,
0.8336852788925171,
0.12981151044368744,
-0.3545213043689728,
0.08997269719839096,
0.6860044598579407,
-0.34214508533477783,
-0.27139389514923096,
0.931523323059082,
-0.08908433467149734,
0.11919502168893814,
-0.7958548069000244,
-0.015535704791545868,
-0.22585800290107727,
-0.6632041931152344,
-0.6255592107772827,
0.19669444859027863,
0.27732589840888977,
-0.2425217479467392,
-0.10219306498765945,
-1.1056653261184692,
-0.6203824877738953,
0.24752885103225708,
-0.9899247288703918,
-0.3617516756057739,
0.26342201232910156,
0.29744383692741394,
-0.5903282165527344,
0.6290720105171204,
-0.32130420207977295,
0.25902217626571655,
0.3365912437438965,
0.20381426811218262,
-0.10557172447443008,
-0.074844129383564,
-0.21297240257263184,
-0.09627225250005722,
-0.23228390514850616,
-0.27204006910324097,
-0.22810791432857513,
0.9216278791427612,
-1.011319875717163,
-0.9656233787536621,
-0.3261686861515045,
0.5980823040008545,
0.3009454309940338,
0.15419770777225494,
-0.08579601347446442,
-0.36078253388404846,
-0.026444975286722183,
-0.15868046879768372,
-0.5668815970420837,
-0.15966828167438507,
-0.34319978952407837,
0.5637754201889038,
-0.014584444463253021,
-0.37035098671913147,
0.11006763577461243,
0.27596086263656616,
0.2741679549217224,
-0.38994812965393066,
-0.11375360935926437,
0.9809607267379761,
0.45129331946372986,
-0.04077747464179993,
0.6571546792984009,
0.09867102652788162,
0.4451685845851898,
0.5373377203941345,
-0.6090970635414124,
0.4144017994403839,
0.7986190319061279,
0.2914769947528839,
0.8608534932136536,
0.3143753707408905,
0.589675784111023,
0.4617599546909332,
0.016235921531915665,
0.05836091563105583,
-0.4029844403266907,
0.17739613354206085,
0.28085029125213623,
0.8749103546142578,
-0.11607465147972107,
0.026636308059096336,
0.5307297110557556,
-0.4713074862957001,
-0.11226698011159897,
-0.16327902674674988,
-0.846909761428833,
-0.7289692163467407,
0.06628581136465073,
0.10748130083084106,
-0.578927218914032,
-0.24695107340812683,
0.09412059932947159,
-0.12367065250873566,
0.39804747700691223,
-0.07071516662836075,
-0.4348175525665283,
0.5578694939613342,
0.9540160894393921,
-0.046611953526735306,
0.12881049513816833,
0.6724708676338196,
0.24335385859012604,
1.203538179397583,
0.37265777587890625,
0.36419469118118286,
0.3298785388469696,
0.4050047695636749,
0.6792298555374146,
-0.8551719188690186,
0.10318382829427719,
-0.11672370880842209,
-0.7373713254928589,
0.27548569440841675,
-0.21589194238185883,
-0.05466187372803688,
-0.6842710971832275,
-0.45151081681251526,
0.3811953067779541,
-1.1423072814941406,
-0.5521766543388367,
0.29204100370407104,
-0.37755852937698364,
-0.10784541070461273,
1.1176742315292358,
0.013593415729701519,
0.0613984614610672,
0.9508635401725769,
-0.1682419627904892,
0.0380869023501873,
1.088181495666504,
1.6916526556015015,
0.36652588844299316,
-0.3540397584438324,
0.3412189483642578,
-0.36428195238113403,
0.6264190077781677,
0.40920698642730713,
-0.6832463145256042,
1.0713505744934082,
-0.8514738082885742,
-0.26622143387794495,
-0.18280425667762756,
-0.09772355109453201,
-0.07297033071517944,
-1.0530256032943726,
0.3431609272956848,
-0.05550694465637207,
-0.8982553482055664,
-0.5143572688102722,
1.591221809387207,
0.631623387336731,
-0.3368742763996124,
-0.33061736822128296,
0.01847962848842144,
-0.11366578936576843,
-0.19831570982933044,
-0.7791215181350708,
0.2332669347524643,
-0.37894776463508606,
-0.31172284483909607,
-0.31326189637184143,
-0.5720647573471069,
-0.9020655155181885,
-0.850844144821167,
0.5772810578346252,
-0.6935284733772278,
0.8878028988838196,
0.2143840789794922,
-0.08359704911708832,
0.23757922649383545,
-0.48290151357650757,
-0.2383933812379837,
-0.008094857446849346,
1.1524969339370728,
-0.07035432755947113,
0.09955741465091705,
0.9377449750900269,
0.226913720369339,
-1.2870757579803467,
0.28488689661026,
0.17378781735897064,
-0.6495497822761536,
0.47983577847480774,
0.1379270851612091,
0.6402761340141296,
0.4109780192375183,
-0.21395307779312134,
0.467883437871933,
-0.4450424611568451,
-0.022435199469327927,
0.7059379816055298,
-0.522588849067688,
-0.28410109877586365,
-0.8908584713935852,
-0.41784217953681946,
-0.4732169210910797,
0.25291720032691956,
-0.09074947237968445,
0.220561221241951,
-0.05296541377902031,
-0.7798815965652466,
4.228979110717773,
0.22665227949619293,
0.4365507662296295,
0.3356461822986603,
0.9649031758308411,
0.7054583430290222,
-0.6563037037849426,
-0.6381275653839111,
0.019835347309708595,
-0.5502891540527344,
-0.39743688702583313,
0.007782932370901108,
0.044857654720544815,
-0.4012959897518158,
0.6594368815422058,
0.21791405975818634,
-0.12404357641935349,
-0.3349944055080414,
0.14087292551994324,
-1.2005188465118408,
-0.5109589099884033,
0.00507036317139864,
-0.08015550673007965,
0.13592812418937683,
0.28740358352661133,
0.5622256398200989,
-0.49909961223602295,
-0.12156466394662857,
-0.28966981172561646,
-0.5298247933387756,
-0.6777977347373962,
-0.6575751304626465,
0.13194940984249115,
-0.016931669786572456,
-0.7415439486503601,
0.10523965209722519,
0.1858876496553421,
-0.5568972826004028,
0.22366280853748322,
0.14102362096309662,
-0.061931874603033066,
-0.2964809536933899,
0.5277184844017029,
-0.15233483910560608,
-0.007523269392549992,
1.1715799570083618,
0.0039400262758135796,
0.3529922068119049,
-0.13396789133548737,
-1.0137094259262085,
0.28058290481567383,
-0.19733783602714539,
0.6326440572738647,
-0.47645846009254456,
-1.190483808517456,
0.3887961804866791,
-0.5108876824378967,
-0.14737121760845184,
0.24932852387428284,
0.3384745121002197,
0.348592072725296,
-0.32583773136138916,
-0.17783433198928833,
0.312675416469574,
-0.33045339584350586,
0.6578159332275391,
-0.09003771096467972,
-0.011425258591771126,
-0.47793665528297424,
0.5066394805908203,
-0.41672995686531067,
-0.5908978581428528,
0.07122065871953964,
-0.07449378073215485,
0.04151033237576485,
0.02446219138801098,
-0.17911289632320404,
0.5063928961753845,
-0.025812886655330658,
0.14605291187763214,
0.6265129446983337,
-0.37080344557762146,
-0.31007030606269836,
-0.2432471066713333,
0.39308756589889526,
0.7832411527633667,
-0.44672611355781555,
0.18614326417446136,
-0.48064616322517395,
0.4908290207386017,
0.1301187425851822,
0.6208133101463318,
0.12899474799633026,
-0.3124006688594818,
-0.7684247493743896
] |
The Running Coupling from SU(3) Lattice Gauge Theory
|
{}From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(3)$ pure gauge theory.
|
The UKQCD Collaboration: S.P. Booth, D.S. Henty, A. Hulsebos, A.C. Irving, C. Michael, P.W. Stephenson
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209008
|
hep-lat/9209009
|
[
-0.05122099816799164,
-0.683563232421875,
-0.17493689060211182,
0.6163941621780396,
-0.162601500749588,
-0.5426075458526611,
-0.4068457782268524,
-0.36292794346809387,
-0.7291545867919922,
1.353943109512329,
0.34603509306907654,
-0.18755415081977844,
0.5180169343948364,
-1.0109202861785889,
-0.566421389579773,
0.4518626034259796,
0.09700381755828857,
-0.7497534155845642,
-1.3426295518875122,
0.3849968910217285,
-0.13725896179676056,
-0.05000217258930206,
-1.9143506288528442,
-0.42867541313171387,
-0.49504655599594116,
1.313359022140503,
0.31111761927604675,
0.21326124668121338,
1.0523524284362793,
0.1338133066892624,
0.35810837149620056,
-0.7980124950408936,
-0.20144887268543243,
-0.8724761009216309,
-0.80254727602005,
-0.0657082349061966,
0.1919826865196228,
-0.0807417556643486,
0.19041115045547485,
0.09908577799797058,
0.8996263742446899,
-0.750868558883667,
0.5169453024864197,
0.3046368956565857,
-0.7395780682563782,
0.38740846514701843,
-0.1759272813796997,
-0.24469666182994843,
0.5933740735054016,
-0.9911893606185913,
0.16571557521820068,
0.3604928255081177,
0.47740432620048523,
-0.265825480222702,
-0.23990900814533234,
-0.7209540605545044,
0.0682382732629776,
0.48711493611335754,
-0.5367422699928284,
-0.4805876314640045,
0.5459226965904236,
0.22894035279750824,
0.5889591574668884,
-0.7999735474586487,
0.046836234629154205,
0.9764982461929321,
-0.24655397236347198,
0.9146747589111328,
0.14062462747097015,
-0.9427337646484375,
-0.17267832159996033,
-0.2610184848308563,
-1.1054332256317139,
0.38595420122146606,
-0.7517387270927429,
-0.048388317227363586,
0.06633637100458145,
-0.9092850089073181,
-1.2019364833831787,
-0.26526713371276855,
-0.14747822284698486,
-0.31627732515335083,
-0.15712511539459229,
0.2831984758377075,
-0.37819886207580566,
-0.10172934830188751,
0.09927142411470413,
0.18001975119113922,
0.7243483066558838,
0.7290742993354797,
0.37326616048812866,
0.6105909943580627,
-0.4457694888114929,
-0.2946416735649109,
0.414690762758255,
0.5382221341133118,
0.14578334987163544,
0.40785107016563416,
0.1697639524936676,
-0.03580242022871971,
0.13270224630832672,
0.4959750771522522,
-0.8387525677680969,
0.41063910722732544,
-0.4623447060585022,
0.5826718807220459,
-0.2068161964416504,
0.10231249779462814,
0.13720308244228363,
-0.898574709892273,
0.0651296004652977,
-0.11610780656337738,
0.19191116094589233,
0.4047417938709259,
0.5084850788116455,
1.1359684467315674,
-0.6321099400520325,
0.3815699815750122,
-0.6244252324104309,
-0.5743571519851685,
0.6572838425636292,
0.04057157412171364,
0.06269749999046326,
0.29035836458206177,
0.08082286268472672,
-0.5194981694221497,
0.3993914723396301,
0.6384920477867126,
-0.42983874678611755,
0.33997470140457153,
0.1492825150489807,
0.25780969858169556,
-0.14353623986244202,
0.8169392347335815,
-0.3038993179798126,
-0.15581119060516357,
-0.0037953697610646486,
0.5718119740486145,
-0.006597765721380711,
0.05565621703863144,
0.6286709308624268,
-0.5571640729904175,
-0.13505250215530396,
1.1996089220046997,
0.2779504358768463,
0.4349377155303955,
-0.3891381025314331,
-0.16495080292224884,
-0.3798445165157318,
0.37991321086883545,
-0.4291903078556061,
-0.3760185241699219,
-0.1385539323091507,
0.48061269521713257,
0.033326391130685806,
1.0688178539276123,
-0.47118857502937317,
0.4027900695800781,
-0.6222161054611206,
-0.6480488181114197,
0.45650073885917664,
-0.3018834590911865,
-1.0544756650924683,
0.24542288482189178,
-0.524729311466217,
-0.1467650681734085,
-0.5674950480461121,
-0.35309290885925293,
0.48993420600891113,
-0.67560213804245,
-0.21690641343593597,
0.20527729392051697,
-0.39890533685684204,
0.899733304977417,
0.45834627747535706,
0.27329158782958984,
0.5950095653533936,
-0.43256399035453796,
-0.3976174294948578,
0.023621251806616783,
-0.8721661567687988,
-0.263078510761261,
0.26943716406822205,
0.1759195327758789,
-0.11977951973676682,
-0.31007152795791626,
-0.5525556802749634,
-0.5744882225990295,
0.2851630449295044,
0.07645384967327118,
0.16312693059444427,
0.47219353914260864,
-0.39777952432632446,
0.549355685710907,
-0.5159711837768555,
-0.02633044682443142,
-1.2121237516403198,
0.49586617946624756,
-0.8286470174789429,
-0.7323775887489319,
-0.018130972981452942,
0.3942050337791443,
-0.7611660957336426,
0.8172662258148193,
-1.326865315437317,
0.10601234436035156,
0.6188094019889832,
-0.21628376841545105,
-0.5526946187019348,
-0.30078694224357605,
0.01853710226714611,
0.030755382031202316,
0.16990439593791962,
-0.4503571391105652,
0.45498836040496826,
0.3165113627910614,
0.06201571598649025,
0.28857752680778503,
0.6275745630264282,
0.06378353387117386,
0.30197620391845703,
-0.2466558814048767,
-0.30922603607177734,
0.6323927640914917,
-0.725396454334259,
-0.39938709139823914,
0.26288390159606934,
0.5002260208129883,
0.016533518210053444,
0.1417454481124878,
-0.15415260195732117,
0.0924440398812294,
-0.21572184562683105,
0.5458821058273315,
0.9616782069206238,
1.1481434106826782,
0.6581684350967407,
0.3768765926361084,
-0.23248165845870972,
-0.24531719088554382,
0.08334805816411972,
0.33026280999183655,
0.21151229739189148,
0.08558478951454163,
-0.43720152974128723,
-0.09202399849891663,
-0.692574143409729,
0.5751468539237976,
-0.4978860020637512,
0.5802327990531921,
-0.5336914658546448,
0.6324508786201477,
0.4250088334083557,
0.27675938606262207,
-0.9209110736846924,
-0.20175275206565857,
-0.37521350383758545,
0.7484671473503113,
-0.19218608736991882,
-0.22626769542694092,
0.2588370442390442,
0.2554858326911926,
-0.26887038350105286,
-0.8262243270874023,
-0.7408508062362671,
1.4216806888580322,
-0.1962183117866516,
-0.29165980219841003,
0.8812092542648315,
-0.3410751223564148,
-1.0401899814605713,
-0.09384052455425262,
-0.7934339046478271,
0.0570775642991066,
-0.39008596539497375,
0.33914095163345337,
1.0524508953094482,
-0.8829823136329651,
0.4365755617618561,
0.0018173655262216926,
0.10679071396589279,
0.66098552942276,
-0.4946897625923157,
0.5529095530509949,
0.4393256902694702,
0.2999061346054077,
-0.6176027655601501,
0.4841599762439728,
-0.914737343788147,
-0.22208385169506073,
-0.4182962477207184,
0.3465222716331482,
0.5587702393531799,
-0.7726840376853943,
0.5030928254127502,
-0.01749032735824585,
-0.9033079147338867,
0.12436461448669434,
0.17591749131679535,
-0.5420301556587219,
0.3360176086425781,
0.6065107583999634,
-0.0958111360669136,
-0.7365893721580505,
-1.083855390548706,
0.3787422776222229,
0.4340873658657074,
-0.6178768277168274,
0.6299999356269836,
-0.07009175419807434,
-0.12893007695674896,
0.3881627321243286,
-0.06359168887138367,
-0.28543898463249207,
0.022505655884742737,
0.9915318489074707,
0.7497730255126953,
0.23844560980796814,
0.04748622328042984,
-0.7213664054870605,
-0.07095655053853989,
-0.11528389900922775,
0.25545868277549744,
-0.4264202117919922,
-0.05508677288889885,
0.5162248015403748,
-0.269842267036438,
-0.7143251299858093,
0.5957813858985901,
-0.49561476707458496,
-0.6493752002716064,
0.47192561626434326,
-0.540507972240448,
0.6456690430641174,
-0.1381748914718628,
-0.11859183013439178,
-0.820155680179596,
0.2931171655654907,
0.17364835739135742,
0.13493667542934418,
0.33714038133621216,
-0.18338580429553986,
0.20564697682857513,
0.19419364631175995,
0.5075745582580566,
-0.40582114458084106,
0.6449114680290222,
-0.2221427708864212,
-0.48966094851493835,
0.3846348822116852,
-0.8721288442611694,
0.058441706001758575,
0.5012442469596863,
-0.10535422712564468,
-0.17302843928337097,
0.1391560137271881,
-0.3324124813079834,
-0.7555683255195618,
-0.24091416597366333,
-0.4602097272872925,
-0.20685145258903503,
0.2569815516471863,
-0.6904285550117493,
-0.30389901995658875,
-0.47742101550102234,
-0.3185783326625824,
0.5491681694984436,
0.06475254893302917,
0.7959004640579224,
-0.9591943621635437,
0.046123065054416656,
-0.04889493063092232,
-0.3392130434513092,
-0.03741864114999771,
-0.27212056517601013,
0.4026898443698883,
0.16616190969944,
0.06630438566207886,
0.7761318683624268,
-0.5411656498908997,
-0.8027114868164062,
-0.4292830228805542,
1.0531364679336548,
0.8965995907783508,
0.9787788391113281,
0.23807214200496674,
0.1654966175556183,
0.22122889757156372,
-0.26059505343437195,
-0.40890732407569885,
-0.2172834426164627,
-0.39295846223831177,
0.054996490478515625,
-0.265310674905777,
0.677746057510376,
0.8115561008453369,
0.6200281381607056,
0.43587833642959595,
0.1405191272497177,
0.3935193121433258,
0.8333883881568909,
0.11549694836139679,
0.5791176557540894,
0.4579700827598572,
-0.2724246680736542,
0.45149514079093933,
-1.071793794631958,
0.49886295199394226,
0.28316599130630493,
0.6372935771942139,
-0.12117422372102737,
-0.5165157914161682,
0.24372166395187378,
-0.7703691720962524,
0.6519509553909302,
0.35326507687568665,
-0.7073732614517212,
0.50309818983078,
0.23274560272693634,
0.550114631652832,
-0.14369049668312073,
0.026549682021141052,
0.9502852559089661,
0.5581353306770325,
0.4020904302597046,
-0.7843983769416809,
0.10000458359718323,
-0.323733925819397,
0.14910468459129333,
0.738929271697998,
-0.9246946573257446,
-0.8367137908935547,
-0.934263288974762,
0.04860715940594673,
-0.37377801537513733,
-0.14437703788280487,
1.3887099027633667,
-0.6639956831932068,
-0.10215893387794495,
-0.3471665382385254,
-0.3336332142353058,
1.0040557384490967,
-0.4040488600730896,
-0.548417866230011,
0.6089262962341309,
-0.2974607050418854,
-0.13916389644145966,
0.6502740979194641,
-0.265503853559494,
-0.2834148705005646,
-0.054567042738199234,
-0.2575003206729889,
0.310804158449173,
-0.4905512034893036,
-0.4083758294582367,
0.14749595522880554,
-0.958518385887146,
-0.3251432776451111,
0.5059363842010498,
0.1860310137271881,
-0.28555116057395935,
0.17746631801128387,
-0.09114470332860947,
-0.3685222268104553,
0.07478337734937668,
-0.20076051354408264,
0.27455535531044006,
1.0656458139419556,
0.6693242192268372,
-0.15141357481479645,
0.6326886415481567,
0.5823230743408203,
-0.38050028681755066,
0.0999092236161232,
0.08078740537166595,
0.7744675874710083,
-0.4167514145374298,
-0.78526371717453,
-0.25878700613975525,
-0.7815889716148376,
-0.293960839509964,
-0.2252039909362793,
-0.04681353643536568,
0.6116625070571899,
0.7055078744888306,
-0.9303086996078491,
-0.1963551938533783,
0.02603938616812229,
-0.5231595039367676,
0.39410775899887085,
-0.0771603211760521,
-0.015369961969554424,
0.5203577876091003,
-0.5498236417770386,
-0.288702130317688,
-0.239898219704628,
0.4679134488105774,
-0.5609903931617737,
0.4022413194179535,
0.8411731123924255,
-0.09198950976133347,
0.4144109785556793,
-1.3475260734558105,
0.7440844178199768,
-0.465142160654068,
0.4038272202014923,
-0.1780233383178711,
0.04071174934506416,
-0.3254435360431671,
-0.0010485706152394414,
0.549094021320343,
-0.1958886682987213,
-0.6180480122566223,
-0.06177585572004318,
-0.0027255439199507236,
-0.04572099447250366,
-0.5315864086151123,
-0.3990078866481781,
-0.5020516514778137,
0.5283265113830566,
-0.17047995328903198,
-0.5398923754692078,
0.1546522080898285,
0.8567283749580383,
-0.2767130732536316,
0.6126810312271118,
0.027776366099715233,
-0.8106899857521057,
0.22696690261363983,
-0.4525952637195587,
0.15841230750083923,
-0.7302631139755249,
-0.6979181170463562,
-0.08176421374082565,
-0.4662496745586395,
0.3160928189754486,
0.5668860077857971,
-0.004961451515555382,
-0.3801286518573761,
-0.5476775765419006,
-0.39372366666793823,
0.4934164881706238,
-0.14883679151535034,
-0.06832829117774963,
-0.45335131883621216,
0.047422125935554504,
-0.6835843920707703,
0.40868911147117615,
-0.03949408233165741,
0.38320139050483704,
0.2517065703868866,
-0.059451498091220856,
-0.02403436228632927,
0.8228102326393127,
0.053403813391923904,
0.11302625387907028,
-0.29077181220054626,
0.7864782214164734,
-0.20075426995754242,
0.9312739968299866,
-0.761762797832489,
0.2636701464653015,
-0.5302815437316895,
0.603157639503479,
-0.4993317127227783,
-0.279059499502182,
-0.38375046849250793,
-0.057099200785160065,
1.073515772819519,
-0.46889036893844604,
0.37337347865104675,
0.8233142495155334,
-0.41590580344200134,
0.7819908261299133,
0.6773651242256165,
-0.8472566604614258,
-0.3196066915988922,
-0.6021687984466553,
-0.8737035393714905,
0.7099281549453735,
0.11202579736709595,
-0.36712849140167236,
-0.3047010004520416,
-1.0075504779815674,
0.16399677097797394,
-0.16213859617710114,
0.23483620584011078,
0.46525466442108154,
-0.631868302822113,
0.3054335415363312,
0.12301681190729141,
-0.20682045817375183,
-0.7685207724571228,
-0.18394675850868225,
-0.03329934552311897,
-0.13402557373046875,
0.14215537905693054,
-0.19060495495796204,
-0.3175995945930481,
-0.6032275557518005,
-0.3374931514263153,
0.5529600381851196,
0.486389696598053,
0.012552192434668541,
0.7745559215545654,
-0.17849232256412506,
-0.5835502743721008,
-0.7844483852386475,
-0.13910865783691406,
0.06232433393597603,
0.22092634439468384,
0.4752902090549469,
0.4145773649215698,
0.1750541627407074,
0.34244412183761597,
0.2990153431892395,
-0.2014586627483368,
-0.2666809558868408,
0.31900107860565186,
-0.1683252602815628,
-0.4061681032180786,
0.6250649094581604,
-0.032114360481500626,
-0.9273512363433838,
-0.27206167578697205,
-0.873615562915802,
-0.33507823944091797,
-0.30893436074256897,
0.13766206800937653,
-0.7104689478874207,
0.4267811179161072,
-0.3392740488052368,
0.6434460282325745,
0.5685986876487732,
0.08163845539093018,
-0.5755341649055481,
-0.06363921612501144,
-0.28289633989334106,
-0.5423035025596619,
-0.34187352657318115,
1.1787848472595215,
-0.3997446298599243,
-0.219303697347641,
0.2538789212703705,
-0.25106319785118103,
-0.40345680713653564,
0.02995355799794197,
0.22541794180870056,
-0.33012115955352783,
0.4300438463687897,
0.34117743372917175,
-0.08701422810554504,
0.54793381690979,
0.7065269947052002,
0.12518012523651123,
-0.005882043857127428,
-0.6641075015068054,
-0.4234941303730011,
-0.37960055470466614,
-0.4950685203075409,
-0.1198396235704422,
0.759136974811554,
-0.19926154613494873,
0.0836070105433464,
-0.1777452975511551,
-0.9389877915382385,
0.02491406537592411,
-0.7901372909545898,
-0.055549245327711105,
-1.117608904838562,
-0.711704432964325,
-0.5646519064903259,
-0.7768654823303223,
-0.24171189963817596,
0.44112080335617065,
-0.08701859414577484,
0.21251317858695984,
-0.900097668170929,
0.3726963400840759,
0.7032842636108398,
0.16810870170593262,
0.10882743448019028,
-0.7993982434272766,
-0.2782955467700958,
-0.20416148006916046,
0.14101099967956543,
-0.3843610882759094,
0.0914151594042778,
0.25993239879608154,
-0.5677332878112793,
0.09796739369630814,
-0.2545498013496399,
1.105545997619629,
-1.3643264770507812,
-0.5462692975997925,
-0.25013917684555054,
0.02066020667552948,
-0.6234579086303711,
0.3611892759799957,
0.3306402862071991,
0.34347009658813477,
0.3480722904205322,
-0.3805426359176636,
-0.42254453897476196,
0.47781625390052795,
-0.6428414583206177,
0.15083996951580048,
0.1441914290189743,
0.29913824796676636,
-0.13880370557308197,
-1.1882482767105103,
-0.039660848677158356,
0.9307051301002502,
-1.0238865613937378,
0.3129855990409851,
-0.4158409535884857,
0.91342693567276,
-0.3305474519729614,
0.36088651418685913,
-0.08843214809894562,
0.7275726199150085,
-0.3667426109313965,
1.277977466583252,
0.019354140385985374,
-0.021037738770246506,
-0.07917197048664093,
-0.00349508598446846,
-0.35980552434921265,
0.07626020908355713,
0.18213263154029846,
-0.22085225582122803,
-0.015606761910021305,
0.79986572265625,
-0.25390541553497314,
-0.040849748998880386,
0.4219437837600708,
-0.040607862174510956,
0.0369160920381546,
-0.6094445586204529,
-0.6187340021133423,
0.3308822512626648,
0.4145086109638214,
-0.849390983581543,
0.005569396074861288,
-0.4725836217403412,
-0.8996817469596863,
0.3680379390716553,
-0.15679389238357544,
-0.7056743502616882,
0.13309501111507416,
-0.20916812121868134,
0.20284469425678253,
0.21384863555431366,
0.21222561597824097,
0.10005679726600647,
-0.05614563450217247,
0.3624855875968933,
0.5305511951446533,
0.5470640659332275,
-0.5343591570854187,
-0.08521731197834015,
-0.70111083984375,
-0.41303884983062744,
-0.004334562458097935,
0.45057037472724915,
-0.7493895292282104,
-0.8073604106903076,
-0.5298252105712891,
0.30095234513282776,
0.7114447355270386,
0.1876629889011383,
-0.48259392380714417,
-0.26666027307510376,
0.009692573919892311,
0.12368098646402359,
-0.3844602406024933,
-0.09164347499608994,
-0.36508381366729736,
0.7126215696334839,
-0.344287246465683,
-0.30968502163887024,
0.8656312823295593,
-0.2196243703365326,
-0.007348107174038887,
-0.38697999715805054,
-0.1138567104935646,
1.4281558990478516,
0.5090000033378601,
-0.5801799893379211,
0.620834231376648,
-0.28384506702423096,
0.2922419011592865,
0.3097408711910248,
-0.5875346064567566,
0.012249539606273174,
0.3520427942276001,
0.1890426129102707,
0.8881561756134033,
0.7596327662467957,
0.5337150692939758,
0.5426817536354065,
0.3272171914577484,
0.3318409025669098,
-0.2579876780509949,
0.19581985473632812,
0.5527653694152832,
0.07415370643138885,
0.11611723154783249,
0.20698879659175873,
-0.16719776391983032,
-0.02752562426030636,
0.17737412452697754,
-0.22664183378219604,
-0.09171587973833084,
0.17499521374702454,
0.21944378316402435,
0.029977260157465935,
-1.0902528762817383,
-0.4089616537094116,
-0.6501333117485046,
0.5025513172149658,
0.5272656083106995,
0.0974426195025444,
0.1852906048297882,
0.33932042121887207,
0.43956050276756287,
-0.15216389298439026,
-0.02998305670917034,
0.6879060864448547,
0.2823973596096039,
0.40651029348373413,
0.5222083330154419,
0.48034676909446716,
0.42958804965019226,
0.21181823313236237,
0.29266074299812317,
-0.8843963146209717,
-0.11131374537944794,
0.5517217516899109,
-1.3404561281204224,
0.397796630859375,
-0.35452479124069214,
-0.028796982020139694,
-0.3251435458660126,
-0.8272704482078552,
0.31262490153312683,
-0.5563139915466309,
0.2491106241941452,
0.8563883900642395,
0.18354591727256775,
0.5585777163505554,
0.4629727900028229,
-0.138865128159523,
-0.2154257446527481,
0.6804839968681335,
-0.15855051577091217,
-0.528652548789978,
1.2026633024215698,
1.4299490451812744,
-0.2184247076511383,
0.28941482305526733,
0.20047128200531006,
-0.8308005928993225,
0.6904820203781128,
0.016666347160935402,
0.036862246692180634,
1.0199975967407227,
-0.9804381132125854,
-0.4179112911224365,
0.14409995079040527,
0.22970542311668396,
-0.39703255891799927,
-0.2148486077785492,
0.12047289311885834,
0.17344515025615692,
-0.0410020686686039,
-0.7019487619400024,
1.2024201154708862,
0.5423809885978699,
-0.721076250076294,
-0.5142291784286499,
0.2345370650291443,
-0.1263827234506607,
-0.7134238481521606,
-0.438425749540329,
0.3342975080013275,
-0.17417941987514496,
0.452338308095932,
-0.2837322950363159,
-0.5033164024353027,
-0.4919239282608032,
-1.0614924430847168,
-0.18615160882472992,
-0.47008374333381653,
0.713546872138977,
-0.013182840310037136,
0.15268230438232422,
0.17913076281547546,
-0.42142537236213684,
-0.18332913517951965,
0.04220357909798622,
0.9211304783821106,
-0.26826196908950806,
-0.2524416744709015,
0.6027712821960449,
0.6851835250854492,
-0.45959416031837463,
0.5854473114013672,
0.27534618973731995,
-0.46795544028282166,
0.6565364599227905,
-0.23128823935985565,
0.6067705750465393,
0.7614148855209351,
-0.059218037873506546,
0.303538978099823,
0.10829376429319382,
0.6213887333869934,
-0.2522980570793152,
-0.5948036909103394,
-0.16914552450180054,
-0.6550354957580566,
-0.21076542139053345,
-0.1851033717393875,
0.19082944095134735,
0.013437346555292606,
0.6116364002227783,
0.484058678150177,
-0.5056444406509399,
4.203524112701416,
0.7986708879470825,
0.5670759677886963,
0.1460999697446823,
0.4382203221321106,
0.6318338513374329,
0.25828686356544495,
-0.6040114760398865,
0.4306522309780121,
-0.2733302116394043,
-0.2023634910583496,
0.36733338236808777,
0.24191297590732574,
-0.21612872183322906,
-0.5778391361236572,
0.6947586536407471,
-0.23172694444656372,
-0.7960092425346375,
0.19526836276054382,
-0.8118436336517334,
-0.5268877148628235,
0.02669747918844223,
0.6104075312614441,
0.24357829988002777,
0.07808035612106323,
-0.10353909432888031,
0.37663522362709045,
-0.1824907809495926,
-0.673369288444519,
-0.516717791557312,
-0.7971356511116028,
-0.937710702419281,
0.26573336124420166,
-0.15968996286392212,
-0.6587545275688171,
0.1653366982936859,
0.038561295717954636,
-0.23497138917446136,
-0.0029694708064198494,
0.2916502058506012,
0.3206082880496979,
-0.2828974425792694,
-0.05149836838245392,
-0.35584262013435364,
-0.7147184014320374,
0.638809084892273,
-0.099710613489151,
0.9650305509567261,
0.5159614682197571,
-0.3163670301437378,
0.3111070692539215,
-0.28189554810523987,
0.7509029507637024,
-0.1317618191242218,
-1.0938564538955688,
0.3185446858406067,
-0.24585866928100586,
-0.5326705574989319,
0.1812783032655716,
0.33567014336586,
0.4779664874076843,
-0.44222119450569153,
-0.2502134442329407,
0.18221817910671234,
-0.3448607921600342,
0.9690651297569275,
0.2645621597766876,
0.14575111865997314,
-0.025618499144911766,
-0.2440711408853531,
-0.03371598944067955,
-0.12636783719062805,
-0.3379518389701843,
0.1458059847354889,
0.04450275003910065,
0.1552656888961792,
0.5302115678787231,
0.2905811667442322,
-0.1304701417684555,
0.0952647402882576,
0.2836383283138275,
-0.1905699074268341,
-0.1839418113231659,
0.5798995494842529,
0.18612274527549744,
0.6250832676887512,
0.05787837132811546,
-0.09472043067216873,
-0.02987399883568287,
0.6198391914367676,
0.19739080965518951,
0.9090919494628906,
0.3487311899662018,
0.08246242254972458,
-1.1230309009552002
] |
Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED
|
We simulate four flavor noncompact lattice QED using the Hybrid Monte Carlo algorithm on $10^4$ and $16^4$ lattices. Measurements of the monopole susceptibility and the percolation order parameter indicate a transition at $\beta = {1/e^2} = .205(5)$ with critical behavior in the universality class of four dimensional percolation. We present accurate chiral condensate measurements and monitor finite size effects carefully. The chiral condensate data supports the existence of a power-law transition at $\beta = .205$ in the same universality class as the chiral transition in the two flavor model. The resulting equation of state predicts the mass ratio $m_\pi^2/m_\sigma^2$ in good agreement with spectrum calculations while the hypothesis of a logarithmically improved mean field theory fails qualitatively.
|
A. Kocic, J.B. Kogut and K.C. Wang
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209009
|
hep-lat/9209010
|
[
0.28654107451438904,
-0.2930071949958801,
0.44414106011390686,
0.17949551343917847,
0.061570607125759125,
-0.16161726415157318,
-0.15293361246585846,
-0.656196117401123,
-0.4348146617412567,
1.104101538658142,
0.3783472180366516,
0.026359200477600098,
-0.0046785855665802956,
-1.3318456411361694,
0.2593679130077362,
0.7458615303039551,
0.012433678843080997,
-0.18717531859874725,
-1.3186688423156738,
0.43767404556274414,
0.37343013286590576,
-0.17439021170139313,
-1.2008378505706787,
-0.3607425093650818,
0.008222521282732487,
0.9307866096496582,
0.05686696246266365,
0.2780764400959015,
1.3698159456253052,
0.333540678024292,
0.22488120198249817,
-1.0287730693817139,
-0.2666863203048706,
-1.0619819164276123,
-0.7893890142440796,
-0.6131241321563721,
-0.11535745859146118,
-0.4344957768917084,
0.3676144778728485,
-0.13900570571422577,
1.0267513990402222,
-0.5493128895759583,
-0.421365886926651,
-0.23432128131389618,
-0.4412640929222107,
0.41620197892189026,
-0.7294149398803711,
-0.7626081705093384,
-0.009307246655225754,
-1.1252257823944092,
0.17471562325954437,
0.7649552822113037,
0.40465930104255676,
-0.13499419391155243,
-0.3568580746650696,
-0.28820332884788513,
0.5448106527328491,
0.0741916075348854,
-0.43550756573677063,
-0.5423562526702881,
0.37562689185142517,
0.16599717736244202,
0.24603129923343658,
-0.9606231451034546,
0.293626993894577,
0.6822053790092468,
-0.2793971300125122,
0.39543697237968445,
0.029886208474636078,
-0.5970243811607361,
-0.39282870292663574,
-0.08300311863422394,
-0.3421204388141632,
0.17033129930496216,
-0.6515665650367737,
-0.16707222163677216,
0.3546525537967682,
-1.0425925254821777,
-0.6925860047340393,
0.28445348143577576,
-0.6799726486206055,
0.22602267563343048,
-0.23905159533023834,
0.4081847369670868,
-0.8447474837303162,
-0.3959864675998688,
-0.5614897608757019,
0.21420513093471527,
0.23784413933753967,
0.9247011542320251,
0.645195722579956,
1.0532273054122925,
-0.183882474899292,
0.4188789129257202,
0.6094883680343628,
0.15582771599292755,
0.2771243453025818,
-0.04342955723404884,
0.33569398522377014,
0.1512235701084137,
0.5833374857902527,
0.6406489610671997,
-0.872147798538208,
0.7793880701065063,
-0.744167149066925,
0.7223495244979858,
0.33812639117240906,
-0.22903254628181458,
-0.380023330450058,
-0.6345809102058411,
0.04524364694952965,
-0.09313958138227463,
0.3215067386627197,
0.4106494188308716,
0.43763700127601624,
0.832933247089386,
-0.384657621383667,
0.3248533010482788,
0.0241934135556221,
-0.9211111068725586,
0.4481993615627289,
0.10891543328762054,
0.04120644927024841,
0.21781638264656067,
0.0009336564689874649,
0.10911764949560165,
0.4084283113479614,
0.5565392374992371,
-0.6558657288551331,
0.7115317583084106,
-0.13800913095474243,
-0.472825288772583,
-0.14985479414463043,
0.3897310495376587,
-0.1125716120004654,
0.07973847538232803,
-0.503807008266449,
0.20208583772182465,
0.11556082963943481,
-0.3081771731376648,
0.3657244145870209,
-0.36173710227012634,
-0.2720251977443695,
1.3885903358459473,
0.8930004239082336,
0.22319479286670685,
-0.0764288678765297,
-0.022921910509467125,
0.3376224637031555,
0.19477088749408722,
-0.4696216583251953,
-0.17250403761863708,
-0.14719949662685394,
-0.07534213364124298,
-0.15019160509109497,
0.7854786515235901,
-0.5795985460281372,
0.38622137904167175,
-0.630557119846344,
-0.49372830986976624,
0.6827421188354492,
-0.3730162978172302,
-1.2763704061508179,
0.16926570236682892,
-0.5213814377784729,
0.014268860220909119,
-0.7269373536109924,
-0.4883756637573242,
0.08643677830696106,
-0.052263058722019196,
0.2720738351345062,
0.5210604667663574,
-0.5743787288665771,
0.18463541567325592,
0.36441418528556824,
-0.17539961636066437,
0.29846957325935364,
-0.41294097900390625,
-0.1273551881313324,
0.15763698518276215,
-0.7389376163482666,
-0.5217010974884033,
-0.4948732554912567,
-0.3621019124984741,
0.0772804319858551,
-0.48198193311691284,
-0.28010958433151245,
-0.32542744278907776,
0.50618976354599,
0.030010294169187546,
-0.014739949256181717,
0.37292197346687317,
-0.6555784940719604,
0.7299847602844238,
-0.33201417326927185,
-0.4269993305206299,
-1.0813794136047363,
0.5619158148765564,
-0.6364487409591675,
-0.11160097271203995,
-0.11709180474281311,
0.301212340593338,
-0.8478227853775024,
0.434537410736084,
-1.3374919891357422,
0.09765954315662384,
0.7948271036148071,
0.10207363963127136,
-0.7481370568275452,
-0.5007046461105347,
0.4687611758708954,
0.06910376250743866,
0.002186800818890333,
-0.17606595158576965,
0.2247745841741562,
0.07520703226327896,
0.2840147912502289,
0.8015066385269165,
0.707222044467926,
0.29365354776382446,
0.8891920447349548,
0.0006813961663283408,
0.03719315677881241,
0.5571731925010681,
0.13030686974525452,
0.10496987402439117,
-0.2391417771577835,
0.7595216631889343,
0.19665895402431488,
-0.32064127922058105,
0.1790042221546173,
0.4177238941192627,
0.025384755805134773,
0.23588527739048004,
0.12064752727746964,
1.1261425018310547,
0.584674596786499,
0.5057316422462463,
-0.07861264795064926,
0.5779523849487305,
0.4019359350204468,
0.0644616037607193,
0.4468853771686554,
-0.3463652729988098,
-0.10899918526411057,
0.42780250310897827,
-0.6363227963447571,
0.06519483029842377,
-0.4900272488594055,
0.36370202898979187,
0.2586544454097748,
0.6101407408714294,
0.4507814347743988,
0.0011053645284846425,
-1.2382899522781372,
-0.16990932822227478,
-0.3113923966884613,
0.6853002905845642,
0.08004207909107208,
0.03342418745160103,
0.5785720944404602,
-0.11337199807167053,
-0.31669673323631287,
-0.3352561891078949,
-0.1019156277179718,
0.9489423632621765,
-0.12076136469841003,
0.042616091668605804,
0.613166093826294,
-0.13436836004257202,
-1.2916003465652466,
0.321521520614624,
-0.7000873684883118,
-0.18448446691036224,
-1.080219030380249,
0.34379443526268005,
0.9900922775268555,
-1.355332612991333,
0.4387197494506836,
0.5449164509773254,
-0.37904414534568787,
0.24113395810127258,
-1.1281468868255615,
0.22862130403518677,
0.704633355140686,
0.6320493817329407,
-0.33119654655456543,
0.3076971173286438,
-0.9911442995071411,
0.19239309430122375,
-0.0997358039021492,
0.7299386858940125,
0.7925325632095337,
-0.4771789610385895,
0.5368164777755737,
-0.5358111262321472,
-0.7177119255065918,
-0.39384499192237854,
-0.18064898252487183,
-1.4824111461639404,
-0.05816524475812912,
0.4183642566204071,
-0.26824259757995605,
-0.4007873833179474,
-1.1038298606872559,
0.6577786207199097,
-0.00048806110862642527,
-0.24103622138500214,
0.21288825571537018,
0.4068470001220703,
0.04523000866174698,
0.7583866119384766,
0.1090252622961998,
-0.06431414932012558,
-0.1546107977628708,
1.253584384918213,
0.3333318829536438,
0.2505796551704407,
0.21569378674030304,
-0.5387541055679321,
-0.11182525008916855,
0.650737464427948,
-0.0858149453997612,
-0.6888884902000427,
-0.10211002826690674,
0.9700289368629456,
0.2660181522369385,
-1.0628570318222046,
0.22581973671913147,
-1.025329828262329,
-1.0864496231079102,
0.611405611038208,
-0.2292245775461197,
0.16633066534996033,
0.30820420384407043,
-0.005815105512738228,
-1.0230889320373535,
0.28961896896362305,
0.08863499760627747,
0.2649815082550049,
0.45090654492378235,
-0.18677374720573425,
0.021848153322935104,
0.23097096383571625,
-0.18292118608951569,
-0.3136362135410309,
0.04874371737241745,
-0.953389048576355,
-0.2685966193675995,
0.5026534795761108,
-0.7174007892608643,
-0.024929044768214226,
0.32118111848831177,
0.6432294249534607,
-0.40930789709091187,
0.6579429507255554,
-0.7770581841468811,
-0.07583066076040268,
-0.6689461469650269,
-0.5763713121414185,
0.35740867257118225,
0.4662919342517853,
-0.6500580906867981,
-0.29288092255592346,
-0.2508697807788849,
-0.10948403924703598,
0.022997435182332993,
-0.24129483103752136,
0.6286094784736633,
-0.8173988461494446,
0.08788850903511047,
0.30085450410842896,
-0.22964636981487274,
0.2937591075897217,
-0.3795197606086731,
0.27546969056129456,
0.759966254234314,
0.2397032082080841,
1.1705288887023926,
-0.4875589907169342,
-0.7312637567520142,
-0.08564761281013489,
0.9007776379585266,
0.5147812962532043,
0.7736008167266846,
-0.137914776802063,
-0.9684309363365173,
0.29111266136169434,
-0.571479082107544,
-0.43219780921936035,
-0.6520408987998962,
-0.15689751505851746,
-0.19410187005996704,
0.15533821284770966,
0.31612998247146606,
0.5153326392173767,
0.8509165048599243,
0.5706365704536438,
0.36989426612854004,
-0.15247546136379242,
0.24174584448337555,
0.5206800103187561,
0.7604462504386902,
0.4350234866142273,
0.055894434452056885,
0.2128354012966156,
-0.9849988222122192,
0.5032547116279602,
0.11279688775539398,
0.20463351905345917,
-0.1221223846077919,
-0.13512486219406128,
-0.38473066687583923,
-0.453300803899765,
0.6411758661270142,
0.7366368174552917,
-0.9184713363647461,
0.3803408145904541,
-0.2529022693634033,
-0.19100138545036316,
-0.622978687286377,
-0.25322794914245605,
0.6217734217643738,
0.06985259056091309,
0.9098184704780579,
-0.8336426615715027,
0.40431228280067444,
-0.15728823840618134,
-0.12920956313610077,
0.823907196521759,
-1.679857611656189,
-0.5679792165756226,
-0.8492110967636108,
-0.051622144877910614,
-0.2248464673757553,
0.021269913762807846,
1.055250883102417,
-0.10973499715328217,
-0.20572751760482788,
-0.37531745433807373,
-0.4289921820163727,
0.5146089196205139,
-0.6633138656616211,
-0.23670782148838043,
0.8447531461715698,
0.31171366572380066,
-0.052520573139190674,
0.7393556833267212,
-0.16107220947742462,
-1.0840202569961548,
-0.19184356927871704,
-0.6733254194259644,
0.4698306620121002,
-0.04506497457623482,
-0.3826369643211365,
0.31267276406288147,
-0.7837632894515991,
-0.6186320781707764,
0.6121245622634888,
0.038035258650779724,
-0.33825448155403137,
-0.26406005024909973,
-0.3054152727127075,
-0.6294008493423462,
-0.003068325575441122,
0.2269047051668167,
-0.034267209470272064,
1.0457549095153809,
0.8314866423606873,
0.05883719027042389,
0.00646634865552187,
0.587801992893219,
-0.45100507140159607,
0.03406210616230965,
0.44328823685646057,
-0.028271494433283806,
-0.5912082195281982,
-0.5836697816848755,
-0.7354537844657898,
-0.9563137292861938,
-0.33504632115364075,
0.1167537122964859,
-0.21624848246574402,
0.31553882360458374,
-0.13443148136138916,
-0.9201415181159973,
-0.49234262108802795,
-0.5453710556030273,
-0.6207009553909302,
0.41955944895744324,
0.5416597127914429,
-0.40825676918029785,
0.7093493342399597,
-0.844641387462616,
0.053082358092069626,
-0.22616374492645264,
0.1445012241601944,
-0.5756378173828125,
0.30748456716537476,
0.5587272644042969,
0.6110475659370422,
0.12581411004066467,
-1.3392480611801147,
0.46640780568122864,
-0.5108827352523804,
0.06517451256513596,
0.025193916633725166,
-0.2902261018753052,
0.3001270592212677,
-0.710102379322052,
0.53090900182724,
-0.28762951493263245,
-0.5291266441345215,
0.062243882566690445,
-0.10139906406402588,
-0.6800673007965088,
0.11076000332832336,
0.0444389209151268,
-0.21422427892684937,
0.8292453289031982,
0.2668682634830475,
-0.3809129297733307,
0.8462117314338684,
0.5101900100708008,
-0.14389099180698395,
0.4965227246284485,
-0.4859030842781067,
-1.0422133207321167,
0.06351301074028015,
-0.2705695331096649,
0.18706601858139038,
-0.4338766038417816,
-0.21869665384292603,
-0.21047744154930115,
-0.437190979719162,
0.30041566491127014,
0.4877970516681671,
0.3446459472179413,
0.2411368042230606,
-0.258922278881073,
-0.31339940428733826,
0.39868345856666565,
-0.2902349531650543,
-0.18562017381191254,
-0.9077503085136414,
-0.10980507731437683,
-0.03845581039786339,
0.5081114172935486,
0.44617876410484314,
0.23011402785778046,
0.1480160355567932,
-0.0851520225405693,
0.6241360902786255,
0.7865700721740723,
0.22437769174575806,
-0.1426054835319519,
0.012340100482106209,
0.9046114087104797,
-0.26120656728744507,
0.4092215597629547,
-0.8377782702445984,
0.6910891532897949,
-0.5410953164100647,
0.6366690397262573,
-0.6707819700241089,
-0.7684561610221863,
-0.6679574847221375,
0.6524623036384583,
1.318205714225769,
-0.44284746050834656,
0.16363173723220825,
1.1302661895751953,
-0.3007144331932068,
0.681979238986969,
0.046232640743255615,
-0.44127073884010315,
0.24602289497852325,
-0.34746772050857544,
-1.046010136604309,
0.19512183964252472,
0.3708864450454712,
-0.2886509597301483,
-0.5903629064559937,
-0.6288700699806213,
0.2564275860786438,
-0.33947840332984924,
0.39470890164375305,
0.18479804694652557,
-0.23113705217838287,
0.3138091266155243,
0.15164022147655487,
-0.4448769688606262,
-0.4050501883029938,
-0.08779047429561615,
0.37140733003616333,
-0.25362321734428406,
0.1934518963098526,
0.07597577571868896,
-0.3959053158760071,
-0.33556458353996277,
-0.06498958170413971,
0.0556047298014164,
0.7082265615463257,
-0.5089290738105774,
0.47741979360580444,
-0.34097135066986084,
-0.5575973987579346,
-0.7185431718826294,
0.4627034068107605,
-0.15925531089305878,
0.5635868310928345,
0.6064370274543762,
-0.44625797867774963,
0.2439635545015335,
0.24760465323925018,
0.2742685377597809,
-0.08318023383617401,
0.2328055053949356,
0.6131818890571594,
-0.16411416232585907,
-0.20631848275661469,
0.3455226421356201,
0.40529826283454895,
-0.693225085735321,
-0.5519658923149109,
-0.6419227719306946,
-0.25288674235343933,
-0.6655446290969849,
0.013572562485933304,
-0.5292564034461975,
0.1626175343990326,
-0.17004968225955963,
0.12082558125257492,
0.22028964757919312,
-0.10003375262022018,
-0.6162468791007996,
-0.34788763523101807,
-0.5207777619361877,
-0.48382455110549927,
-0.5526668429374695,
1.7055543661117554,
-0.38471367955207825,
0.09075039625167847,
-0.2759968042373657,
-0.09675980359315872,
-0.26671555638313293,
-0.041562605649232864,
0.32014480233192444,
-0.736113965511322,
0.05824887007474899,
0.023437069728970528,
0.35429391264915466,
0.33881622552871704,
0.6961970329284668,
0.6897563338279724,
0.5855388045310974,
-0.20183499157428741,
-0.6163163185119629,
0.07151394337415695,
0.40170830488204956,
0.3384600579738617,
1.0317823886871338,
-0.01979011669754982,
-0.11062373965978622,
-0.11795202642679214,
-0.7463639974594116,
0.06934043020009995,
-0.8879676461219788,
0.5181203484535217,
-1.378825068473816,
-0.5113803744316101,
-0.46139779686927795,
-0.7620379328727722,
-0.03967105597257614,
0.18863803148269653,
-0.29815882444381714,
0.06068703159689903,
-0.6511921286582947,
-0.23495519161224365,
0.6308158040046692,
0.006185023579746485,
-0.08795106410980225,
-0.7265939116477966,
-0.3240445852279663,
-0.7040848135948181,
-0.38582709431648254,
-0.43918412923812866,
0.13432537019252777,
0.5401418209075928,
-0.2204563319683075,
0.4558238685131073,
0.3204990327358246,
0.7953164577484131,
-1.0294225215911865,
-0.6730639338493347,
-0.31260961294174194,
-0.21445032954216003,
0.12898676097393036,
0.2926909327507019,
0.3003557324409485,
0.5115407705307007,
0.26562368869781494,
-0.29289710521698,
0.1253255158662796,
0.6644231677055359,
-0.7175428867340088,
0.195549875497818,
0.328212708234787,
-0.07683032751083374,
-0.20977981388568878,
-0.28521794080734253,
0.1250695288181305,
-0.007794340141117573,
-0.8030575513839722,
0.3103446960449219,
-0.5489742755889893,
0.13069100677967072,
-0.5591460466384888,
-0.11308899521827698,
0.30410295724868774,
0.1299172043800354,
-0.04499261453747749,
1.1956706047058105,
-0.3272876441478729,
-0.046448223292827606,
0.5976400971412659,
-0.06970645487308502,
-0.15878704190254211,
-0.41949278116226196,
0.1878727525472641,
-0.4036319851875305,
-0.12486675381660461,
0.40276724100112915,
0.11508913338184357,
0.3354651629924774,
0.07915126532316208,
-0.43630334734916687,
0.014604669995605946,
-0.2324085235595703,
-0.33708512783050537,
0.20594021677970886,
0.1729177087545395,
-0.44693607091903687,
-0.2581614553928375,
-0.684833288192749,
-1.344011902809143,
-0.15176980197429657,
-0.15118376910686493,
-0.2705068290233612,
0.00448831170797348,
-0.33351537585258484,
0.03397965431213379,
0.6426136493682861,
0.012237905524671078,
0.1156233549118042,
0.05733971670269966,
0.07455778121948242,
-0.18801556527614594,
0.3763745427131653,
-0.09006915241479874,
0.244254931807518,
-0.437247633934021,
-0.2846441864967346,
-0.13149727880954742,
0.76544189453125,
-0.4169384241104126,
-0.24191154539585114,
-0.44715696573257446,
0.521202027797699,
0.05397171527147293,
-0.3448438048362732,
-0.06686168909072876,
-0.07342226058244705,
-0.32730793952941895,
-0.18477921187877655,
-0.03034401871263981,
-0.27406319975852966,
-0.251175194978714,
0.3809961676597595,
-0.5282317996025085,
-1.078532099723816,
0.8900557160377502,
-0.12808364629745483,
-0.19548049569129944,
-0.16781866550445557,
-0.05991196632385254,
0.8281549215316772,
0.5697791576385498,
-0.6075214743614197,
0.3984948992729187,
0.04609987884759903,
-0.08280621469020844,
0.11652511358261108,
-1.0768792629241943,
-0.29733502864837646,
0.5787280201911926,
0.5307968854904175,
0.40868356823921204,
0.8406853079795837,
0.023713042959570885,
0.949251651763916,
0.3878794312477112,
0.7475191950798035,
-0.8473169207572937,
0.017865974456071854,
0.2332911491394043,
0.2814576029777527,
-0.057499002665281296,
0.13801106810569763,
0.015782665461301804,
-0.665003776550293,
-0.021565528586506844,
-0.4747215509414673,
-0.7633773684501648,
-0.14715445041656494,
0.29536157846450806,
0.16310781240463257,
-0.8600925207138062,
-0.05564450845122337,
0.0408724881708622,
0.19507957994937897,
0.43398141860961914,
0.0789324939250946,
0.09979548305273056,
0.5054723620414734,
0.48302599787712097,
-0.2720644772052765,
-0.0712246224284172,
0.19691281020641327,
0.5016178488731384,
0.393409788608551,
0.7828682065010071,
0.3322857618331909,
0.09823063015937805,
0.44091659784317017,
0.28944849967956543,
-1.0331931114196777,
0.03565805405378342,
0.5913893580436707,
-1.0337891578674316,
0.4459597170352936,
-0.30383017659187317,
0.03584607318043709,
-0.4430581033229828,
-0.17214298248291016,
0.3215250074863434,
-0.7450222969055176,
0.43506646156311035,
0.8148616552352905,
-0.33051052689552307,
0.49590080976486206,
0.7734092473983765,
-0.0712890625,
0.5289767384529114,
0.5587905645370483,
-0.3331562876701355,
-0.5317304730415344,
1.3346084356307983,
1.936519980430603,
-0.21500292420387268,
0.2722104787826538,
0.6390591263771057,
-0.858231246471405,
-0.26751574873924255,
0.04190357029438019,
-0.1093912422657013,
0.7739120721817017,
-0.5469361543655396,
-0.5158761143684387,
0.6455655097961426,
0.5546963214874268,
-0.26215860247612,
-0.592130184173584,
0.27590689063072205,
0.2678723931312561,
-0.28752070665359497,
-0.5750066041946411,
1.163783311843872,
0.9413987994194031,
-0.3516736626625061,
-0.4141068756580353,
0.4591870903968811,
-0.0785270631313324,
-0.5981942415237427,
-0.17962707579135895,
0.3999159038066864,
-0.0027619360480457544,
0.21024268865585327,
-0.07076277583837509,
-0.1814691424369812,
-0.44093042612075806,
-1.296045184135437,
-0.13737937808036804,
-0.8848080635070801,
0.12938985228538513,
-0.06493150442838669,
0.6851200461387634,
0.5568368434906006,
-0.8979521989822388,
0.36335113644599915,
-0.23786592483520508,
0.23103299736976624,
-0.08439067006111145,
-0.047619085758924484,
1.1255024671554565,
0.9787244200706482,
-0.695038378238678,
0.26961877942085266,
0.8826818466186523,
-0.3407510221004486,
0.5786290168762207,
-0.349658727645874,
0.6573596596717834,
0.6281142234802246,
-0.2680410146713257,
0.6102501749992371,
0.8150277733802795,
0.09127059578895569,
-0.13648481667041779,
-0.23646587133407593,
-0.03784657269716263,
-0.5891247391700745,
0.2956545650959015,
-0.9413662552833557,
0.13918274641036987,
0.15150968730449677,
0.20151203870773315,
0.7614011168479919,
-0.6657628417015076,
4.118664264678955,
0.3630697727203369,
0.5861234664916992,
0.16052797436714172,
0.32506781816482544,
0.9605259895324707,
-0.2985495924949646,
-1.052751064300537,
0.2593687176704407,
-0.3982967436313629,
-0.643927812576294,
0.14593450725078583,
0.08849359303712845,
-0.12183178961277008,
0.5068067312240601,
0.53852778673172,
-0.6331721544265747,
-0.7773382663726807,
0.13034331798553467,
-0.9820110201835632,
-0.6044490337371826,
0.12978500127792358,
-0.04848967120051384,
-0.26290395855903625,
0.17082740366458893,
0.20350955426692963,
-0.17386391758918762,
-0.28235259652137756,
-0.24892498552799225,
-0.7243216633796692,
-1.2757960557937622,
-0.8914065957069397,
0.45882853865623474,
-0.04367264732718468,
-0.4624539613723755,
0.5811898708343506,
-0.06063137203454971,
-0.0744367465376854,
0.2412058562040329,
0.5839155316352844,
-0.12888877093791962,
-0.5974894762039185,
0.6924561262130737,
-0.2152186930179596,
-0.3178858160972595,
0.7351517677307129,
0.09011506289243698,
0.6140431761741638,
-0.08927546441555023,
-0.3229428231716156,
0.7810968160629272,
-0.30604973435401917,
0.07265756279230118,
0.18150684237480164,
-1.3171254396438599,
0.4074104130268097,
-0.781573474407196,
-0.03812972828745842,
0.234599769115448,
0.04764406755566597,
0.8529536724090576,
-0.1672164797782898,
-0.2258569747209549,
-0.4735269844532013,
-0.6066816449165344,
1.073925256729126,
0.38026419281959534,
0.5428926348686218,
-0.4675549864768982,
0.2079114019870758,
-0.08034440129995346,
-0.10845755785703659,
0.11978936195373535,
0.7595729231834412,
0.27448272705078125,
0.3477610945701599,
0.05948641151189804,
0.34683865308761597,
0.4329223334789276,
0.3319983184337616,
0.7408090233802795,
0.19871819019317627,
-0.5598686337471008,
0.1410733312368393,
0.29915735125541687,
0.8219584822654724,
-0.5524110794067383,
0.26397526264190674,
-0.23614546656608582,
0.46438589692115784,
0.21928554773330688,
0.9025863409042358,
0.3194809854030609,
0.3035315275192261,
-0.8426745533943176
] |
Universal Properties of Chiral Simmetry Breaking
|
We discuss chiral symmetry breaking critical points from the perspective of PCAC, correlation length scaling and the chiral equation of state. A scaling theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The Goldstone character of the pion and properties of the longitudinal and transverse chiral susceptibilities determine the ratio $R_\pi$ which can be used to locate critical points and measure critical indices such as $\delta$. We show how PCAC and correlation length scaling determine the pion mass' dependence on the chiral condensate and lead to a practical method to measure the anomalous dimension $\eta$. These tools are proving useful in studies of the chiral transition in lattice QED and the quark-gluon plasma transition in lattice QCD.
|
A. Kocic, J.B. Kogut and M.-P. Lombardo
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209010
|
hep-lat/9209011
|
[
0.5440608859062195,
-0.09764596819877625,
0.3560888469219208,
-0.016648266464471817,
0.5936959981918335,
-0.06500959396362305,
-0.2086501121520996,
-0.24838753044605255,
-0.5379088521003723,
1.3778749704360962,
0.6800917983055115,
0.010940412990748882,
0.24965296685695648,
-1.0651229619979858,
0.18013891577720642,
0.39732199907302856,
-0.4163091480731964,
-0.2856391966342926,
-1.153887391090393,
0.5377963781356812,
0.7136069536209106,
-0.3676054775714874,
-0.9110223650932312,
-0.6911118030548096,
-0.4879021942615509,
0.4205036759376526,
-0.2507293224334717,
0.5113460421562195,
1.4229605197906494,
1.1291024684906006,
0.26629015803337097,
-0.745214581489563,
-0.6670792102813721,
-0.5726597905158997,
-0.622622549533844,
0.11628513783216476,
-0.13991940021514893,
-0.07638546079397202,
0.8751060962677002,
-0.39417678117752075,
0.8077173233032227,
-0.559421718120575,
0.9662556648254395,
-0.02221244014799595,
-0.40296417474746704,
0.4105803370475769,
-0.40286320447921753,
-0.12858538329601288,
-0.012777167372405529,
-1.5509889125823975,
0.7374416589736938,
0.36147767305374146,
1.2083122730255127,
-0.7714791297912598,
-0.2773946225643158,
-0.13654883205890656,
-0.006467587314546108,
0.39836952090263367,
-0.11611326783895493,
-0.3336854577064514,
0.7434395551681519,
0.013214441947638988,
0.4732948839664459,
-1.1856622695922852,
0.1745844930410385,
0.4539017677307129,
-0.5565659403800964,
0.9305194020271301,
0.10302871465682983,
-0.4812900722026825,
-0.3322000205516815,
-0.6305855512619019,
-0.2613440752029419,
-0.23901699483394623,
-0.48366785049438477,
0.3304770588874817,
0.0184849314391613,
-0.6681053638458252,
-1.728917121887207,
-0.46913889050483704,
-0.24831227958202362,
-0.18229451775550842,
-0.24757786095142365,
0.6524677276611328,
0.04128039628267288,
-0.502047061920166,
0.1366613358259201,
-0.785676896572113,
0.059423986822366714,
0.5090396404266357,
0.039005205035209656,
1.0064481496810913,
0.20123375952243805,
0.11442597955465317,
0.8018238544464111,
0.2259581983089447,
0.6770045161247253,
0.43602171540260315,
-0.21759825944900513,
0.014895480126142502,
-0.07703126966953278,
0.4280116558074951,
-0.7823765873908997,
0.4647364318370819,
-0.3254210352897644,
0.5699770450592041,
0.3826371431350708,
0.0060135116800665855,
0.04212508723139763,
-0.5655743479728699,
0.25424328446388245,
0.19446459412574768,
1.050349235534668,
0.7942463755607605,
0.09459392726421356,
0.35741010308265686,
0.011348575353622437,
-0.3421485424041748,
-1.1779277324676514,
-0.3245675563812256,
-0.05359199643135071,
0.1871349960565567,
0.3795911967754364,
0.4783651828765869,
-0.2699625790119171,
-0.0009789582109078765,
0.2912837266921997,
0.43070775270462036,
-0.3628435730934143,
-0.04247044771909714,
-0.2869618237018585,
-0.25306349992752075,
-0.12222127616405487,
0.7403773665428162,
-0.09650978446006775,
0.23649588227272034,
-0.19997505843639374,
0.5646750926971436,
0.3808921277523041,
-0.6591408848762512,
0.8849179744720459,
-0.8577945828437805,
0.5369988083839417,
1.4045324325561523,
0.25982874631881714,
0.283111572265625,
0.24314971268177032,
-0.7055010199546814,
0.3527660369873047,
0.44052496552467346,
-0.3475300967693329,
0.07586418092250824,
-0.526334822177887,
0.2851720154285431,
0.06645780801773071,
-0.23759828507900238,
-0.4604099690914154,
0.42139866948127747,
-0.47996437549591064,
-1.0470900535583496,
0.9825653433799744,
-0.2753065228462219,
0.012369786389172077,
-0.19160374999046326,
-0.727515459060669,
0.16519352793693542,
-0.3307812809944153,
-0.24884910881519318,
-0.1275804191827774,
-0.5695092678070068,
0.2812211215496063,
0.15701961517333984,
-0.06816142797470093,
0.3398103415966034,
0.3421820104122162,
-0.05519384890794754,
0.38661989569664,
-0.763401448726654,
0.34872108697891235,
0.5319892168045044,
-0.04122594743967056,
-0.4922351837158203,
0.5851314663887024,
0.15982012450695038,
-0.1921449601650238,
0.20767907798290253,
-0.17440122365951538,
-0.012799199670553207,
-0.16792099177837372,
0.007775117643177509,
-0.18642060458660126,
-0.42638397216796875,
-0.44582051038742065,
0.09218307584524155,
-0.7135144472122192,
-0.6779263019561768,
-0.7202659249305725,
0.3531637191772461,
-0.24517765641212463,
-0.39874550700187683,
-0.06876059621572495,
0.3577055037021637,
-0.46686071157455444,
-0.1859782189130783,
-1.326144814491272,
-0.02202121540904045,
0.5196576118469238,
-0.1756533980369568,
-0.6919342875480652,
0.4075210690498352,
0.8166530132293701,
-0.2087574303150177,
0.355130136013031,
-0.17551948130130768,
-0.03315894678235054,
0.5564934611320496,
-0.28854721784591675,
-0.18525241315364838,
0.6431332230567932,
0.08409526944160461,
1.1587774753570557,
0.26452937722206116,
-0.0005799102364107966,
1.0187032222747803,
0.014386172406375408,
-0.6125377416610718,
0.09272632747888565,
0.932693362236023,
0.06389451771974564,
0.14170868694782257,
-0.18679504096508026,
0.316905677318573,
-0.06057405099272728,
0.5698813796043396,
0.5124130249023438,
0.43259018659591675,
1.1767542362213135,
0.8009006381034851,
0.7674672603607178,
0.44153621792793274,
-0.9129769206047058,
-0.18485428392887115,
0.6762089729309082,
0.33449143171310425,
0.0599810816347599,
0.6082589030265808,
-0.7477641105651855,
-0.32442113757133484,
-0.4203811287879944,
0.15329618752002716,
-0.20550931990146637,
1.0664604902267456,
-0.1661674827337265,
0.38060539960861206,
-1.2045791149139404,
-0.3638790547847748,
0.14558196067810059,
0.02294379658997059,
0.16429904103279114,
-0.3052119314670563,
-0.03813066706061363,
-0.14192403852939606,
-0.14697879552841187,
-0.599407970905304,
-0.25862011313438416,
0.836129903793335,
-0.5340533256530762,
-0.341291218996048,
0.4046875238418579,
-0.36979350447654724,
-1.1922193765640259,
-0.18407177925109863,
-0.9735549688339233,
-0.24645279347896576,
-0.5957985520362854,
0.36144569516181946,
0.7836092710494995,
-1.0084234476089478,
-0.13032682240009308,
0.3380888104438782,
0.30594122409820557,
0.5325556993484497,
-0.2503349184989929,
0.9983112215995789,
0.22742067277431488,
0.0734989121556282,
-0.6504529714584351,
0.24572287499904633,
-0.6160839200019836,
-0.13573595881462097,
-0.24699667096138,
0.12245975434780121,
0.812829315662384,
-0.5101780295372009,
0.34050190448760986,
-0.2302808314561844,
-0.6835946440696716,
-0.2801343500614166,
-0.1759198009967804,
-0.5165687203407288,
-0.1843731850385666,
0.5268568992614746,
-0.8264710903167725,
-0.8071383237838745,
-0.26131996512413025,
0.6327760815620422,
0.11692198365926743,
-0.3692946434020996,
0.4591739773750305,
-0.013936758041381836,
-0.42077746987342834,
0.6506269574165344,
0.14266225695610046,
-0.20678532123565674,
0.22769781947135925,
0.6346496343612671,
0.6931197643280029,
0.4625757932662964,
0.25108182430267334,
-0.19470477104187012,
-0.9160932302474976,
0.4197167456150055,
-0.00937409233301878,
-0.642884373664856,
-0.054617565125226974,
0.6582286357879639,
0.1904338300228119,
-0.6840492486953735,
0.34137773513793945,
-1.161139965057373,
-0.5832144618034363,
0.09361773729324341,
-0.2536553740501404,
0.7465637922286987,
-0.3300720453262329,
-0.06725745648145676,
-1.0502903461456299,
0.12279658764600754,
0.7194781303405762,
0.36421582102775574,
0.5062369108200073,
-0.03511906787753105,
0.4438951015472412,
0.42228996753692627,
0.3386692702770233,
-0.11357113718986511,
0.13560082018375397,
-0.20326930284500122,
-0.9154389500617981,
0.552583634853363,
-0.5391563177108765,
-0.26905128359794617,
0.11146005243062973,
0.23640264570713043,
0.570372462272644,
0.5146312713623047,
-0.2374705672264099,
-0.7719922065734863,
-0.6638152003288269,
-0.47572675347328186,
0.5796070694923401,
0.5899943709373474,
-0.289256751537323,
0.1462133675813675,
-0.46675023436546326,
-0.024886080995202065,
0.5989415049552917,
-0.03334445506334305,
0.2793307304382324,
-1.221601963043213,
0.7750388979911804,
0.5474010705947876,
-0.6547183990478516,
-0.08713296055793762,
-0.04924875870347023,
0.28108277916908264,
0.3809347152709961,
0.5841807723045349,
0.8535975217819214,
-0.42552149295806885,
-0.26986244320869446,
0.003073732368648052,
0.7069533467292786,
0.03643670678138733,
-0.028296051546931267,
0.29096701741218567,
-0.2544337213039398,
-0.06157389655709267,
-0.4283028244972229,
-0.6488216519355774,
-0.49251052737236023,
-0.0014392519369721413,
-0.7239670753479004,
-0.45080551505088806,
-0.8387513160705566,
0.38480567932128906,
0.7705694437026978,
-0.14043962955474854,
0.21787965297698975,
-0.01005573384463787,
0.15357598662376404,
0.41931453347206116,
0.8348231911659241,
0.816868245601654,
0.10843513160943985,
-0.009177260100841522,
-0.8314965963363647,
0.3800069987773895,
-0.0474274605512619,
0.32195720076560974,
0.038506921380758286,
-0.2763233184814453,
-0.1773802787065506,
-0.43285343050956726,
0.7547491788864136,
0.6358239054679871,
-0.3851075768470764,
0.6244961619377136,
0.32783791422843933,
-0.005086746532469988,
-0.007599396165460348,
0.21590404212474823,
0.7288939952850342,
0.3174578547477722,
0.6065558791160583,
-0.7363343238830566,
0.5944401621818542,
-0.6171776652336121,
0.13220280408859253,
0.3873741328716278,
-0.7906038165092468,
-1.000439167022705,
-0.8007309436798096,
0.4674270451068878,
0.026963084936141968,
-0.2441226840019226,
0.5442648530006409,
0.5589221715927124,
0.6563954949378967,
-0.524603545665741,
-0.47456029057502747,
0.36748719215393066,
-0.5872724056243896,
-0.394011527299881,
0.07419200986623764,
-0.30077940225601196,
-0.04514230787754059,
1.1041665077209473,
0.22866591811180115,
-0.523983895778656,
0.08833465725183487,
-0.191572368144989,
0.3786626160144806,
-0.016388608142733574,
-0.423247754573822,
-0.21026663482189178,
-0.5724648237228394,
-0.2992200553417206,
0.44163283705711365,
0.18656237423419952,
-0.03557928651571274,
0.493434339761734,
-0.1337786167860031,
-0.03993586450815201,
-0.5406658053398132,
0.05837531015276909,
0.44201481342315674,
1.028899073600769,
0.6328526735305786,
0.5440458655357361,
0.3937402069568634,
0.3008638024330139,
-0.020028328523039818,
0.4049946963787079,
-0.1152074933052063,
-0.17790818214416504,
-0.04162931442260742,
-0.48993128538131714,
-0.18745145201683044,
-0.3530195951461792,
-0.723560094833374,
0.45620349049568176,
-0.4604633152484894,
0.6826855540275574,
-0.06432043761014938,
-0.4684024453163147,
0.1314709186553955,
-0.1224282756447792,
-0.5747814178466797,
0.2121778130531311,
-0.3975752294063568,
-1.0392225980758667,
-0.2841759920120239,
-0.9116936326026917,
-0.5234806537628174,
0.1768367439508438,
-0.15562015771865845,
-0.06079987436532974,
0.17479786276817322,
-0.05503544583916664,
-0.15598034858703613,
0.6577953100204468,
-0.3933597505092621,
0.5377130508422852,
-0.624312698841095,
0.1398347020149231,
-0.5150701403617859,
-0.07530765980482101,
-0.4798414707183838,
-0.20693069696426392,
0.1714353710412979,
-0.843906044960022,
-0.2584749162197113,
-0.1899450272321701,
-0.017812367528676987,
-0.09149061888456345,
-0.055831801146268845,
-0.14794421195983887,
-0.5618016123771667,
0.3932630717754364,
0.2642814815044403,
-0.30986112356185913,
0.12543702125549316,
1.147815465927124,
0.17664290964603424,
0.1873624324798584,
-0.11232412606477737,
-0.4855842888355255,
0.046492863446474075,
0.2720099985599518,
0.26452386379241943,
-0.970425009727478,
0.20215319097042084,
-0.0005724165239371359,
-0.20382320880889893,
0.47651657462120056,
0.6073555946350098,
0.10959106683731079,
-0.05098777264356613,
-0.6771554350852966,
-0.24829353392124176,
0.10510516911745071,
-0.6992031931877136,
-0.496379554271698,
-0.6023856401443481,
-0.9053319096565247,
-0.4224812686443329,
0.6176591515541077,
-0.2922038733959198,
0.49191075563430786,
0.2658044099807739,
-0.27875179052352905,
-0.25059372186660767,
0.392710417509079,
0.09763047099113464,
0.06045246124267578,
0.28503644466400146,
0.36231109499931335,
0.2436985820531845,
0.18074265122413635,
-0.43294230103492737,
0.6613881587982178,
-1.3724960088729858,
1.031639575958252,
-0.2534029483795166,
-0.2159055471420288,
-0.3673434257507324,
0.7168948650360107,
0.6515271067619324,
-0.8303447961807251,
0.1853625476360321,
0.4162324070930481,
-0.10626352578401566,
0.5954110622406006,
0.16372743248939514,
-0.17596907913684845,
-0.7996186017990112,
-0.668126106262207,
-0.7093098759651184,
0.5188066959381104,
-0.11543729156255722,
-0.30936142802238464,
-0.5135715007781982,
-0.996708869934082,
-0.4992982745170593,
-0.08229685574769974,
0.7140150666236877,
0.4817711412906647,
0.2784922420978546,
0.30079054832458496,
-0.37094342708587646,
0.6562744379043579,
0.0838962122797966,
-0.4026046097278595,
0.19104258716106415,
-0.278039813041687,
-0.6273049712181091,
0.44515228271484375,
-0.3176993727684021,
-1.3316349983215332,
-0.19834297895431519,
0.5147321820259094,
0.17255325615406036,
-0.43443581461906433,
0.8471395373344421,
-0.4085334241390228,
-0.09042829275131226,
-0.44233253598213196,
0.05269176512956619,
-0.41873466968536377,
-0.1003483310341835,
0.5630210041999817,
-0.14212176203727722,
0.4915659725666046,
0.42088788747787476,
1.0832960605621338,
-0.33799466490745544,
-0.08542948216199875,
0.4563415050506592,
-0.42031624913215637,
-0.10796467959880829,
0.8042973875999451,
-0.13774316012859344,
-0.3643765151500702,
-0.32790035009384155,
-0.5226278901100159,
-0.42136481404304504,
-0.23725080490112305,
-0.5495352149009705,
0.6070763468742371,
-0.31754329800605774,
-0.723414421081543,
0.7207457423210144,
0.5576252937316895,
-0.7046250700950623,
0.017274266108870506,
-0.03623966500163078,
-0.6722996830940247,
-0.5140305161476135,
-0.22579313814640045,
1.2552512884140015,
-0.3947479724884033,
-0.6012493968009949,
-0.20516648888587952,
0.18207556009292603,
-0.44459986686706543,
0.5268242359161377,
0.24150234460830688,
-0.4489745497703552,
0.5167131423950195,
0.34272313117980957,
0.23392637073993683,
0.5447797775268555,
0.08014510571956635,
-0.38664859533309937,
-0.6224782466888428,
0.055227506905794144,
-0.889725923538208,
-1.0937455892562866,
-0.571478009223938,
0.27679580450057983,
0.6346438527107239,
-0.171075701713562,
0.5436167120933533,
0.39693930745124817,
-0.5647465586662292,
-0.02514738030731678,
-1.209198236465454,
0.23300917446613312,
-1.182938814163208,
-0.339387983083725,
-0.04828731715679169,
-0.4679202735424042,
0.27127066254615784,
0.2597489058971405,
0.30143502354621887,
-0.7129819393157959,
-0.4451381266117096,
0.0024637782480567694,
0.6133123636245728,
0.150516077876091,
0.5040552616119385,
-0.5531794428825378,
-0.7161462903022766,
0.17852869629859924,
-0.028713980689644814,
0.19113655388355255,
0.20330810546875,
0.1921205222606659,
0.41806378960609436,
0.32694679498672485,
-0.0937528908252716,
0.6472557783126831,
-0.26279810070991516,
-0.7332959175109863,
0.21662193536758423,
-0.2525631785392761,
-0.8753478527069092,
0.3998171091079712,
-0.5939611792564392,
0.8271263241767883,
-0.3141058385372162,
-0.09674859791994095,
0.255581796169281,
-0.05373530462384224,
-0.7854136824607849,
-0.3308336138725281,
-0.6659586429595947,
0.5010506510734558,
-0.3646751344203949,
-0.5299261212348938,
0.04639074206352234,
0.23611293733119965,
-0.7127866148948669,
0.0775536298751831,
-0.6181851029396057,
0.3493531048297882,
-0.4804794490337372,
0.19328849017620087,
0.1430974155664444,
0.05103294551372528,
-0.1106763407588005,
0.21153193712234497,
-0.5661717653274536,
-0.5052375793457031,
0.26818010210990906,
0.2991059422492981,
-0.7024763822555542,
0.3777370750904083,
0.3931090235710144,
-0.8260194063186646,
0.12216516584157944,
0.44072145223617554,
-0.4359288513660431,
0.656571090221405,
-0.30419036746025085,
-0.7301827669143677,
-0.6480342149734497,
0.5777984857559204,
-0.575390636920929,
0.8248801231384277,
0.6174858212471008,
-0.42522019147872925,
-0.49074944853782654,
-0.6829827427864075,
-0.8683390021324158,
0.782724916934967,
-0.7640985250473022,
0.1141490787267685,
-0.2510060667991638,
-0.7426411509513855,
0.31948453187942505,
-0.4361337423324585,
-0.3420300781726837,
0.9435427784919739,
0.4748404920101166,
0.5453534126281738,
-0.06625863909721375,
-0.03576107323169708,
-0.08147764205932617,
0.4512442946434021,
-0.9559096097946167,
0.04246949031949043,
-0.8222178220748901,
0.7764686942100525,
-0.267943799495697,
-0.6534690260887146,
-0.15293988585472107,
0.7246778607368469,
-0.40243178606033325,
0.17112679779529572,
0.21347925066947937,
-0.2722681164741516,
0.07915868610143661,
0.08461251854896545,
-0.29762184619903564,
-0.10019384324550629,
0.041842538863420486,
0.7072337865829468,
-0.06566797196865082,
-0.40442726016044617,
0.006392780225723982,
0.16239523887634277,
-0.32011502981185913,
0.03958600014448166,
0.036919236183166504,
0.40807828307151794,
0.23121097683906555,
-0.5977143049240112,
0.9878922700881958,
0.08868841826915741,
0.24607446789741516,
0.07492087781429291,
-0.8299890756607056,
-0.23289069533348083,
0.2436676174402237,
0.5976548194885254,
0.625131368637085,
0.554804265499115,
0.1207459345459938,
0.5892888903617859,
0.5747787356376648,
0.2618660628795624,
0.019449567422270775,
0.12220580130815506,
0.5140027403831482,
1.142298936843872,
0.07897187769412994,
0.6350221037864685,
0.4468301236629486,
0.04453098028898239,
-0.0947420746088028,
0.04840944707393646,
-0.2034151703119278,
-0.292028546333313,
0.2042059302330017,
0.5364311337471008,
-0.479606568813324,
-0.3121650815010071,
-0.16074292361736298,
-0.0038488944992423058,
0.19242404401302338,
0.017526792362332344,
0.090692438185215,
0.6732311248779297,
0.5274407863616943,
0.1582651436328888,
0.43777337670326233,
0.3298957943916321,
0.1890505850315094,
0.8775310516357422,
0.24997924268245697,
0.20998714864253998,
0.460512638092041,
0.5527182817459106,
0.460600882768631,
-0.9395419359207153,
-0.06640248745679855,
0.10694888234138489,
-1.2860666513442993,
0.022897491231560707,
-0.11130984127521515,
-0.29915356636047363,
-0.07922809571027756,
-0.5141905546188354,
0.6108612418174744,
-0.6768399477005005,
-0.08967186510562897,
0.74175626039505,
-0.5231437683105469,
0.7773476243019104,
1.3240838050842285,
-0.03722976893186569,
0.3667965233325958,
0.6233055591583252,
0.2090453803539276,
-0.31018245220184326,
1.368674874305725,
1.341112494468689,
-0.2615025043487549,
0.08143540471792221,
-0.00027522252639755607,
-0.5653411746025085,
-0.05164667218923569,
0.6654981374740601,
-0.2079368531703949,
0.4509790241718292,
-0.24692115187644958,
-0.1400729864835739,
-0.10157667845487595,
0.03539926931262016,
-0.26994460821151733,
-0.3496202826499939,
0.13831980526447296,
0.005948166828602552,
-0.4073996841907501,
-0.4188484847545624,
1.0855917930603027,
0.7273043394088745,
-0.5353557467460632,
-0.8607934713363647,
-0.22136980295181274,
-0.36435171961784363,
-0.41165366768836975,
-0.5132746696472168,
0.5405948162078857,
0.2633417546749115,
-0.00895373709499836,
0.015735339373350143,
-0.10817215591669083,
-0.5947396159172058,
-0.8366981148719788,
-0.22973814606666565,
-0.9265603423118591,
0.35673657059669495,
0.11400607973337173,
0.44297730922698975,
0.5604115724563599,
-0.8983204364776611,
0.037822939455509186,
-0.2031499594449997,
0.946534276008606,
-0.18018203973770142,
-0.17836427688598633,
0.44914159178733826,
0.628298282623291,
-0.9663057923316956,
0.5099915862083435,
0.830748975276947,
-0.4983692765235901,
0.6329484581947327,
-0.7266819477081299,
-0.0024623938370496035,
0.3287322521209717,
-0.02351246029138565,
0.44502630829811096,
0.20854999125003815,
-0.05883997678756714,
-0.11201480776071548,
0.01279214397072792,
-0.7722048759460449,
-1.1288634538650513,
0.09356407076120377,
-0.7725270986557007,
0.5083282589912415,
0.06788165867328644,
0.9585809707641602,
0.16415217518806458,
-0.5777971744537354,
4.190948963165283,
1.0284101963043213,
0.5714398622512817,
0.0732545331120491,
0.510459840297699,
0.5970855355262756,
0.04360062628984451,
-0.3193928599357605,
0.2559450566768646,
-0.9701810479164124,
-0.8682259917259216,
0.4293103814125061,
0.09887666255235672,
-0.6897073984146118,
-0.5158916115760803,
0.5456938743591309,
-0.6470119953155518,
-0.24834419786930084,
-0.2731533348560333,
-1.1288195848464966,
-0.4866114556789398,
0.3514982759952545,
0.1550702601671219,
-0.2612067461013794,
0.5427625775337219,
0.10721203684806824,
0.22010818123817444,
-0.8343411087989807,
-0.04404487460851669,
-0.31803444027900696,
-0.601947009563446,
-1.0942050218582153,
-0.4412003755569458,
-0.02375580556690693,
-0.6576231122016907,
0.5809721946716309,
-0.2820252478122711,
-0.3397933542728424,
0.4742394983768463,
-0.2193734347820282,
-0.2486099898815155,
-0.6511641144752502,
0.06924286484718323,
0.08943916857242584,
-1.0476462841033936,
0.7473759055137634,
-0.2701249122619629,
1.195708990097046,
0.4388613998889923,
-0.23437075316905975,
0.35204508900642395,
-0.3873101472854614,
0.45935675501823425,
-0.057193052023649216,
-0.5875632166862488,
0.20961354672908783,
-0.42770904302597046,
-0.31525588035583496,
0.07708553224802017,
0.15780095756053925,
0.6823710203170776,
-0.22411653399467468,
-0.5354264378547668,
0.1358509063720703,
-0.2523673176765442,
0.865391194820404,
-0.19097410142421722,
0.4678725600242615,
-0.49471142888069153,
-0.16180308163166046,
0.10808346420526505,
-0.319787859916687,
-0.49089881777763367,
0.07277953624725342,
0.47149860858917236,
0.0492870956659317,
-0.39511698484420776,
0.10518431663513184,
0.12097972631454468,
-0.0223466157913208,
0.09925981611013412,
0.00813715998083353,
-0.35509300231933594,
0.206503763794899,
-0.08590294420719147,
1.0350977182388306,
-0.182305246591568,
0.0917687639594078,
0.3971896767616272,
0.7204312086105347,
0.3838662803173065,
1.3035569190979004,
0.12402775138616562,
-0.2526171803474426,
-0.9878689646720886
] |
A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through $\beta^{20}$
|
High temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order $\beta^{20}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order $l=0,1,2$. The expansion coefficients through $\beta^{15}$ for the vorticity are also tabulated. Our analysis of the series supports the Kosterlitz-Thouless predictions on the structure of the critical singularities and leads to fairly accurate estimates of the critical parameters.
|
P. Butera and M. Comi (Istituto Nazionale di Fisica Nucleare Dipartimento di Fisica, Universit\`a di Milano Via Celoria 16...
|
hep-lat cond-mat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209011
|
hep-lat/9209012
|
[
0.4714178740978241,
-0.32556846737861633,
-0.4278320074081421,
0.14699400961399078,
0.11063455790281296,
-0.006883108522742987,
-0.1412995308637619,
-0.5394778847694397,
-0.7307808995246887,
1.3709697723388672,
0.9607809782028198,
0.1351553201675415,
0.3241744637489319,
-0.7141470313072205,
-0.4389486312866211,
0.5503610968589783,
-0.6385573744773865,
-0.15968790650367737,
-1.7788456678390503,
0.6285837888717651,
0.3921404778957367,
-0.17719408869743347,
-1.3008261919021606,
-0.37879693508148193,
-0.393179714679718,
0.8842654228210449,
0.4439032971858978,
0.8152020573616028,
1.1971330642700195,
0.5688313245773315,
0.5934169292449951,
-0.1411903202533722,
0.26877158880233765,
-0.5513896942138672,
-0.45852938294410706,
-0.15384380519390106,
-0.3429517149925232,
0.0874609425663948,
0.8684780597686768,
-0.6929261088371277,
0.6703791618347168,
-0.011885460466146469,
0.4787047505378723,
0.11845725774765015,
-0.6650516390800476,
0.14850427210330963,
-0.2229648232460022,
-0.0807674378156662,
0.08476604521274567,
-1.256191372871399,
0.1360030174255371,
0.015558506362140179,
0.6032737493515015,
-0.9317799210548401,
-0.474141389131546,
-0.8182979822158813,
0.5229645371437073,
0.3459547460079193,
-0.4515027105808258,
-0.4979689121246338,
0.802544116973877,
-0.09134312719106674,
0.33647486567497253,
-1.311834454536438,
0.5345222353935242,
0.7227205634117126,
-0.06320184469223022,
0.8134908080101013,
0.4043467938899994,
-0.7566972970962524,
-0.5823573470115662,
-0.8097634315490723,
-0.6112082004547119,
0.02412407658994198,
-0.5216604471206665,
0.26808834075927734,
-0.3577311933040619,
-0.1729370504617691,
-1.5924224853515625,
-0.3272639811038971,
-0.32590222358703613,
-0.6896157264709473,
-0.7339619994163513,
0.17863944172859192,
-0.5712624192237854,
-0.5440476536750793,
-0.10159613937139511,
0.005489252507686615,
0.5607061982154846,
0.29389306902885437,
-0.1242806613445282,
0.6653221845626831,
-0.37831106781959534,
-0.23760002851486206,
0.3704107701778412,
0.5254302620887756,
0.332010418176651,
0.4584669768810272,
0.3004670739173889,
0.04772547259926796,
-0.06348256021738052,
0.3553372621536255,
0.03391621261835098,
0.83411705493927,
-0.48077845573425293,
0.20951002836227417,
-0.15591499209403992,
0.1937798708677292,
-0.7479122877120972,
-0.41936174035072327,
-0.02343117818236351,
-0.2952573001384735,
0.21036534011363983,
0.9730208516120911,
0.5256765484809875,
0.4896188974380493,
0.06624209135770798,
-0.08293818682432175,
-0.8495133519172668,
-0.24333108961582184,
0.15220659971237183,
0.5952392220497131,
0.6362907886505127,
0.6436485648155212,
0.5923326015472412,
0.1531853973865509,
0.5681127309799194,
0.686931312084198,
-0.6807726621627808,
0.22225508093833923,
0.23046739399433136,
-0.12091623246669769,
-0.16857580840587616,
0.22340703010559082,
-0.6915998458862305,
0.2058981955051422,
-0.15356963872909546,
0.03039051964879036,
0.33008381724357605,
-0.09444918483495712,
0.9443391561508179,
-0.9227045774459839,
0.02419654279947281,
0.5866819620132446,
-0.1347803920507431,
-0.18770654499530792,
0.19263364374637604,
0.004319119732826948,
0.06974062323570251,
0.611152708530426,
-0.9338452219963074,
0.2432473748922348,
0.18405641615390778,
0.021880872547626495,
-0.8029032349586487,
0.6775703430175781,
-0.7413097023963928,
0.5162128806114197,
-0.6981841921806335,
-0.6032334566116333,
0.3055495023727417,
-0.3309200704097748,
-0.2971790134906769,
0.18866944313049316,
-0.3052026629447937,
0.34406542778015137,
-0.5604140162467957,
-0.022672535851597786,
0.2400389313697815,
-0.4968539774417877,
0.040620654821395874,
0.44639572501182556,
-0.3708963692188263,
0.6607564091682434,
0.13900357484817505,
0.0032455427572131157,
0.6794100403785706,
-0.7712448835372925,
0.4040759801864624,
0.3001965582370758,
-0.4106152355670929,
-0.5009434819221497,
0.9890177845954895,
0.1957368403673172,
-0.550954282283783,
-0.5857750773429871,
-0.6345610022544861,
-0.37370964884757996,
-0.18694418668746948,
-0.23276512324810028,
-0.3151700794696808,
0.2931012213230133,
-0.33365434408187866,
0.6324594616889954,
-0.7835696339607239,
-0.12323115020990372,
-1.0932942628860474,
0.2887967526912689,
-0.38837990164756775,
-0.4964275658130646,
-0.04398709908127785,
0.741476833820343,
-0.7642992734909058,
0.26638153195381165,
-2.0685625076293945,
-0.0261989738792181,
0.02745339833199978,
0.1607721447944641,
-0.33960670232772827,
0.05512931942939758,
0.2919362485408783,
-0.5526986718177795,
0.17094546556472778,
-0.6720840334892273,
0.0551096573472023,
0.374203085899353,
0.10145612806081772,
0.6569615602493286,
0.19634360074996948,
0.07861600071191788,
0.6143105030059814,
0.7962982654571533,
-0.6898382306098938,
0.7185673713684082,
0.4583014249801636,
-0.7243752479553223,
0.04598037153482437,
0.4702974557876587,
0.24239568412303925,
-0.3700482249259949,
-0.06374240666627884,
0.0628204494714737,
0.22334885597229004,
0.047348182648420334,
0.2672141194343567,
0.6895260810852051,
0.6263378262519836,
0.459764689207077,
0.08985099196434021,
0.6929489970207214,
0.19096611440181732,
0.27022409439086914,
0.5412244200706482,
-0.40891140699386597,
-0.08794672042131424,
0.6615015864372253,
-0.4162128269672394,
0.18828240036964417,
-0.6809276342391968,
0.8302851319313049,
-0.01838979497551918,
0.635279655456543,
0.35755980014801025,
0.6587147116661072,
-0.8100465536117554,
-0.08699025958776474,
0.44087129831314087,
0.03603167086839676,
-0.22677718102931976,
-0.2812652885913849,
0.013105947524309158,
-0.16784287989139557,
0.36467599868774414,
-0.6978192925453186,
-0.6078425645828247,
0.32570680975914,
0.022884724661707878,
-0.1653118133544922,
0.19927839934825897,
-0.24441875517368317,
-0.8893530368804932,
0.19118739664554596,
-0.9539294838905334,
0.061661869287490845,
-0.7748314738273621,
-0.025975758209824562,
0.34430670738220215,
-0.8028240203857422,
0.9960195422172546,
0.06947475671768188,
-0.27983832359313965,
0.5093061923980713,
-0.19907547533512115,
0.693552553653717,
0.6178640127182007,
0.1677824854850769,
-0.6498417854309082,
0.16231323778629303,
-0.9946520328521729,
0.00035992212360724807,
-0.025706883519887924,
-0.20564523339271545,
1.0162510871887207,
-0.031402863562107086,
0.540187656879425,
-0.019191481173038483,
-0.5922682881355286,
-0.042563389986753464,
-0.3072812557220459,
-0.5696799159049988,
0.30728861689567566,
0.6360162496566772,
0.0596625953912735,
0.2399607002735138,
-1.1257482767105103,
0.6153071522712708,
0.946832001209259,
-0.24824558198451996,
0.5229393839836121,
0.022460227832198143,
-0.4981531500816345,
0.46256721019744873,
-0.5868378281593323,
0.1060536578297615,
0.06462190300226212,
0.7669841647148132,
0.6755441427230835,
0.45018112659454346,
-0.3316721022129059,
-0.5090152025222778,
-0.5710815191268921,
-0.11740727722644806,
0.04875292256474495,
-0.46537357568740845,
-0.2094266563653946,
0.6355742812156677,
0.11283392459154129,
-0.6172094345092773,
0.6310492753982544,
-0.9022682905197144,
-0.9303045272827148,
-0.030359243974089622,
-0.7538655996322632,
0.3460317850112915,
0.3944470286369324,
0.14025601744651794,
-0.1603214144706726,
-0.11841189861297607,
-0.18875917792320251,
0.9040113687515259,
0.44798797369003296,
0.3528105914592743,
0.24817273020744324,
-0.14039596915245056,
0.17772400379180908,
0.23099063336849213,
0.02504141256213188,
0.015588859096169472,
-0.04959874227643013,
0.9093145728111267,
-0.3906612694263458,
0.27622243762016296,
-0.222441628575325,
-0.20018190145492554,
-0.05332386493682861,
0.24486209452152252,
-0.10063505917787552,
0.009292423725128174,
-1.2260944843292236,
-0.025339387357234955,
0.6139087080955505,
0.8458833694458008,
-0.0005788637790828943,
-0.35844185948371887,
-0.510870099067688,
0.16947045922279358,
0.12104471772909164,
0.27277064323425293,
0.456245481967926,
-0.4845183491706848,
-0.12463735789060593,
0.1262957751750946,
-0.44350871443748474,
0.11255647987127304,
-0.46903032064437866,
0.2579807639122009,
0.35965240001678467,
0.6201483607292175,
0.27932512760162354,
-0.37899747490882874,
-0.6683533191680908,
0.16130806505680084,
0.8866525292396545,
-0.005498950835317373,
1.036588191986084,
0.38146114349365234,
-0.46451544761657715,
0.18888120353221893,
-0.6606207489967346,
-0.401842325925827,
0.08732053637504578,
-0.24155978858470917,
-0.2999751567840576,
-0.2626022398471832,
-0.09704627096652985,
-0.2441534548997879,
0.3125442564487457,
0.3693183362483978,
0.4992137849330902,
0.04248882830142975,
0.37172016501426697,
0.7211064100265503,
0.35142210125923157,
1.1959551572799683,
-0.16839756071567535,
0.10280132293701172,
-0.8751739263534546,
0.4570998251438141,
-0.02530210092663765,
0.31961292028427124,
-0.21621985733509064,
-0.30644068121910095,
-0.28957974910736084,
-0.7427983283996582,
0.941702663898468,
-0.05411681532859802,
-0.9002330303192139,
0.5201395750045776,
0.17938262224197388,
0.40215152502059937,
-0.27383899688720703,
-0.09679355472326279,
0.4490375518798828,
-0.07487057894468307,
0.16703401505947113,
-0.7773514986038208,
0.45779433846473694,
-0.2122444212436676,
0.2574175298213959,
0.4961533844470978,
-0.33061426877975464,
-0.8469181060791016,
-0.5437014102935791,
0.018157396465539932,
-0.8207482099533081,
0.0005229783710092306,
0.5928049683570862,
0.6717789173126221,
0.1005067303776741,
-0.5979390144348145,
0.04014908894896507,
0.4015246629714966,
-0.9056641459465027,
-0.7137730121612549,
0.3897946774959564,
-0.22085945308208466,
-0.45574063062667847,
0.417883038520813,
-0.1930338740348816,
-0.7415803074836731,
0.15878891944885254,
-0.19371719658374786,
0.190120667219162,
-0.17295894026756287,
-0.4227827489376068,
-0.5040019750595093,
-0.17621693015098572,
-0.4039025902748108,
0.8289933800697327,
0.08373014628887177,
0.17394669353961945,
0.026709115132689476,
0.2745893895626068,
-0.32515081763267517,
0.07330898940563202,
0.4153762459754944,
0.6514085531234741,
0.797668993473053,
0.9697483777999878,
0.3106229901313782,
0.03924037516117096,
0.22897373139858246,
-0.4354844093322754,
0.024833474308252335,
0.11285625398159027,
-0.006890969350934029,
-0.5200352072715759,
-0.3240680694580078,
-0.02771853655576706,
-0.6772729158401489,
-0.4797147512435913,
0.3223634958267212,
-0.47871315479278564,
0.6994143724441528,
-0.21595339477062225,
-0.9583840370178223,
-0.9229373931884766,
-0.6752851605415344,
-0.8315460681915283,
-0.04503579065203667,
-0.02511562779545784,
-0.017649812623858452,
0.8289158344268799,
-0.613884449005127,
-0.014225110411643982,
-0.1443292498588562,
-0.66761314868927,
0.41223013401031494,
0.4413219392299652,
0.8327797055244446,
0.05501218140125275,
0.9552100896835327,
-0.740959644317627,
0.41342106461524963,
-0.04992955923080444,
0.6240803003311157,
-0.2249002605676651,
-0.41696494817733765,
-0.3735583424568176,
0.20698685944080353,
0.22677959501743317,
-0.4768335521221161,
0.3170185685157776,
0.3436584174633026,
-0.007993005216121674,
-0.3789738714694977,
-0.17111241817474365,
-0.845695972442627,
-0.4434908330440521,
0.5515046119689941,
0.257323294878006,
-0.8085028529167175,
-0.10397441685199738,
0.29193007946014404,
0.2584279179573059,
-0.04535762593150139,
0.2819759249687195,
-0.5336831212043762,
0.02933650091290474,
-0.5832998752593994,
0.17757585644721985,
-1.1842397451400757,
-0.7712600827217102,
-0.16455711424350739,
-0.29804158210754395,
0.4087259769439697,
0.532243549823761,
0.4111952781677246,
-0.025507070124149323,
0.07172396034002304,
-0.7296485900878906,
0.1548730581998825,
-0.7877386808395386,
-0.6556565165519714,
-0.04740636795759201,
-0.3256579637527466,
-0.5320470333099365,
0.5428889393806458,
-0.0524476021528244,
0.37337806820869446,
0.34037208557128906,
0.02553415484726429,
0.13680724799633026,
0.31755465269088745,
0.798311173915863,
-0.0741850957274437,
-0.14531569182872772,
0.44739827513694763,
0.0826190635561943,
-0.04735710844397545,
-0.5707530975341797,
0.8552599549293518,
-1.1523743867874146,
1.103447675704956,
-0.5282430052757263,
-0.4509354829788208,
-0.04849987477064133,
-0.16878721117973328,
0.5764234066009521,
-0.776601254940033,
-0.16644792258739471,
0.04199318215250969,
0.30891942977905273,
0.7173837423324585,
-0.32875320315361023,
-0.8384401202201843,
-0.45526939630508423,
-0.2559671700000763,
-0.7121008634567261,
0.46743637323379517,
0.18635277450084686,
-0.19023346900939941,
-0.733517587184906,
-1.369753360748291,
0.14560052752494812,
0.14740411937236786,
0.12665146589279175,
0.31992605328559875,
0.533706784248352,
-0.3684037923812866,
0.09561671316623688,
0.4896871745586395,
-0.2547803223133087,
0.23317600786685944,
-0.15653161704540253,
-0.2629787027835846,
-0.12370865792036057,
-0.2405896782875061,
-0.29262402653694153,
-0.5750662088394165,
-0.1519022285938263,
0.07952020317316055,
0.15597082674503326,
-0.1974734365940094,
0.6631724834442139,
-0.7342464327812195,
-0.3448445796966553,
0.1143568903207779,
0.022757109254598618,
-0.3445395231246948,
0.5492730140686035,
0.6102238297462463,
0.5268835425376892,
-0.021646538749337196,
0.1012677475810051,
0.16370010375976562,
-0.7248697280883789,
-0.08004322648048401,
0.8099741339683533,
-0.9357224106788635,
-0.2631133794784546,
0.6089558005332947,
0.09772881120443344,
-0.42611876130104065,
-0.4216996133327484,
-0.7133296132087708,
-0.42336946725845337,
0.06399649381637573,
-0.414026141166687,
0.11343511193990707,
-0.2555098533630371,
-0.4150623083114624,
0.3649057447910309,
0.6852750182151794,
0.1293339878320694,
0.45538845658302307,
-0.1494642198085785,
-0.1607334166765213,
-0.8384860157966614,
0.10577676445245743,
1.3064528703689575,
-0.727889358997345,
-0.9821255803108215,
0.34516409039497375,
0.16683250665664673,
-0.2614448666572571,
0.08789163827896118,
0.43048256635665894,
-0.285493403673172,
0.6043274998664856,
0.37141260504722595,
0.21516335010528564,
0.12743093073368073,
-0.05994360148906708,
0.3277665078639984,
0.03416186943650246,
-0.042766083031892776,
-0.6785172820091248,
-0.6766853928565979,
-0.5173038244247437,
0.6190629601478577,
0.8273481726646423,
0.22903603315353394,
0.28426793217658997,
0.36902040243148804,
-0.06481441110372543,
0.05003436654806137,
-0.7025181651115417,
0.21505923569202423,
-0.885735034942627,
-0.3778579831123352,
-0.5046876072883606,
-0.35873788595199585,
0.7034577131271362,
0.2576441764831543,
0.17591004073619843,
-0.09031682461500168,
-0.16446562111377716,
-0.7471178770065308,
0.3474673628807068,
-0.2522760033607483,
-0.57465660572052,
-0.4499945342540741,
-0.46293479204177856,
0.41264572739601135,
-0.3725733757019043,
-0.28496280312538147,
0.0533788800239563,
0.89896160364151,
-0.34816867113113403,
0.47068753838539124,
0.028411705046892166,
1.0693188905715942,
-0.7172280550003052,
-0.5211672782897949,
0.20885254442691803,
-0.19441775977611542,
-0.5347239971160889,
0.3788645267486572,
-0.07393376529216766,
0.6314446926116943,
0.6226561069488525,
0.1061595007777214,
-0.37414059042930603,
0.1613604873418808,
-1.0051642656326294,
-0.34602031111717224,
-0.38497012853622437,
0.09991823881864548,
-0.12493742257356644,
-0.5490220189094543,
-0.10640418529510498,
-0.11329132318496704,
-0.8982928991317749,
0.4634328782558441,
-0.5514220595359802,
0.004765884019434452,
-0.41869333386421204,
0.3757568895816803,
-0.33262717723846436,
0.023095274344086647,
0.008711379021406174,
1.1966021060943604,
-0.4691554605960846,
-0.38408464193344116,
-0.5681313276290894,
0.18359899520874023,
-0.18417319655418396,
0.9059523344039917,
0.013363910838961601,
-0.22155973315238953,
-0.3448556363582611,
0.4621414840221405,
0.04809066280722618,
-0.2637682259082794,
-0.1861482411623001,
-0.44314447045326233,
-0.1366589069366455,
0.1345410943031311,
-0.44780468940734863,
1.0115810632705688,
0.5045580267906189,
-0.6192881464958191,
-0.26610618829727173,
-0.6056883335113525,
-0.7824956178665161,
0.04898631200194359,
-0.9810513257980347,
-0.16411863267421722,
0.011783535592257977,
-0.12099279463291168,
0.2546499967575073,
-0.08507087826728821,
-0.525313138961792,
0.14214260876178741,
0.4936332106590271,
0.3503330945968628,
0.17951805889606476,
0.21550384163856506,
-0.4077100455760956,
0.25327128171920776,
-0.5601118206977844,
-0.46274638175964355,
-0.36316975951194763,
0.5124637484550476,
-0.6354183554649353,
-0.7906078696250916,
-0.6515299677848816,
0.22863128781318665,
0.09473033249378204,
0.14262191951274872,
0.07911810278892517,
-0.008648443035781384,
0.004252746235579252,
-0.17314690351486206,
-0.1972169131040573,
0.0698295533657074,
-0.5126849412918091,
0.8723475933074951,
-0.23665010929107666,
-0.8235006928443909,
0.5837425589561462,
0.339651495218277,
0.16904990375041962,
0.4993946850299835,
0.3305487036705017,
0.22393319010734558,
-0.05468183010816574,
-0.5534284114837646,
0.8636358976364136,
0.285195529460907,
0.44217297434806824,
0.41170209646224976,
-0.5910475254058838,
0.21622571349143982,
0.6387960910797119,
0.35330140590667725,
0.5213527083396912,
0.7467537522315979,
-0.23185840249061584,
0.5543851852416992,
0.2907114624977112,
0.11523597687482834,
0.222415491938591,
0.5179543495178223,
0.31140410900115967,
0.15106144547462463,
-0.24920685589313507,
-0.27150291204452515,
0.17244204878807068,
0.1167236939072609,
0.058192797005176544,
0.24293673038482666,
-0.15590623021125793,
-0.033959101885557175,
0.37928837537765503,
0.37912026047706604,
-0.8559145331382751,
-0.527260959148407,
-0.5417172312736511,
0.27595096826553345,
0.39877083897590637,
0.05623902007937431,
0.2510785460472107,
1.128448724746704,
0.7862532734870911,
0.2713961601257324,
-0.06840480118989944,
0.483761727809906,
0.42374885082244873,
0.17660808563232422,
0.30807095766067505,
-0.008448319509625435,
0.9241703748703003,
0.4125291407108307,
-0.11019829660654068,
-0.5661025643348694,
0.019201498478651047,
0.5154924988746643,
-1.7060450315475464,
-0.4232051968574524,
-0.2644241750240326,
-0.04046974331140518,
-0.8418184518814087,
-0.4688025712966919,
0.9163845777511597,
-0.5102947354316711,
0.19064632058143616,
0.6448668241500854,
-0.20466196537017822,
0.7552245259284973,
0.7343397736549377,
0.33348122239112854,
0.2730313539505005,
0.35270753502845764,
0.6203795075416565,
-0.2233693152666092,
0.9046889543533325,
1.4902311563491821,
0.40031084418296814,
0.005688260775059462,
0.24414896965026855,
-0.8510819673538208,
0.48701369762420654,
0.8470789790153503,
-0.014896441251039505,
0.5690772533416748,
-0.2659485638141632,
-0.32096439599990845,
0.029776446521282196,
0.16493362188339233,
-0.006819332484155893,
-0.04059039428830147,
0.2894231677055359,
0.3740849196910858,
-0.24137504398822784,
-0.5816887617111206,
1.6915132999420166,
0.5342122316360474,
-0.6562988758087158,
-0.5406758785247803,
-0.33724504709243774,
-0.521136999130249,
0.2660413682460785,
-0.7342897057533264,
0.43109047412872314,
0.2841832935810089,
0.30375906825065613,
-0.3235144317150116,
-0.8724619746208191,
-0.5104668736457825,
-0.7450554966926575,
0.07459212839603424,
-0.9949014186859131,
0.14947545528411865,
0.6497887969017029,
0.3375932276248932,
0.7360141277313232,
-0.7186874151229858,
-0.163124680519104,
0.024357816204428673,
0.7846373915672302,
-0.507060170173645,
-0.2789131700992584,
0.36634156107902527,
0.6298196315765381,
-0.7040953636169434,
0.5540698170661926,
0.7793989777565002,
-0.8328144550323486,
0.5999428629875183,
-0.5819241404533386,
0.11154411733150482,
0.6755646467208862,
-0.20657965540885925,
0.33636438846588135,
-0.3160148859024048,
0.25451135635375977,
-0.16967177391052246,
-0.3100735545158386,
-0.7101867198944092,
-0.8810644745826721,
0.39046230912208557,
-0.6327731609344482,
0.3276870548725128,
-0.42298179864883423,
0.553450882434845,
0.2892846465110779,
-0.9040311574935913,
4.236715793609619,
1.4457862377166748,
0.6860553026199341,
0.16015392541885376,
0.9879207611083984,
1.0546646118164062,
-0.7513449192047119,
-0.24038392305374146,
0.4098084270954132,
-0.8234201073646545,
-0.5199705362319946,
0.30979040265083313,
0.028030376881361008,
-0.515614926815033,
0.036938730627298355,
0.37759673595428467,
-0.015719005838036537,
0.07534532994031906,
0.09193471074104309,
-1.0512983798980713,
-0.7827022075653076,
0.04859946295619011,
0.33792078495025635,
0.07296730577945709,
0.07968257367610931,
0.19838571548461914,
0.38679006695747375,
-0.37128502130508423,
-0.16163140535354614,
-0.13625119626522064,
-0.7053114175796509,
-0.39177313446998596,
0.3104115426540375,
0.029830757528543472,
-0.8909851312637329,
0.3231316804885864,
-0.482261061668396,
-0.3896157443523407,
0.21580958366394043,
-0.29345861077308655,
0.07518549263477325,
-0.7187475562095642,
-0.39929118752479553,
-0.2975993752479553,
-0.6635420918464661,
0.1766207069158554,
0.08096257597208023,
0.6724130511283875,
0.35339200496673584,
-0.6874299049377441,
0.8014553189277649,
0.06627241522073746,
0.6526567339897156,
-0.1388346403837204,
-1.192328691482544,
-0.2772645056247711,
-0.2758311927318573,
-0.25149568915367126,
0.2867400050163269,
0.10184261202812195,
0.09421356767416,
-0.15082286298274994,
-0.1151755303144455,
0.6900328993797302,
0.2435908168554306,
0.206440731883049,
0.07806681096553802,
0.09127456694841385,
-0.6357026100158691,
-0.02650611661374569,
-0.34009572863578796,
0.32513394951820374,
-0.26868000626564026,
0.3817233443260193,
0.009676939807832241,
-0.03380317986011505,
-0.11647917330265045,
0.5525661110877991,
-0.7228037118911743,
0.42133015394210815,
-0.42585453391075134,
-0.6264659762382507,
-0.20085467398166656,
0.4266979396343231,
-0.19714881479740143,
0.8939403295516968,
0.09155447781085968,
0.2291419506072998,
0.27956250309944153,
0.05737285315990448,
0.10513361543416977,
0.7553942203521729,
0.46673667430877686,
0.19855518639087677,
-0.58408123254776
] |
Rotational Symmetry and Regularization Dependence in the $\Phi^4_4$-Model
|
We study the one component $\Phi^4$ model for four different lattice actions in the Gaussian limit and for the Ising model in the broken phase. Emphasis is put on the euclidean invariance properties of the boson propagator. A measure of the violation of rotational symmetry serves as a tool to compare the regularization dependence of the triviality bound.
|
C.B. Lang and U. Winkler
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209012
|
hep-lat/9209013
|
[
-0.26112687587738037,
0.34935954213142395,
0.47864291071891785,
-0.039771221578121185,
0.34510254859924316,
0.262179434299469,
-0.08256633579730988,
-0.6743118762969971,
-0.785161018371582,
1.0313823223114014,
0.5063171982765198,
-0.3530731499195099,
0.5679948925971985,
-1.556229829788208,
0.3489716351032257,
0.45926326513290405,
-0.5633582472801208,
-0.6626263856887817,
-0.9652446508407593,
-0.24380463361740112,
-0.06405111402273178,
-0.5660746097564697,
-1.182056188583374,
-0.9079625010490417,
-0.3964708149433136,
0.8267481327056885,
-0.449806272983551,
0.38300129771232605,
1.0798168182373047,
0.6366963386535645,
-0.005108049139380455,
-0.3090207278728485,
-0.5212127566337585,
-0.5839969515800476,
-0.3047647774219513,
-0.31229645013809204,
0.19288434088230133,
-0.014637944288551807,
0.37622472643852234,
-0.2986705005168915,
1.000521183013916,
-0.0503770187497139,
0.35371220111846924,
-0.33117637038230896,
-0.32444673776626587,
0.34145015478134155,
-0.38265010714530945,
-0.09047040343284607,
-0.5293740630149841,
-1.0881576538085938,
0.25205713510513306,
0.5305530428886414,
0.8389994502067566,
-0.8695330023765564,
-0.42555147409439087,
0.23541802167892456,
-0.4019652009010315,
-0.12646986544132233,
-0.9805666208267212,
-0.08351913839578629,
0.6240747570991516,
-0.18814688920974731,
1.0211020708084106,
-0.5005784034729004,
0.5605822205543518,
0.9634113907814026,
0.2888689339160919,
0.4040818512439728,
0.2708592414855957,
-0.3403535783290863,
-1.1037299633026123,
-0.4984953999519348,
-0.2100989818572998,
-0.3010316491127014,
-0.6220095753669739,
0.22371132671833038,
-0.20546580851078033,
-0.023100027814507484,
-0.8411243557929993,
-0.5642024874687195,
-0.09359235316514969,
-0.25581246614456177,
-0.809826135635376,
0.8781459331512451,
0.05557401478290558,
-0.21041157841682434,
-0.15719550848007202,
0.008592612110078335,
0.20978304743766785,
0.07054927945137024,
0.14968426525592804,
0.845999538898468,
0.41040053963661194,
-0.16852058470249176,
0.5307029485702515,
0.5532532930374146,
-0.051097750663757324,
0.8311892151832581,
0.06524298340082169,
0.6373143196105957,
-0.07735849916934967,
1.0870767831802368,
-1.1241668462753296,
0.7999152541160583,
-0.4597438871860504,
0.1560186892747879,
0.10929696261882782,
0.15194229781627655,
-0.09799520671367645,
-0.23231181502342224,
-0.08092553168535233,
0.10706889629364014,
0.5166396498680115,
0.8881701231002808,
0.169343039393425,
0.5319316387176514,
0.26147934794425964,
-0.16435657441616058,
-0.4083572030067444,
0.2812555730342865,
-0.3242512047290802,
0.11795840412378311,
0.4088713526725769,
0.5247767567634583,
-0.7216650247573853,
-0.7455803751945496,
-0.027721423655748367,
1.0227687358856201,
-0.032863520085811615,
0.2144014984369278,
-0.15166154503822327,
-0.2026919573545456,
-0.07038700580596924,
1.0928020477294922,
0.11878418177366257,
0.4207899570465088,
-0.08272221684455872,
0.07366624474525452,
0.41539740562438965,
0.1439732164144516,
0.20124170184135437,
-0.5332630276679993,
0.2273644208908081,
0.9979633092880249,
0.04513661935925484,
0.05675072222948074,
0.7304034233093262,
-0.3525228500366211,
0.2033434957265854,
0.18263934552669525,
-1.506655216217041,
0.19528913497924805,
-0.027028588578104973,
-0.6469342112541199,
0.2280307561159134,
0.17205210030078888,
-0.6280260682106018,
1.2676700353622437,
-0.7115431427955627,
-1.093853235244751,
0.5585628747940063,
-0.32657548785209656,
-0.6591177582740784,
-0.2473732978105545,
-0.48278552293777466,
-0.23960110545158386,
0.03406192734837532,
-0.3168381452560425,
0.42523327469825745,
-0.21798411011695862,
-0.040998395532369614,
0.3906618356704712,
0.12485505640506744,
0.5485945343971252,
-0.07099661231040955,
0.5530539155006409,
0.2028072625398636,
-0.10649776458740234,
0.38360998034477234,
0.6348274350166321,
-0.5074060559272766,
-0.486049622297287,
0.7538098692893982,
0.06375718861818314,
0.02743065170943737,
0.3669842779636383,
-0.21997226774692535,
-0.31721675395965576,
-0.09646683931350708,
0.35174560546875,
-0.011944661848247051,
0.652595043182373,
0.06680281460285187,
0.5155556797981262,
-0.4596654176712036,
-0.15293867886066437,
-0.2785373628139496,
0.6837342977523804,
-0.6069852709770203,
-0.39537474513053894,
-0.5069278478622437,
0.4971608519554138,
-0.5515576601028442,
-0.13838090002536774,
-1.3933531045913696,
0.4525797367095947,
0.45009300112724304,
-0.21311387419700623,
-1.087143063545227,
-0.5044564008712769,
0.5922948718070984,
0.0885925218462944,
0.2802303731441498,
0.14650596678256989,
-0.08604302257299423,
0.12297315895557404,
-0.7116599678993225,
0.10701087862253189,
0.9700396656990051,
-0.1571701020002365,
0.49293702840805054,
0.2814898192882538,
-0.8574584126472473,
0.7634966373443604,
-0.29112929105758667,
-0.4135625958442688,
-0.053780898451805115,
0.19217070937156677,
0.4320153594017029,
0.07732586562633514,
0.409451425075531,
1.0405510663986206,
-0.5708544254302979,
0.14024189114570618,
1.3175090551376343,
0.7516559958457947,
0.5481826663017273,
0.8105573058128357,
0.32294565439224243,
-0.04453860968351364,
0.01806921884417534,
-0.2182408571243286,
0.2559308707714081,
0.42685556411743164,
-0.006843733601272106,
-0.25184503197669983,
-0.9366918802261353,
-0.14680996537208557,
-0.3787655830383301,
0.23133449256420135,
-0.9628264307975769,
1.167971134185791,
0.15838027000427246,
0.2525036633014679,
-1.1053365468978882,
-0.563430905342102,
0.024866800755262375,
0.3398175537586212,
-0.27350395917892456,
-0.5026972889900208,
-0.26603230834007263,
0.3019252121448517,
0.5696855187416077,
0.12906138598918915,
-0.04577219858765602,
1.0710698366165161,
0.0753650814294815,
0.13174237310886383,
-0.1653139889240265,
-0.23931430280208588,
-1.2314821481704712,
-0.30526092648506165,
-0.8841145038604736,
0.21162456274032593,
-0.6843885183334351,
-0.539982259273529,
0.944057822227478,
-0.8430519104003906,
0.6979548931121826,
0.019592000171542168,
0.011710548773407936,
0.6483051776885986,
-0.7760778069496155,
0.6080281734466553,
0.7387030124664307,
-0.4854769706726074,
-0.9376224279403687,
0.020664652809500694,
0.04821399971842766,
0.13530820608139038,
0.008657815866172314,
0.7747975587844849,
0.8500372767448425,
-0.4955197870731354,
0.20445546507835388,
-0.4703912138938904,
-0.7233928442001343,
-0.26328861713409424,
0.2570977509021759,
-0.09059444814920425,
-0.32953938841819763,
-0.04421151801943779,
-0.4386347830295563,
-0.16931882500648499,
-0.6813139319419861,
1.2116965055465698,
0.29209667444229126,
-0.298581600189209,
1.1509582996368408,
0.21918128430843353,
-0.1344946324825287,
0.1926780343055725,
-0.5565185546875,
-0.17113648355007172,
0.04064593464136124,
0.9541187882423401,
0.8525424003601074,
-0.03919120877981186,
0.3605523407459259,
-0.5716057419776917,
-0.2198934704065323,
0.0195465087890625,
0.03178931400179863,
-0.9106232523918152,
-0.516607403755188,
0.8047917485237122,
0.4254630506038666,
-0.8162091970443726,
-0.003701678942888975,
-0.9378032684326172,
0.0147376898676157,
-0.2231300175189972,
-0.48628848791122437,
0.9845996499061584,
0.12373857945203781,
-0.3953772485256195,
-0.4961070418357849,
0.1911398470401764,
0.10784012824296951,
0.01654021069407463,
-0.05159300938248634,
-0.23600320518016815,
0.9465517401695251,
0.2081151306629181,
0.2521464228630066,
0.033637966960668564,
0.3599037528038025,
-0.18489614129066467,
0.6127976775169373,
0.5251873135566711,
-0.7198200225830078,
-0.33705249428749084,
0.16084352135658264,
0.41686829924583435,
-0.10744993388652802,
0.5030922293663025,
-0.7350746989250183,
-0.7579415440559387,
-1.0242547988891602,
-0.24153392016887665,
0.731225311756134,
0.45114901661872864,
-0.4557587206363678,
0.6319247484207153,
-0.8608013391494751,
-0.4642796814441681,
0.3536764979362488,
0.34017884731292725,
0.9737539291381836,
-0.239477276802063,
0.27644237875938416,
0.23057834804058075,
-0.006702103652060032,
-0.02157994918525219,
-0.29735463857650757,
0.29334282875061035,
0.25373101234436035,
0.5153876543045044,
1.1199870109558105,
-0.9528123736381531,
-0.2729387581348419,
0.40646740794181824,
1.5444891452789307,
1.2534282207489014,
0.9373955726623535,
0.9881983995437622,
-0.77864670753479,
-0.036530300974845886,
-0.6472902894020081,
-0.49738380312919617,
0.22916369140148163,
0.2264324575662613,
-1.1615548133850098,
-0.650109589099884,
0.205568328499794,
-0.1763480007648468,
0.5599995851516724,
0.550334095954895,
0.5684483051300049,
0.2498120665550232,
0.4227279722690582,
0.42999371886253357,
0.8670022487640381,
0.6694324016571045,
0.22845299541950226,
-0.8616524338722229,
-1.0485045909881592,
0.4020916819572449,
-0.09459880739450455,
0.34670281410217285,
-0.016142893582582474,
-0.7443709969520569,
-0.3374444544315338,
-0.38047513365745544,
0.5099479556083679,
0.4024423658847809,
-0.4936002194881439,
0.5197813510894775,
-0.5909906625747681,
0.004796554800122976,
-0.10826339572668076,
-0.6141851544380188,
0.021059921011328697,
0.7754246592521667,
-0.33549705147743225,
-0.7680879235267639,
0.449649453163147,
-0.18636773526668549,
0.3903605043888092,
0.19734619557857513,
-0.5595446825027466,
-0.853065550327301,
-0.06472314149141312,
0.3168771266937256,
-1.1929365396499634,
-0.4358034133911133,
1.0668810606002808,
-0.4936258792877197,
0.3052787780761719,
-0.7305774688720703,
-0.9834644794464111,
-0.1343964785337448,
-0.1718626320362091,
-0.4124043583869934,
0.1738046258687973,
-0.11549340933561325,
-0.486891508102417,
0.8779928684234619,
-0.17573313415050507,
-0.5115583539009094,
-0.3205570578575134,
-0.033352237194776535,
0.04079475253820419,
-0.24144400656223297,
-0.7435505986213684,
-0.3169299364089966,
-0.7809611558914185,
-0.42295533418655396,
1.072940707206726,
-0.3452267050743103,
0.42387065291404724,
0.6022347211837769,
0.21520228683948517,
-0.2371847778558731,
-0.8676310181617737,
0.05867064744234085,
0.3223085105419159,
0.41984736919403076,
0.950762152671814,
0.9105679988861084,
0.11148934066295624,
0.050594914704561234,
0.42348945140838623,
0.07423531264066696,
0.12472080439329147,
-0.029519228264689445,
0.3024786412715912,
-0.4236556887626648,
-0.25326865911483765,
-1.0121819972991943,
-1.222185492515564,
0.5732219219207764,
-0.21111765503883362,
1.067681908607483,
0.056868720799684525,
-0.24295485019683838,
-0.14923454821109772,
-0.5366536974906921,
-0.6207646131515503,
0.36725524067878723,
0.036095429211854935,
-0.7700139284133911,
0.6197762489318848,
-0.7620153427124023,
-0.09784799814224243,
-0.1106000766158104,
0.49120473861694336,
-0.471318781375885,
0.4813835620880127,
0.07496684789657593,
-0.921737551689148,
0.4923706650733948,
-0.6724222898483276,
0.4558282196521759,
-0.21573291718959808,
-0.11289988458156586,
-0.3818315863609314,
-0.07644639164209366,
-0.1936350166797638,
-0.2105056494474411,
0.14625394344329834,
-0.818298876285553,
-0.10238299518823624,
-0.017866909503936768,
0.6583520174026489,
0.3918169140815735,
-0.3357664942741394,
0.3283432424068451,
-0.7932752966880798,
0.5389496088027954,
-0.09321551769971848,
-0.23685020208358765,
-0.10846482217311859,
1.208616852760315,
0.2503722012042999,
-0.1769268959760666,
0.20188863575458527,
-0.060306116938591,
0.10032285749912262,
0.3117395341396332,
0.30584660172462463,
-0.6905428171157837,
-0.41887131333351135,
-0.40016546845436096,
0.042992450296878815,
0.6120527982711792,
0.7904677987098694,
-0.013948358595371246,
0.0764196366071701,
0.09877675771713257,
-0.9564218521118164,
0.5565654039382935,
-0.19917137920856476,
-0.4153400659561157,
-0.45280393958091736,
-0.18424981832504272,
-0.7479485273361206,
0.9690018892288208,
0.19420009851455688,
-0.1719246804714203,
0.6406676173210144,
-0.13648073375225067,
0.019713615998625755,
0.43875887989997864,
-0.15969698131084442,
-0.15873384475708008,
0.41964203119277954,
0.37867674231529236,
0.1655464917421341,
0.31652674078941345,
-0.7448536157608032,
0.7385342121124268,
-1.112439751625061,
0.9611220359802246,
-0.383043497800827,
0.42414993047714233,
0.36340153217315674,
-0.23152299225330353,
0.8705930113792419,
-0.6436521410942078,
0.26877906918525696,
0.7205019593238831,
-0.012867091223597527,
0.9734020829200745,
0.2331654578447342,
-0.2576179802417755,
-0.3572459816932678,
-1.0632057189941406,
-0.9960438013076782,
0.4510039687156677,
-0.3082674741744995,
-0.5672650933265686,
-0.8350992202758789,
-0.9729315638542175,
0.41734257340431213,
0.09030013531446457,
1.0943270921707153,
0.22626283764839172,
0.12065379321575165,
0.16111032664775848,
0.3398580849170685,
-0.09015610069036484,
-0.11318986862897873,
-0.31435009837150574,
0.4676867723464966,
-0.4379549026489258,
-0.7556814551353455,
0.23565372824668884,
-0.5836337208747864,
-1.312942385673523,
0.030393684282898903,
0.5739742517471313,
0.4737597107887268,
-0.5365748405456543,
0.3546587824821472,
-0.47367605566978455,
-0.5541998744010925,
-0.44570183753967285,
-0.10676542669534683,
-0.3707188665866852,
0.5847168564796448,
0.6930149793624878,
-0.16308365762233734,
0.13680194318294525,
-0.11544989794492722,
0.6450971961021423,
-0.14459411799907684,
-0.6346672177314758,
0.4714764356613159,
-0.4274243116378784,
-0.5702944993972778,
-0.18493817746639252,
0.14868462085723877,
-0.8933500647544861,
-1.2373007535934448,
-0.6658151745796204,
0.17222021520137787,
-0.0381312221288681,
-0.8776795268058777,
0.37597647309303284,
-0.9482831358909607,
-0.4785190522670746,
0.5029563307762146,
0.6068220734596252,
-0.18334494531154633,
-0.580041229724884,
0.0800483226776123,
-1.0554343461990356,
-0.18691131472587585,
0.23025746643543243,
1.3678714036941528,
0.035688500851392746,
0.19933651387691498,
-0.31453222036361694,
-0.5859156250953674,
-0.4143395721912384,
0.5219265222549438,
0.31845128536224365,
-0.5333064198493958,
0.3520105481147766,
0.5916685461997986,
0.39179107546806335,
0.5224182605743408,
0.4639050364494324,
0.2438797503709793,
-0.19639882445335388,
0.6889157891273499,
-0.8407502770423889,
-0.6978214383125305,
0.03565998747944832,
0.3537457585334778,
0.7190358638763428,
-0.4501425325870514,
0.616832435131073,
-0.022787343710660934,
-0.3124125301837921,
-0.4655293822288513,
-0.876833975315094,
0.18236695230007172,
-1.477359652519226,
-0.4594801664352417,
-0.5975024700164795,
-0.5418558120727539,
0.016841638833284378,
0.04850279167294502,
0.6542288661003113,
-0.1363287717103958,
-0.9399168491363525,
0.12986482679843903,
0.7703475952148438,
0.6652807593345642,
0.01651880517601967,
-0.3550108075141907,
-0.5345220565795898,
-0.5095641613006592,
-0.5470525622367859,
0.31705430150032043,
0.3061147630214691,
0.27761131525039673,
-0.5253069996833801,
-0.21876941621303558,
-0.32010576128959656,
0.5483264327049255,
-0.7962300181388855,
-0.2696816027164459,
0.4194197952747345,
0.07612349838018417,
-0.3762141466140747,
-0.253511518239975,
-0.46872541308403015,
0.27097371220588684,
0.35777413845062256,
-0.12178435176610947,
-0.33185693621635437,
0.5552074313163757,
-1.0029700994491577,
-0.5791744589805603,
-0.10929516702890396,
0.9876182675361633,
-0.20367982983589172,
-0.7721409797668457,
0.34849023818969727,
0.1591912806034088,
-0.6977507472038269,
0.29873037338256836,
-0.4098188877105713,
-0.3726804554462433,
-0.18438230454921722,
0.1997470110654831,
0.2359737753868103,
0.48514774441719055,
-0.45494264364242554,
0.6961314678192139,
-0.3701319694519043,
-0.4039967954158783,
0.18113350868225098,
-0.4168373942375183,
-0.17781919240951538,
0.0581183135509491,
0.8776935935020447,
-1.4091057777404785,
0.5218745470046997,
0.4544738233089447,
-0.4281036853790283,
-0.19289442896842957,
-0.5396996736526489,
-0.11360102146863937,
-0.25562575459480286,
-0.668369710445404,
-0.2531651556491852,
0.760715126991272,
-0.30650365352630615,
-0.2333279550075531,
0.1433624029159546,
-0.5370119214057922,
-0.5462306141853333,
0.6237263679504395,
-0.6366501450538635,
-0.37673455476760864,
-0.318916380405426,
-0.01953340694308281,
0.011050194501876831,
-0.14137479662895203,
-0.10444177687168121,
0.5640542507171631,
-0.1078035905957222,
0.2578888237476349,
-0.08716286718845367,
0.09977507591247559,
0.3744335472583771,
-0.1466875672340393,
-0.4162692129611969,
-0.2656647861003876,
0.022419007495045662,
0.6594610810279846,
-0.7095146775245667,
-0.6404931545257568,
-0.21501462161540985,
0.18401826918125153,
-0.15026944875717163,
-0.0157601498067379,
-0.5909534692764282,
0.12087631225585938,
0.3487178385257721,
0.10188108682632446,
-0.2854887843132019,
-0.22447220981121063,
-0.40749281644821167,
0.6600440144538879,
0.1346110701560974,
-0.8653001189231873,
0.37210342288017273,
0.49774646759033203,
0.18868066370487213,
0.12235432118177414,
-0.5193800926208496,
0.44860827922821045,
0.08835222572088242,
-0.36103737354278564,
1.3987417221069336,
-0.24533481895923615,
1.1241497993469238,
-0.14911971986293793,
-0.28397852182388306,
-0.04211832582950592,
0.05879132077097893,
1.0927326679229736,
0.09575893729925156,
0.46290817856788635,
0.02805439941585064,
0.5417975187301636,
-0.018293388187885284,
-0.010981950908899307,
0.051334213465452194,
0.14023925364017487,
0.09454112499952316,
0.6104700565338135,
-0.4840479791164398,
0.44554051756858826,
0.15962862968444824,
0.3109494745731354,
-0.6033939123153687,
-0.1803162842988968,
-0.9108775854110718,
-0.33805787563323975,
-0.16077914834022522,
0.3563113212585449,
0.14196625351905823,
-0.19382035732269287,
0.09263311326503754,
-0.054303109645843506,
-0.026581380516290665,
-0.06714683771133423,
0.3088921904563904,
0.6891875863075256,
0.33599555492401123,
0.3597525954246521,
-0.2288709431886673,
0.2787574827671051,
0.3164202868938446,
0.14524325728416443,
0.002415979979559779,
1.013176441192627,
0.8519120216369629,
0.32245510816574097,
0.41618841886520386,
-1.0324127674102783,
-0.3138614892959595,
0.8612557053565979,
-1.6675002574920654,
0.3201037347316742,
-0.48230165243148804,
-0.3482731282711029,
-0.39136335253715515,
-0.19469445943832397,
0.6416311264038086,
-0.44721561670303345,
0.00307106482796371,
0.7806766033172607,
0.2087046355009079,
0.37114325165748596,
0.6340146660804749,
-0.4192228317260742,
0.5545971393585205,
1.104997992515564,
-0.20099905133247375,
-0.19600582122802734,
0.7656119465827942,
1.0664567947387695,
0.05547843128442764,
-0.02533465437591076,
-0.2124837040901184,
-0.49048763513565063,
0.08552921563386917,
0.25285929441452026,
0.17959555983543396,
1.0030217170715332,
-1.0722085237503052,
-0.6558008790016174,
0.5638611316680908,
0.3564688563346863,
-0.4174874722957611,
-0.1310095638036728,
-0.5732868313789368,
0.4174821078777313,
-0.412676602602005,
-0.3803544044494629,
1.2587007284164429,
0.5325425267219543,
-0.03574240952730179,
0.06275555491447449,
-0.21352270245552063,
-0.2941124439239502,
0.03980017825961113,
-0.5629859566688538,
0.15925171971321106,
0.7989567518234253,
0.1198451891541481,
-0.021231502294540405,
-0.9901562333106995,
-0.4577731192111969,
-0.6014893054962158,
0.41136521100997925,
-0.6231978535652161,
0.7510507106781006,
0.05405152589082718,
0.8047698736190796,
-0.06619561463594437,
-0.6493401527404785,
0.16792801022529602,
0.34166020154953003,
1.4225516319274902,
0.3983403146266937,
0.6349989175796509,
0.4756520390510559,
0.35203537344932556,
-0.7801631093025208,
0.3389807343482971,
0.3508756458759308,
-0.6820048689842224,
0.07384302467107773,
-0.43041545152664185,
-0.08451932668685913,
-0.06588966399431229,
-0.10463227331638336,
0.8900911808013916,
-0.05014843866229057,
0.3564222753047943,
-0.6454986333847046,
-0.2294132113456726,
-0.33327794075012207,
-1.0659077167510986,
0.3927679657936096,
-1.0811303853988647,
0.11124920845031738,
0.7819339036941528,
0.28928542137145996,
0.24678067862987518,
0.04561708867549896,
3.923011064529419,
1.0472943782806396,
0.46778371930122375,
-0.579007089138031,
0.5786333680152893,
0.43966224789619446,
0.03172527998685837,
-0.3774409592151642,
0.4029337465763092,
-0.8308829665184021,
0.12577225267887115,
0.3647814989089966,
0.6958504319190979,
-0.5505141019821167,
-0.06696408241987228,
0.32440322637557983,
0.04556570574641228,
0.21350936591625214,
0.1404954344034195,
-1.1864532232284546,
-0.4275883734226227,
0.4247206747531891,
0.44701141119003296,
-0.2527436912059784,
0.6283435225486755,
-0.44352492690086365,
-0.018432995304465294,
-0.3827735483646393,
-0.7423369288444519,
-0.06526550650596619,
-0.37604063749313354,
-0.9325214624404907,
-0.15431948006153107,
-0.5525298118591309,
-0.7306230664253235,
1.0251750946044922,
0.7668156623840332,
0.2141420692205429,
-0.09790686517953873,
0.985588788986206,
-0.3370591700077057,
-0.18362313508987427,
-0.06346577405929565,
0.35049107670783997,
-0.5153788924217224,
0.8119572401046753,
-0.14639362692832947,
1.0637272596359253,
0.24842119216918945,
-0.6398683786392212,
0.10903172940015793,
-0.6315138936042786,
0.44069916009902954,
-0.5012086629867554,
-1.13121497631073,
-0.0289282388985157,
-0.9591196775436401,
-0.7163590788841248,
-0.08026198297739029,
0.2525573670864105,
0.8802124261856079,
0.15281729400157928,
-0.34354445338249207,
0.3830908536911011,
-0.1912047564983368,
0.5871422290802002,
0.6906726956367493,
0.3608287572860718,
-0.052107688039541245,
-0.11279744654893875,
-0.22791776061058044,
-0.33138707280158997,
-0.8511662483215332,
0.34787946939468384,
0.07249131798744202,
-0.21377672255039215,
-0.31204953789711,
0.8697693943977356,
-0.05944748967885971,
0.08698496222496033,
-0.7061783075332642,
-0.35143953561782837,
-0.5656260251998901,
0.40316587686538696,
-0.1777103841304779,
0.721435010433197,
-0.5007845163345337,
-0.5521873831748962,
-0.2733173370361328,
0.25434067845344543,
-0.22338224947452545,
1.614158272743225,
0.40871259570121765,
-0.659534215927124,
-0.7688054442405701
] |
Surface Tension, Surface Stiffness, and Surface Width of the 3-dimensional Ising Model on a Cubic Lattice
|
We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface tension sigma is obtained by integrating the surface energy density over the inverse temperature beta. We use lattices of size L x L x T, with L up to 64, and T up to 27. The simulations with antiperiodic boundary conditions in T-direction are done with the Hasenbusch-Meyer interface cluster algorithm that turns out to be very efficient. We demonstrate that in the rough phase the large distance behavior of the interface is well described by a massless Gaussian dynamics. The surface stiffness coefficient kappa is determined. We also attempt to determine the correlation length xi and study universal quantities like xi^2 * sigma and xi^2 * kappa. Results for the interfacial width on lattices up to 512 x 512 x 27 are also presented.
|
Martin Hasenbusch and Klaus Pinn
|
hep-lat cond-mat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209013
|
hep-lat/9209014
|
[
-0.22400574386119843,
-0.7300050258636475,
-0.05576614290475845,
-0.18194863200187683,
-0.13066919147968292,
-0.436816930770874,
-0.18512938916683197,
-0.37580838799476624,
0.18463975191116333,
1.1454336643218994,
0.47178781032562256,
0.5476580262184143,
0.3143511116504669,
-0.6276838779449463,
-0.3112107217311859,
0.7357227802276611,
-0.10933076590299606,
-0.5193479657173157,
-1.5780673027038574,
0.6771512031555176,
0.20478259027004242,
0.24801652133464813,
-1.3908936977386475,
-0.5134391784667969,
0.0013092183507978916,
1.0114394426345825,
1.025835633277893,
0.47094297409057617,
1.028626799583435,
0.017373811453580856,
0.08093668520450592,
-0.3953498899936676,
-0.27379438281059265,
-0.2172132432460785,
-0.4345304071903229,
-0.2865380346775055,
-0.47182247042655945,
0.16944141685962677,
0.6135619282722473,
-0.13323834538459778,
0.35957908630371094,
-0.4436943531036377,
-0.06685300916433334,
-0.5923563241958618,
-0.390718013048172,
-0.19329655170440674,
-0.26500046253204346,
-0.27107352018356323,
0.39917269349098206,
-1.2901791334152222,
0.38635653257369995,
0.3611936569213867,
0.9098622798919678,
-0.7212942838668823,
-0.5954601168632507,
-0.43268972635269165,
0.13886205852031708,
-0.2509108781814575,
-0.50884610414505,
-0.07451571524143219,
0.4290265142917633,
0.3136846721172333,
0.40771958231925964,
-0.9185565114021301,
-0.1318730264902115,
0.40736865997314453,
-0.18413743376731873,
0.9775696992874146,
0.12500318884849548,
-0.8024551272392273,
-0.23441094160079956,
-0.3907391130924225,
-1.110174298286438,
0.14397670328617096,
-0.8773596882820129,
0.03779526427388191,
-0.04187869280576706,
-0.1371471881866455,
-1.0267176628112793,
-0.3657469153404236,
-0.03980660066008568,
0.09214241802692413,
-0.18616124987602234,
-0.034471165388822556,
-0.7256690859794617,
0.1132284477353096,
-0.3682958483695984,
-0.16738709807395935,
-0.20416827499866486,
0.5140759348869324,
0.03022315353155136,
1.0788880586624146,
-0.7132485508918762,
-0.3758707344532013,
0.295748770236969,
0.09875825047492981,
0.06665905565023422,
0.3803958296775818,
0.2854745388031006,
0.14185914397239685,
0.016028376296162605,
-0.04865014925599098,
-0.6871755719184875,
0.31746384501457214,
0.15994276106357574,
0.20400653779506683,
-0.24327819049358368,
0.07803413271903992,
0.02551896870136261,
-0.395785927772522,
0.295143723487854,
-0.7240721583366394,
-0.0924922525882721,
0.7364477515220642,
0.12153681367635727,
0.5565154552459717,
0.4460795521736145,
0.37444695830345154,
-0.5673460364341736,
-0.3036477863788605,
0.6091225147247314,
0.13244497776031494,
0.17169588804244995,
0.24416154623031616,
0.13262899219989777,
0.04456188902258873,
-0.32876044511795044,
0.1835051327943802,
-1.011043906211853,
0.5031680464744568,
0.24528801441192627,
-0.46872687339782715,
-0.26673364639282227,
0.04872582480311394,
-0.7776954770088196,
-0.22068911790847778,
-0.38483336567878723,
0.04851812869310379,
-0.042154017835855484,
-0.1765807867050171,
0.7877241373062134,
-0.6149098873138428,
0.3041790723800659,
1.2049694061279297,
0.6376141309738159,
0.5223878622055054,
0.26023364067077637,
0.24853013455867767,
-0.3949287235736847,
0.23241963982582092,
-0.9358749985694885,
-0.6574220061302185,
0.17519481480121613,
0.2845815122127533,
-0.503756582736969,
0.2460298240184784,
0.2781306505203247,
0.20975874364376068,
-0.19754156470298767,
-0.5369760394096375,
0.25522559881210327,
-0.020989516749978065,
0.1620054990053177,
0.1762804090976715,
-0.20766006410121918,
-0.10005504637956619,
-0.19194045662879944,
-0.2057681828737259,
-0.1535743921995163,
-0.6444295644760132,
-0.3455030024051666,
0.22436463832855225,
0.1067052036523819,
0.9850085377693176,
0.2676636278629303,
0.26527926325798035,
0.6116067171096802,
-0.4343993663787842,
0.01720389537513256,
0.5312106013298035,
0.18230518698692322,
-0.08609367907047272,
0.40933889150619507,
0.35059666633605957,
0.5022610425949097,
-0.23415230214595795,
-0.26119229197502136,
-0.16866134107112885,
0.3161725103855133,
0.43680280447006226,
-0.048758238554000854,
0.4599001705646515,
-0.7042336463928223,
0.9965477585792542,
-0.6005308032035828,
0.029476329684257507,
-0.5250170826911926,
0.5313074588775635,
-0.7110820412635803,
0.32892242074012756,
-0.06513915210962296,
0.08349470794200897,
-0.8543459177017212,
-0.08936373144388199,
-0.6759299039840698,
-0.3712964653968811,
0.36983752250671387,
0.9896169900894165,
-0.256963849067688,
-0.12098527699708939,
-0.2732146978378296,
0.015106375329196453,
0.03689766675233841,
-0.6180759072303772,
0.5533957481384277,
0.4640286862850189,
0.18055254220962524,
0.16863541305065155,
0.1548534631729126,
0.5917763113975525,
0.5292773842811584,
0.8737538456916809,
0.1247846707701683,
0.8053931593894958,
-1.0473005771636963,
-0.23949134349822998,
0.19477880001068115,
-0.03315311670303345,
0.11760753393173218,
-0.03342001512646675,
-0.26597848534584045,
0.23222899436950684,
-0.30180588364601135,
0.07457005232572556,
-0.06987372040748596,
0.17441408336162567,
0.22091762721538544,
0.2981209456920624,
0.5178514122962952,
0.3494575619697571,
0.0133657306432724,
-0.1861213743686676,
0.14377279579639435,
-0.3549351990222931,
-0.2674250602722168,
-0.14664393663406372,
-0.08428094536066055,
-0.06906644254922867,
-0.6314918994903564,
0.681505024433136,
0.15206278860569,
0.5044746398925781,
0.050230804830789566,
0.6449205279350281,
-1.0577497482299805,
-0.267939954996109,
0.5513376593589783,
0.05863214284181595,
-0.1841488927602768,
-0.09644787013530731,
0.3379276394844055,
-0.39705559611320496,
-0.10568967461585999,
-0.6989161968231201,
0.02001139335334301,
0.9763177037239075,
-0.2996523678302765,
-0.4109412729740143,
0.47324246168136597,
-0.4023527204990387,
-1.3003774881362915,
-0.5022770762443542,
-0.7646440267562866,
-0.11768367886543274,
-0.705962598323822,
0.2496650069952011,
0.6635130643844604,
-0.8643283843994141,
0.5600078701972961,
-0.6559585928916931,
-0.46613138914108276,
0.39357927441596985,
-0.5859714150428772,
0.6595998406410217,
0.35986757278442383,
0.01888139173388481,
-0.27922484278678894,
0.7133653163909912,
-0.4115571081638336,
-0.39252957701683044,
-0.381685346364975,
0.5701940655708313,
1.2542765140533447,
-0.6074422597885132,
0.64848792552948,
-0.4333045184612274,
-0.22032475471496582,
0.12451305240392685,
0.1868165284395218,
-0.3068462610244751,
-0.052781056612730026,
0.9646697640419006,
0.3326861262321472,
0.17147962749004364,
-1.0526173114776611,
-0.007844356819987297,
-0.17506426572799683,
-0.6015068292617798,
-0.08197061717510223,
0.0006819988484494388,
-0.39378079771995544,
0.41606587171554565,
0.622459352016449,
0.1557312309741974,
0.08098314702510834,
0.6042443513870239,
0.438183069229126,
0.375772088766098,
-0.31252482533454895,
-0.24780841171741486,
-0.2950045168399811,
0.09252811968326569,
0.24285566806793213,
0.12014106661081314,
-0.4461824297904968,
0.44759702682495117,
0.3426365256309509,
-0.5420457124710083,
0.7724356055259705,
-0.9441215395927429,
-0.6079135537147522,
0.41071584820747375,
-0.2901424169540405,
0.26099103689193726,
0.10583017021417618,
0.3969328999519348,
-0.7271286249160767,
-0.18353864550590515,
1.0323269367218018,
0.35431909561157227,
0.1351202428340912,
0.30370235443115234,
0.3149874210357666,
0.11155339330434799,
0.25094568729400635,
0.045603521168231964,
-0.37792709469795227,
-0.11567112803459167,
-0.22885246574878693,
-0.048690252006053925,
-0.5591649413108826,
0.43380218744277954,
-0.012181638740003109,
-0.08915489912033081,
0.18746426701545715,
0.689007043838501,
-0.825897216796875,
-0.37783196568489075,
-0.7171146273612976,
-0.5889734029769897,
-0.1641945093870163,
0.6402543187141418,
0.5537368059158325,
-0.5528249740600586,
-0.36996522545814514,
-0.32262539863586426,
-0.02004839852452278,
0.10802967101335526,
0.18191716074943542,
-0.3822304308414459,
0.2623697519302368,
-0.5246067047119141,
-0.8291417956352234,
0.38371214270591736,
-0.5319634675979614,
0.2608110308647156,
0.7602582573890686,
0.3563869297504425,
1.254285454750061,
-0.5691553354263306,
-0.3934890925884247,
-0.16341103613376617,
0.06511158496141434,
0.13017553091049194,
0.41449880599975586,
0.3289656937122345,
-0.29693353176116943,
0.054370682686567307,
-0.22466225922107697,
-0.18961124122142792,
-0.5504196882247925,
-0.3946068286895752,
0.02997899055480957,
-0.10042206943035126,
0.4506334364414215,
-0.17664611339569092,
0.676803469657898,
0.132619246840477,
0.28134071826934814,
0.5616551041603088,
0.9211001396179199,
0.27983802556991577,
0.23646368086338043,
-0.32283228635787964,
0.10228283703327179,
0.6531828045845032,
-0.37334582209587097,
-0.21910881996154785,
0.4561040997505188,
-0.2097727656364441,
-0.39201340079307556,
-0.46267807483673096,
-0.2913236618041992,
-0.43512147665023804,
0.3845863938331604,
0.43346065282821655,
-1.1835832595825195,
0.48380985856056213,
0.14564654231071472,
0.5425812602043152,
-0.12388593703508377,
0.15268592536449432,
0.5658148527145386,
0.2762082517147064,
-0.00013970842701382935,
-0.7718070149421692,
0.2308882176876068,
-0.23619185388088226,
0.04498688131570816,
0.030055401846766472,
-1.3429441452026367,
-0.4173823595046997,
-0.9111987352371216,
0.008111669681966305,
-0.08816420286893845,
0.5458849668502808,
0.7514926195144653,
0.37601029872894287,
0.35662397742271423,
-0.02982436679303646,
-0.5803622007369995,
0.9318611025810242,
0.25156623125076294,
-0.19786199927330017,
0.41498470306396484,
0.4414590299129486,
-0.1515795886516571,
1.122298002243042,
-0.15327465534210205,
-0.5398964881896973,
0.1949039250612259,
-0.7676352262496948,
0.35487279295921326,
-0.1672825813293457,
-0.07545950263738632,
-0.038960836827754974,
-0.5091007351875305,
-0.8162791728973389,
0.16837601363658905,
0.051358722150325775,
-0.1977253258228302,
-0.6594525575637817,
0.1203039139509201,
-0.09902778267860413,
0.37458643317222595,
-0.27321499586105347,
-0.20703616738319397,
0.9279744029045105,
0.7098791599273682,
0.25028613209724426,
0.11873902380466461,
0.1304614245891571,
0.27319851517677307,
-0.1894686222076416,
0.8412165641784668,
0.3979693353176117,
0.03930092602968216,
-0.22856836020946503,
-0.09617149084806442,
-0.4256387948989868,
-0.5610361695289612,
0.0676455870270729,
-0.33456867933273315,
-0.14582271873950958,
-0.1366906613111496,
-0.7159518003463745,
-0.6923272609710693,
-0.20029345154762268,
-0.43689125776290894,
0.11258084326982498,
-0.05453420802950859,
-0.04806230962276459,
0.7320125699043274,
0.16603951156139374,
-0.015290988609194756,
-1.017885446548462,
-0.028625674545764923,
-0.5108679533004761,
0.5049434900283813,
0.9408093690872192,
0.13397298753261566,
0.04609091207385063,
-1.107483983039856,
0.42288628220558167,
-0.4659025967121124,
0.26919984817504883,
-0.7096208333969116,
-0.23746345937252045,
-0.13802482187747955,
0.1069374531507492,
0.052296921610832214,
0.39134481549263,
-0.3523328900337219,
-0.030243748798966408,
0.005470796953886747,
0.43232855200767517,
-0.08033276349306107,
-0.4284108281135559,
-0.2743799388408661,
0.2659217119216919,
-0.22184139490127563,
0.2184184193611145,
-0.4515652358531952,
-0.13434520363807678,
0.134847491979599,
0.7625688314437866,
0.07507534325122833,
-1.0945641994476318,
-0.35831528902053833,
-0.16047200560569763,
0.49899810552597046,
-0.8440423607826233,
-0.3465430736541748,
-0.251971036195755,
-0.4673926532268524,
-0.04074656963348389,
0.19525060057640076,
0.25761517882347107,
-0.8685290813446045,
-0.3850695788860321,
-0.24056749045848846,
0.35244977474212646,
-0.350037157535553,
-0.44944319128990173,
-0.376099556684494,
-0.5071309208869934,
-0.04942459613084793,
0.5879061222076416,
-0.3082560896873474,
0.4965188503265381,
-0.11160360276699066,
0.13765843212604523,
0.2154894471168518,
0.5948837995529175,
0.022211000323295593,
-0.11791523545980453,
0.003870190354064107,
-0.0850374698638916,
-0.06834612786769867,
0.4704289734363556,
-0.6995263695716858,
0.21183596551418304,
-1.2778396606445312,
0.5354869365692139,
-0.058893561363220215,
-0.6275714635848999,
0.467413991689682,
-0.0816132128238678,
0.5813032984733582,
-0.6184693574905396,
0.2926033139228821,
0.22425557672977448,
0.042204730212688446,
0.4552607536315918,
0.4301135838031769,
-1.0421216487884521,
0.013322604820132256,
-0.6596464514732361,
-0.5020862817764282,
0.36296725273132324,
0.15305757522583008,
-0.13100284337997437,
-0.6855481266975403,
-0.4585622549057007,
0.028218047693371773,
-0.16492675244808197,
0.27872711420059204,
0.35200950503349304,
-0.2608444392681122,
0.21301910281181335,
-0.09259293973445892,
-0.525380551815033,
0.030044224113225937,
0.059197235852479935,
-0.198012113571167,
0.648811399936676,
0.1957770138978958,
0.577246904373169,
-1.144745111465454,
-0.6216663718223572,
-0.12122178822755814,
0.39925774931907654,
0.7223227024078369,
-0.11588739603757858,
0.6515927314758301,
0.45860591530799866,
0.11120117455720901,
-0.2773928940296173,
0.28748568892478943,
-0.34653323888778687,
0.2082550823688507,
0.2856241762638092,
0.5613270998001099,
0.3517502248287201,
0.20295867323875427,
0.26791515946388245,
-0.17871740460395813,
-0.4617810547351837,
0.6033815741539001,
-0.9308532476425171,
-0.27078697085380554,
0.3673759698867798,
0.12378343939781189,
-0.9445451498031616,
-0.5079099535942078,
-0.965266227722168,
0.09700298309326172,
-0.7553309202194214,
-0.002805710071697831,
-0.5586065053939819,
-0.5506749749183655,
-0.8503156304359436,
0.4091803729534149,
0.9817185997962952,
0.14925925433635712,
0.11269837617874146,
-0.42484667897224426,
-0.11608175188302994,
-0.1606292575597763,
-0.30785417556762695,
1.6235707998275757,
0.12851843237876892,
-1.103551983833313,
0.07426843792200089,
0.29583412408828735,
-0.16273309290409088,
-0.1348097026348114,
0.49521568417549133,
-0.2021753489971161,
0.6408946514129639,
0.24902810156345367,
0.2540600299835205,
0.5785295367240906,
1.1052944660186768,
-0.0882914811372757,
0.28213945031166077,
-0.0821896344423294,
-0.7737931609153748,
-0.25209930539131165,
-0.6635783910751343,
0.26488134264945984,
0.49971437454223633,
0.21691246330738068,
0.17203788459300995,
0.4208146631717682,
-0.27431121468544006,
0.03796866163611412,
-1.2381446361541748,
-0.07463187724351883,
-1.1677665710449219,
-0.20338977873325348,
-0.13264647126197815,
-0.1753281056880951,
0.07081744074821472,
0.7045022249221802,
-0.35026225447654724,
0.32181990146636963,
-0.5892170667648315,
0.5515867471694946,
0.3741183578968048,
0.30666583776474,
-0.7233133316040039,
-0.7282061576843262,
0.24957001209259033,
-0.3337841331958771,
-0.7297652363777161,
0.23416700959205627,
-0.48863381147384644,
0.1840187907218933,
-0.1433202177286148,
0.3630910813808441,
0.30806222558021545,
0.9764869809150696,
-0.7043883204460144,
-0.8675462007522583,
0.5084847807884216,
0.0494961254298687,
-1.302627444267273,
0.3396574854850769,
0.44046634435653687,
0.6601410508155823,
0.761364221572876,
-0.32943710684776306,
-0.33071810007095337,
0.15512177348136902,
-0.5435927510261536,
0.29313862323760986,
0.15022477507591248,
0.7482689023017883,
-0.31393224000930786,
-0.28732219338417053,
-0.6314995288848877,
0.686860978603363,
-0.9880568981170654,
0.17715154588222504,
-0.4952855408191681,
0.5794970989227295,
-0.4645688235759735,
0.13979612290859222,
0.07713465392589569,
0.24064096808433533,
0.1250561773777008,
1.654396891593933,
0.20210251212120056,
-0.10717913508415222,
-0.14836256206035614,
0.12390995025634766,
-0.2852526903152466,
0.17433468997478485,
0.06362876296043396,
-0.7624411582946777,
-0.6315323114395142,
0.5728888511657715,
-0.02653883956372738,
0.38388654589653015,
0.3106182813644409,
-0.4440057873725891,
-0.38329634070396423,
-0.5214446187019348,
-0.6857956647872925,
0.3094047009944916,
0.7850298881530762,
-0.913220226764679,
0.46451810002326965,
-0.19325044751167297,
-0.6250370740890503,
0.69789719581604,
-0.5452930331230164,
-0.4901534914970398,
-0.020444922149181366,
-0.28949278593063354,
0.1802733689546585,
0.08020719140768051,
-0.040139853954315186,
-0.326813668012619,
-0.04426099732518196,
0.8265725374221802,
-0.5378186106681824,
-0.20229749381542206,
-0.28783705830574036,
0.4311586916446686,
-0.6231158971786499,
-0.34739211201667786,
-0.6783363223075867,
0.40757688879966736,
-1.055635929107666,
-1.178716778755188,
0.44806787371635437,
0.9337165355682373,
-0.5927405953407288,
-0.5323141813278198,
-0.008861184120178223,
-0.3435719609260559,
-1.079189419746399,
-0.43033504486083984,
-0.586527407169342,
-0.6234109401702881,
-0.7346820831298828,
-0.05304209142923355,
-0.23610354959964752,
-0.10977433621883392,
0.07271863520145416,
0.5776656866073608,
0.40580588579177856,
-0.0221759844571352,
-0.18452778458595276,
1.0991313457489014,
0.4569971263408661,
-0.46661949157714844,
0.7807665467262268,
0.5975257754325867,
0.09970594197511673,
0.19950485229492188,
-0.6011961698532104,
0.5854067206382751,
0.34211888909339905,
-0.2513086795806885,
0.7105785608291626,
0.14386388659477234,
0.33055296540260315,
-0.04309658333659172,
0.2611726224422455,
0.2908152937889099,
0.06796468794345856,
0.7405726909637451,
0.11754505336284637,
0.5790019631385803,
-0.03818029537796974,
0.398906409740448,
0.23833464086055756,
-0.28082871437072754,
-0.44665324687957764,
-0.046641018241643906,
-0.49156680703163147,
0.010670114308595657,
-0.26923754811286926,
-0.36973196268081665,
-0.6359558701515198,
-0.04887085780501366,
0.06599750369787216,
0.15367700159549713,
0.5038998126983643,
-0.03830746188759804,
-0.12585198879241943,
0.6071560382843018,
0.909109354019165,
-0.3237324059009552,
-0.005448850337415934,
0.8809341192245483,
-0.7713398933410645,
1.3505668640136719,
0.3763849139213562,
0.3511335849761963,
0.4873237609863281,
0.5679677724838257,
-0.05293991416692734,
-0.38026002049446106,
0.08691182732582092,
0.3769955039024353,
-0.5910584926605225,
-0.4081747829914093,
-0.24959801137447357,
0.1575220823287964,
0.03348396345973015,
-0.11669400334358215,
0.5121376514434814,
-0.44016340374946594,
0.38703909516334534,
0.4699118137359619,
-0.02071032114326954,
-0.15994952619075775,
0.6429248452186584,
0.19414487481117249,
0.20040453970432281,
0.8984357118606567,
0.13328824937343597,
-0.32613158226013184,
1.3441734313964844,
1.1875720024108887,
-0.029123684391379356,
0.7259680032730103,
0.37215617299079895,
-0.46598052978515625,
0.14109599590301514,
0.7299091219902039,
-0.5491335391998291,
0.21862901747226715,
-0.6649763584136963,
-0.6220723986625671,
-0.13082239031791687,
0.06282868981361389,
-0.09809644520282745,
-0.2183830589056015,
0.6452476382255554,
-0.15097704529762268,
-0.16421180963516235,
-0.25889796018600464,
1.2194470167160034,
0.2831417918205261,
-0.38261139392852783,
-0.19266724586486816,
0.37533310055732727,
-0.32694050669670105,
-0.28883036971092224,
-0.6435935497283936,
0.38605785369873047,
-0.3127119243144989,
-0.8441364169120789,
0.16519008576869965,
0.1448243260383606,
-0.6721881031990051,
-0.23413656651973724,
-0.07239849120378494,
-0.4422815144062042,
0.25232237577438354,
0.5184880495071411,
0.4778589904308319,
0.4531286060810089,
-0.8922708630561829,
0.04405112564563751,
-0.2688978314399719,
0.686916708946228,
-0.5861568450927734,
0.20771783590316772,
0.5943669676780701,
0.45731255412101746,
-0.6395815014839172,
0.1572074443101883,
1.0532110929489136,
-0.5800749063491821,
0.6653444766998291,
-0.1803804636001587,
1.116121768951416,
0.8937045931816101,
-0.48472630977630615,
0.4988323748111725,
0.5525075197219849,
0.020931314677000046,
0.09729333966970444,
-0.7482519745826721,
0.07289743423461914,
-0.9349961280822754,
0.6052613854408264,
-0.7756837010383606,
0.8611180186271667,
-0.8032604455947876,
-0.34940412640571594,
0.22530941665172577,
-0.7812861800193787,
4.316821575164795,
0.025868358090519905,
0.7799714207649231,
0.4208872318267822,
0.18086552619934082,
0.7808772325515747,
-0.06396857649087906,
-0.40150216221809387,
0.4241868257522583,
-0.4641984701156616,
-0.18617263436317444,
0.28686654567718506,
0.3832707703113556,
-0.11582233011722565,
0.22102275490760803,
0.8401186466217041,
-0.4743279814720154,
-0.18507717549800873,
0.4479479193687439,
-0.9470076560974121,
-0.411022812128067,
-0.035989463329315186,
0.30359408259391785,
0.18944081664085388,
0.02609175629913807,
0.03359818458557129,
0.5099314451217651,
-0.8448530435562134,
-0.46797192096710205,
-0.23454226553440094,
-0.8016224503517151,
-1.1930806636810303,
0.3957439064979553,
-0.2469296157360077,
-0.9488969445228577,
0.5375702381134033,
0.27986133098602295,
0.3291884660720825,
-0.3043382465839386,
0.14657680690288544,
0.07498539984226227,
-0.3178556263446808,
0.9117478728294373,
-0.6951272487640381,
-0.17429642379283905,
0.7503399848937988,
-0.30362361669540405,
0.9939671158790588,
0.8268243670463562,
-0.5397480726242065,
0.7529091835021973,
-0.07789122313261032,
0.2815217673778534,
-0.5646966099739075,
-0.8736058473587036,
0.07144726812839508,
-0.6446741223335266,
0.07431723922491074,
0.2891087830066681,
0.023596463724970818,
-0.003993129823356867,
0.00448123924434185,
-0.3296995162963867,
0.009872297756373882,
-0.10847704112529755,
0.09214488416910172,
0.08258292824029922,
0.4490147531032562,
-0.324922114610672,
-0.5149459838867188,
-0.25671255588531494,
-0.6012458205223083,
-0.1770717352628708,
0.3264806270599365,
0.879979133605957,
0.15079882740974426,
-0.12450389564037323,
-0.13327975571155548,
0.21267782151699066,
-0.5041110515594482,
0.12802697718143463,
-0.6542766094207764,
-0.9357412457466125,
-0.3869416117668152,
-0.06367490440607071,
0.6448226571083069,
-0.48302194476127625,
0.06396634131669998,
0.2733655571937561,
0.6782150864601135,
0.15417100489139557,
1.1843572854995728,
0.2304612398147583,
0.7204226851463318,
-0.97059166431427
] |
Glueballs and Hybrid Mesons
|
We discuss states in the meson spectrum which have explicit gluonic components. Glueballs (with no valence quarks) and hybrid mesons (with valence quarks) are both reviewed. We present in some detail lattice simulation results. ( to appear in proceedings of QCD-20 years, Aachen Workshop)
|
Chris Michael
|
hep-lat hep-ph
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209014
|
hep-lat/9209015
|
[
-0.11323666572570801,
-0.45501986145973206,
-0.35938432812690735,
0.34322816133499146,
0.07779417186975479,
0.06521313637495041,
0.1487332284450531,
-0.36494165658950806,
-0.7562796473503113,
1.339126706123352,
0.25985243916511536,
0.05714600905776024,
0.7020308971405029,
-0.9410493969917297,
-0.02997816540300846,
0.3963136076927185,
0.15853077173233032,
-0.37125271558761597,
-1.5575910806655884,
0.46088212728500366,
0.7720032930374146,
-0.07409686595201492,
-0.7955808043479919,
-0.7675754427909851,
-0.0707697793841362,
1.2298897504806519,
0.6015955805778503,
0.27885282039642334,
1.1594822406768799,
0.784062922000885,
0.38111504912376404,
-0.542481541633606,
-0.39737194776535034,
-0.6553066372871399,
-0.5510983467102051,
-0.47525501251220703,
-0.7936931252479553,
-0.6972967982292175,
0.4468964636325836,
-0.46176475286483765,
0.6848810315132141,
-0.10063720494508743,
-0.24814921617507935,
-0.29945582151412964,
-0.6877642869949341,
0.43766599893569946,
-0.795352041721344,
-0.11056652665138245,
0.30934590101242065,
-1.3012408018112183,
0.6066293716430664,
0.3022519052028656,
0.7511450052261353,
-0.867439329624176,
0.22949856519699097,
-0.40942972898483276,
-0.06151334196329117,
0.5075487494468689,
-0.5114452242851257,
-0.6398217678070068,
-0.13505591452121735,
-0.22152817249298096,
0.005238812416791916,
-0.6369588375091553,
0.12674811482429504,
0.3985689580440521,
-0.1971108615398407,
0.754091739654541,
0.18316544592380524,
-0.5227749347686768,
-0.2419404536485672,
0.12548434734344482,
-1.2058796882629395,
0.032703641802072525,
-0.8609264492988586,
-0.007866432890295982,
-0.08186483383178711,
-0.17907623946666718,
-1.5605266094207764,
-0.7098020911216736,
-0.24143323302268982,
-0.44161567091941833,
-0.15464138984680176,
0.5638391971588135,
-0.10390316694974899,
-0.3850301206111908,
-0.15027114748954773,
-0.3348783254623413,
0.06933210045099258,
0.5119159817695618,
0.650351345539093,
1.1205514669418335,
-0.008218332193791866,
-0.38172316551208496,
0.8165308237075806,
0.30412015318870544,
-0.3866109848022461,
0.7614847421646118,
0.07566320151090622,
0.01600036397576332,
0.5109838247299194,
0.5698351860046387,
-0.5131759643554688,
0.8804095387458801,
-0.500773012638092,
0.20926398038864136,
-0.5955120325088501,
0.1428879052400589,
0.07981470227241516,
-0.300628125667572,
0.5206194519996643,
-1.0883718729019165,
0.5895993709564209,
0.5716713070869446,
0.08106987923383713,
0.3151884078979492,
-0.04191799834370613,
0.39724981784820557,
-0.488576203584671,
-0.2216738760471344,
0.44949471950531006,
-0.03579232469201088,
0.7541854977607727,
0.7968109846115112,
-0.4755515456199646,
-0.28430408239364624,
0.297014981508255,
0.7435738444328308,
-0.5270054936408997,
0.26237305998802185,
0.29523515701293945,
0.42840445041656494,
-0.4062865376472473,
0.1966077834367752,
-0.6760413646697998,
-0.2468094676733017,
-0.748382568359375,
0.19018618762493134,
0.77311772108078,
-0.4767471253871918,
0.5705229640007019,
-0.6316314935684204,
0.22257351875305176,
1.1474196910858154,
0.125359907746315,
0.6758400797843933,
0.3647657632827759,
0.15717235207557678,
-0.09213478118181229,
0.055174291133880615,
-0.7971279621124268,
-0.16756823658943176,
0.3288682699203491,
0.6767610907554626,
0.49196478724479675,
0.7325599789619446,
-0.21978849172592163,
0.5148199796676636,
-0.22383183240890503,
-0.5687541961669922,
0.14283056557178497,
-0.0847192108631134,
0.031969163566827774,
0.03936757892370224,
-0.4910314381122589,
0.16912488639354706,
-0.29075542092323303,
-0.6515576839447021,
0.10844403505325317,
-0.6419421434402466,
0.31254708766937256,
0.7336811423301697,
-0.2469577044248581,
0.792377233505249,
0.8544960021972656,
0.22604359686374664,
0.48362693190574646,
-0.8593921065330505,
-0.3061859905719757,
0.03469768539071083,
0.15891727805137634,
-0.6190280318260193,
0.13001419603824615,
0.5116207599639893,
-0.5176572203636169,
0.011338373646140099,
0.16039371490478516,
-0.3677631914615631,
0.2795940339565277,
-0.06446698307991028,
-0.20914143323898315,
0.5094759464263916,
0.7653634548187256,
0.7736328840255737,
-0.3303658664226532,
1.3233187198638916,
-1.3650672435760498,
0.4347667396068573,
0.1470087468624115,
-0.11292016506195068,
-0.11545752733945847,
0.12243244796991348,
-0.7917333841323853,
0.291531503200531,
-1.1907577514648438,
0.15713517367839813,
1.435184121131897,
0.32362425327301025,
-0.28170791268348694,
-0.5354400277137756,
0.09372970461845398,
0.4001321792602539,
0.37555551528930664,
-0.7630202770233154,
0.47104141116142273,
-0.0051223584450781345,
-0.040786512196063995,
0.3147304952144623,
-0.3156961500644684,
0.21039709448814392,
-0.30018502473831177,
0.773436427116394,
-0.18183544278144836,
0.7928440570831299,
-0.35887807607650757,
-0.9178266525268555,
-0.06907426565885544,
0.5547022223472595,
-0.0777878388762474,
-0.07955378293991089,
-0.015324476175010204,
0.09182053059339523,
-0.1402597278356552,
0.7384955883026123,
-0.09829337149858475,
-0.4271557629108429,
0.9463562965393066,
0.6585823893547058,
0.4394865036010742,
0.9513805508613586,
-0.36422961950302124,
0.4390098750591278,
0.567717432975769,
-0.23882713913917542,
-0.4419434070587158,
0.06848105043172836,
-0.6242832541465759,
0.3160640299320221,
-0.6290819048881531,
0.7752718925476074,
-0.640995442867279,
-0.3394911587238312,
0.03273333981633186,
0.34200042486190796,
-1.345151424407959,
-0.4546467363834381,
-0.6967906951904297,
0.206180602312088,
-0.06511329859495163,
0.0894402340054512,
0.08244078606367111,
0.26813915371894836,
0.17461423575878143,
-0.547209620475769,
-0.3779345750808716,
0.5570968985557556,
-0.04448224976658821,
-0.2297109216451645,
0.34956231713294983,
-0.09036034345626831,
-1.0978327989578247,
-0.006341282743960619,
-1.1142405271530151,
0.5200314521789551,
-1.2873696088790894,
0.10495208203792572,
0.7238331437110901,
-0.6301955580711365,
1.3065603971481323,
-0.3339768350124359,
-0.7154752016067505,
0.4251111149787903,
-0.09943889081478119,
0.3347991108894348,
0.3026817739009857,
-0.060094356536865234,
-1.156758427619934,
0.26071467995643616,
-0.6293998956680298,
-0.6638278365135193,
-0.7646645307540894,
-0.6552417874336243,
1.0440561771392822,
-0.29969096183776855,
0.5451750755310059,
0.35586559772491455,
0.022761045023798943,
-0.1730690747499466,
0.10465210676193237,
-0.649742841720581,
-0.10438696295022964,
0.050977084785699844,
-0.27452126145362854,
0.09572581201791763,
-1.507420539855957,
0.533793568611145,
-0.312078595161438,
-0.06218922138214111,
0.08008358627557755,
0.031984101980924606,
-1.2724096775054932,
0.7074099779129028,
0.32804250717163086,
-0.16657701134681702,
-0.12965022027492523,
1.248740315437317,
0.2756245732307434,
-0.0642731711268425,
-0.03647921234369278,
-0.41306790709495544,
-0.4404103755950928,
0.5848281383514404,
0.25627803802490234,
-0.6070469617843628,
0.09905548393726349,
0.29601991176605225,
-0.27010613679885864,
-0.4269503355026245,
0.5295954942703247,
-0.8175548911094666,
-0.43858587741851807,
0.2090977430343628,
-0.6364539861679077,
0.2637823820114136,
0.01736518181860447,
-0.21041898429393768,
-0.7827950716018677,
-0.44866475462913513,
0.5827298164367676,
0.2987169921398163,
0.4722718894481659,
0.1985979676246643,
0.32601872086524963,
0.7808457612991333,
0.3819725811481476,
-0.4353393614292145,
-0.4201161563396454,
-0.2775656282901764,
-0.4127292037010193,
0.10837695002555847,
-0.29429569840431213,
0.5078015327453613,
-0.2661316692829132,
0.4315110146999359,
0.3902973532676697,
0.4633944034576416,
-0.007021965924650431,
-0.7387097477912903,
-0.3659708499908447,
0.18041305243968964,
0.18444448709487915,
0.8039580583572388,
0.2127809077501297,
-0.8019835948944092,
-1.2889245748519897,
-0.6146911382675171,
-0.5034589171409607,
-0.15309050679206848,
0.8377442955970764,
-0.9854570031166077,
0.7404240369796753,
0.6117225885391235,
-0.27234014868736267,
0.3996165692806244,
-0.4533175528049469,
0.3785499036312103,
0.12291044741868973,
-0.5494309663772583,
0.806959331035614,
-0.6268739104270935,
-0.7389158010482788,
0.30917903780937195,
0.12488565593957901,
0.25283366441726685,
0.6221634149551392,
0.13218025863170624,
-0.2858524024486542,
0.16137832403182983,
-0.33550044894218445,
0.05370229855179787,
-0.22400759160518646,
-0.5894331932067871,
-0.3246389329433441,
0.33651062846183777,
0.09648088365793228,
-0.11173160374164581,
0.45537909865379333,
0.7464938163757324,
0.3337596356868744,
0.3884424865245819,
0.753460705280304,
0.8848691582679749,
0.874678373336792,
0.701610803604126,
-0.48275819420814514,
0.48846009373664856,
-0.888446569442749,
0.3333144187927246,
0.5419299006462097,
-0.05789561569690704,
0.051262352615594864,
-0.016921116039156914,
0.40010860562324524,
-0.12212290614843369,
0.5078961849212646,
0.06714613735675812,
-0.800277829170227,
0.17384366691112518,
0.6961185932159424,
0.12691564857959747,
0.015946315601468086,
-0.28768017888069153,
1.4299371242523193,
-0.027562187984585762,
0.7698680758476257,
-0.8955554366111755,
-0.12045058608055115,
-0.4472368061542511,
0.11999823898077011,
0.3763408362865448,
-1.295054316520691,
-0.6770074367523193,
-1.417413592338562,
0.013460258953273296,
-0.6312246322631836,
0.1356276422739029,
0.8774570822715759,
0.6717501282691956,
0.674282431602478,
-0.6877228617668152,
0.11794404685497284,
0.49650686979293823,
-0.5773456692695618,
-0.14325441420078278,
-0.11704043298959732,
0.23110008239746094,
0.07754149287939072,
0.7752324342727661,
0.2161528617143631,
-0.643348217010498,
-0.00457497825846076,
-0.5929500460624695,
-0.00773956160992384,
-0.03727559745311737,
-0.283895879983902,
-0.6419633626937866,
-0.39111146330833435,
0.12272895872592926,
0.4563157260417938,
0.15290795266628265,
-0.6446806192398071,
-0.31704479455947876,
0.08165675401687622,
0.22249437868595123,
0.17657050490379333,
0.5484858155250549,
0.41159912943840027,
1.3093100786209106,
0.4572703242301941,
0.5883973240852356,
0.27634352445602417,
-0.9871236681938171,
0.33111679553985596,
-0.08405043184757233,
0.37771332263946533,
-0.12391098588705063,
-0.3119593858718872,
-0.1746026575565338,
-0.4101426601409912,
-0.45103752613067627,
-0.34602102637290955,
0.8863667249679565,
-0.1642535775899887,
-0.08483286947011948,
-0.214694082736969,
-0.8822795748710632,
-0.29696160554885864,
-0.49932435154914856,
-1.1067125797271729,
0.479360431432724,
0.0817878246307373,
-0.03080492839217186,
0.8947460055351257,
-0.3925143778324127,
0.5122889280319214,
-1.0290462970733643,
-0.5415289402008057,
-0.10905376076698303,
-0.16368404030799866,
1.1031981706619263,
0.6458035111427307,
0.7220189571380615,
-0.38803622126579285,
-0.07139312475919724,
-0.20950739085674286,
0.4944680631160736,
-0.039356593042612076,
-0.2736184298992157,
-0.4273192286491394,
-0.16892167925834656,
0.15353511273860931,
0.0999244973063469,
0.2693111300468445,
0.0028711166232824326,
0.4491030275821686,
-0.18477869033813477,
0.1335410177707672,
-0.1401902735233307,
-0.09214422106742859,
0.6032323837280273,
0.43356040120124817,
-0.2208220213651657,
0.07666367292404175,
0.942440927028656,
-0.540606677532196,
0.28873375058174133,
0.36042824387550354,
-0.36451002955436707,
0.031629882752895355,
-0.6041549444198608,
0.9291669726371765,
-0.9321728348731995,
-0.36869049072265625,
0.16629037261009216,
-0.20009537041187286,
0.6338659524917603,
0.4490000903606415,
-0.2665006220340729,
-0.31258901953697205,
-0.6967296004295349,
-0.29363077878952026,
0.4157218635082245,
-0.05502818897366524,
-0.00008939737745095044,
-0.208585724234581,
-0.8961796760559082,
-0.5737943649291992,
1.1007678508758545,
-0.03189534693956375,
0.19574487209320068,
0.09294351935386658,
0.39641422033309937,
0.2910345196723938,
0.2345363199710846,
0.09998038411140442,
-0.2248236984014511,
-0.10836167633533478,
0.06169021129608154,
-0.08374162763357162,
0.68438321352005,
-0.39439070224761963,
0.5290533304214478,
-0.9684147834777832,
0.14012648165225983,
-0.23752249777317047,
-0.5235835313796997,
0.09304805099964142,
0.03649231046438217,
1.1224608421325684,
-0.6647329330444336,
0.5521641969680786,
0.3468902111053467,
0.2837507724761963,
0.10502322018146515,
-0.26884928345680237,
-0.5156042575836182,
-0.5682218074798584,
-0.8885908722877502,
-1.2504217624664307,
0.3851403594017029,
-0.2224632352590561,
-0.25368213653564453,
-0.3711393177509308,
-0.7162022590637207,
0.5118311047554016,
-0.09455721825361252,
0.4146861433982849,
0.20579399168491364,
0.39743638038635254,
0.1981404423713684,
0.1936188042163849,
-0.5290008783340454,
-0.4375835955142975,
-0.07758451998233795,
-0.02815343625843525,
-0.1079326942563057,
0.10630596429109573,
0.02482381835579872,
-0.3607422709465027,
-0.8025025725364685,
-0.282193660736084,
0.28737008571624756,
-0.14112168550491333,
-0.42754361033439636,
0.4424801766872406,
0.2099638432264328,
-0.10610910505056381,
-0.03862309083342552,
0.572526752948761,
0.4231388568878174,
0.5685800909996033,
0.751006007194519,
0.8752357959747314,
0.2528185546398163,
0.0808420404791832,
0.39846089482307434,
-0.8173488974571228,
-0.6073856353759766,
0.7725673913955688,
-0.31711164116859436,
-0.14599210023880005,
0.6636931300163269,
0.25377774238586426,
-0.1613759845495224,
0.25748366117477417,
-0.3566688895225525,
-0.35175561904907227,
0.028857897967100143,
-0.2622751295566559,
-0.32353705167770386,
-0.23787526786327362,
-0.22911114990711212,
0.6225979924201965,
0.45528286695480347,
0.2176554799079895,
0.6146080493927002,
0.4540197551250458,
-0.2301870882511139,
-0.1850387006998062,
0.3420483469963074,
1.6364961862564087,
0.09251081198453903,
-1.1795316934585571,
0.018197055906057358,
-0.21062038838863373,
-0.19279883801937103,
-0.4088405966758728,
0.9180461168289185,
-0.095675989985466,
0.11668983101844788,
-0.061969030648469925,
0.7156798839569092,
0.7120325565338135,
0.2962191104888916,
-0.5821464657783508,
0.37268078327178955,
-0.42225199937820435,
-0.6525028347969055,
-0.10166733711957932,
-0.5277736186981201,
-0.24944794178009033,
0.41867220401763916,
-0.25909140706062317,
-0.3880682587623596,
0.38168901205062866,
0.024208132177591324,
-0.5777377486228943,
-0.9387919306755066,
-0.44041624665260315,
-0.9045988321304321,
-0.10186497867107391,
-1.0521140098571777,
-0.2790667712688446,
0.11356250196695328,
0.2734443247318268,
-0.1990080326795578,
-0.17541377246379852,
-0.32347625494003296,
0.5714787244796753,
0.12978963553905487,
0.6219951510429382,
-0.2889161705970764,
-0.7506635785102844,
-0.4591085612773895,
-0.3920702338218689,
-0.36234021186828613,
0.08777903765439987,
-0.17475876212120056,
-0.5321548581123352,
-0.035833653062582016,
0.2622126638889313,
0.23642607033252716,
0.6807310581207275,
-0.2813696265220642,
-0.6877502202987671,
-0.2066030502319336,
-0.5369811058044434,
-0.3912694752216339,
0.6994307041168213,
0.012110761366784573,
0.7423704266548157,
0.9515642523765564,
0.8446111679077148,
0.021179988980293274,
0.33856073021888733,
-0.927791178226471,
0.1671166867017746,
0.25603729486465454,
0.6856862306594849,
-0.5193608403205872,
-0.5839477181434631,
-0.659620463848114,
0.1214267760515213,
-0.9307170510292053,
0.36364689469337463,
-0.6530171632766724,
0.15321092307567596,
-0.7959810495376587,
-0.08062700182199478,
0.6208347678184509,
0.25824856758117676,
0.06498850882053375,
0.6845976114273071,
-0.36052992939949036,
0.08887363970279694,
0.3625350594520569,
0.2566789388656616,
-0.14583992958068848,
0.20347116887569427,
0.0401667021214962,
-0.48107025027275085,
-0.04915948957204819,
-0.033755943179130554,
0.1320391595363617,
0.6645565032958984,
0.01932302489876747,
-0.6577196717262268,
-0.6508689522743225,
-0.591533362865448,
-0.33305031061172485,
0.6684169769287109,
0.5480614900588989,
-0.5332363247871399,
0.8650355935096741,
-0.8258997797966003,
-0.9082638621330261,
-0.32330551743507385,
-0.6327308416366577,
-0.20688363909721375,
0.08588055521249771,
-0.28918543457984924,
-0.33650609850883484,
0.5281319618225098,
-0.46597233414649963,
0.32378095388412476,
0.284884512424469,
0.8320542573928833,
0.18731240928173065,
-1.1128090620040894,
-0.3544793725013733,
0.02076847106218338,
-0.9095739722251892,
-0.4246658384799957,
-0.4358299672603607,
0.7305118441581726,
-0.09555204212665558,
-0.7447678446769714,
0.2355574071407318,
0.20599864423274994,
0.1881653368473053,
-0.49658849835395813,
-0.1361141800880432,
-0.1741582453250885,
-0.14078468084335327,
-0.09481987357139587,
-0.011182958260178566,
-0.6697311401367188,
-1.5076676607131958,
-0.29674988985061646,
0.42525264620780945,
-0.4643058180809021,
0.1606166809797287,
0.49957475066185,
-0.04906117543578148,
-0.5475183725357056,
-0.6185172200202942,
1.0444135665893555,
0.19571420550346375,
0.16088958084583282,
0.7259508967399597,
0.38565248250961304,
-0.6237683892250061,
-0.20128019154071808,
-0.37170517444610596,
0.23779526352882385,
0.03181847929954529,
0.7099206447601318,
1.0078086853027344,
0.44498369097709656,
0.3959963917732239,
0.2391006350517273,
0.3542306423187256,
-0.016303619369864464,
0.21332228183746338,
-0.4314735233783722,
0.19320565462112427,
0.750789225101471,
0.05448660999536514,
-0.3020906448364258,
-0.006545115727931261,
-0.16206005215644836,
0.5928434133529663,
-0.41085541248321533,
-0.6014270186424255,
-0.22559329867362976,
0.490547776222229,
-0.119056336581707,
-1.2442325353622437,
-0.28551551699638367,
-0.29494616389274597,
0.117325559258461,
0.9056119918823242,
-0.1645578294992447,
-0.3698555827140808,
0.2526223957538605,
0.5230242609977722,
0.08768055588006973,
-0.46609926223754883,
0.33877310156822205,
0.2024581879377365,
1.1367440223693848,
0.8045607805252075,
-0.10459963977336884,
0.5538787245750427,
0.9981710910797119,
0.17735432088375092,
-1.1897822618484497,
-0.12210148572921753,
0.2333834022283554,
-0.23213158547878265,
0.4070265591144562,
0.09909757226705551,
-0.4662090241909027,
0.026610203087329865,
-0.0918930321931839,
1.021393895149231,
0.5192699432373047,
0.12434136122465134,
0.24463330209255219,
-0.6749911904335022,
-0.306267112493515,
0.6851794719696045,
-0.0070000821724534035,
0.422607421875,
0.3304908275604248,
-0.03890182450413704,
-0.18162493407726288,
0.3980509638786316,
1.3802319765090942,
0.016608456149697304,
0.2571633756160736,
-0.020621035248041153,
-0.2602536380290985,
0.09829770773649216,
0.25290194153785706,
-0.48944413661956787,
0.6471707224845886,
-0.6049864888191223,
0.36012789607048035,
0.14364981651306152,
0.43866851925849915,
0.3826380670070648,
-0.2412521243095398,
0.4298345446586609,
0.22505556046962738,
-0.8575478792190552,
-0.6301984190940857,
1.2213844060897827,
0.5880303978919983,
-0.5881590247154236,
-0.48932787775993347,
0.18711687624454498,
-0.8113770484924316,
-0.44030964374542236,
-1.0492260456085205,
0.3491455316543579,
-0.6554543375968933,
0.010373339988291264,
-0.5450838804244995,
-0.44806036353111267,
0.0055797346867620945,
-0.3428793251514435,
0.5940380692481995,
-1.0124528408050537,
0.2750895321369171,
0.6793763637542725,
-0.17757689952850342,
0.627341628074646,
-0.3502599596977234,
-0.6118036508560181,
-0.05928632244467735,
0.8611264228820801,
-0.18712206184864044,
-0.2192329466342926,
0.6728748679161072,
0.2247796654701233,
-0.30024781823158264,
0.3964534103870392,
0.5414328575134277,
-0.6930099725723267,
0.8890560269355774,
-0.7612410187721252,
0.29411816596984863,
0.5562580823898315,
-0.5088422894477844,
0.24885761737823486,
-0.29854512214660645,
0.3815743923187256,
0.31004598736763,
-0.19263491034507751,
-0.38685745000839233,
-0.23319514095783234,
0.23948107659816742,
-0.7116706371307373,
0.15784160792827606,
-0.058475565165281296,
-0.11111170798540115,
0.1275525987148285,
-1.085062026977539,
4.030919551849365,
0.38265737891197205,
0.8062173128128052,
0.45013317465782166,
0.6124051213264465,
1.5871775150299072,
-0.39905616641044617,
0.5736797451972961,
0.41397595405578613,
-1.2799885272979736,
-0.8174934387207031,
0.22259783744812012,
0.21218647062778473,
-0.12900851666927338,
0.34244289994239807,
1.0311285257339478,
-0.1525787115097046,
0.0677681490778923,
-0.2393607646226883,
-0.8766096234321594,
-0.41929197311401367,
-0.05330314114689827,
0.07492265105247498,
-0.14765046536922455,
0.12998750805854797,
-0.26729196310043335,
-0.3426404595375061,
-0.8921160697937012,
-0.8658817410469055,
-0.6929040551185608,
-0.6596735715866089,
-0.7827275991439819,
-0.19984890520572662,
-0.11753903329372406,
-1.4229294061660767,
0.01742350310087204,
0.17949645221233368,
-0.15833742916584015,
-0.18517763912677765,
-0.05398755893111229,
-0.6869242191314697,
-0.38493794202804565,
0.5552421808242798,
-0.9209390878677368,
-0.1076495423913002,
0.781310498714447,
-0.39939823746681213,
0.5142677426338196,
0.5038202404975891,
-0.469860315322876,
0.6695765852928162,
0.2212630659341812,
0.6399275064468384,
-0.5258541107177734,
-0.4553936719894409,
0.4989083707332611,
0.13161751627922058,
-0.28624027967453003,
-0.08665300160646439,
0.3421086072921753,
-0.024385055527091026,
-0.2830813527107239,
-0.11958151310682297,
0.12632280588150024,
0.1793801188468933,
0.16543422639369965,
0.15854935348033905,
-0.14070232212543488,
-0.17609824240207672,
0.07878297567367554,
0.3164829909801483,
-0.8776463866233826,
-0.37612786889076233,
0.7435648441314697,
-0.002795492298901081,
0.3242722749710083,
-0.16433501243591309,
1.2329602241516113,
0.2852839231491089,
0.4029920995235443,
-0.5447274446487427,
0.030365152284502983,
-0.647235095500946,
-0.30119770765304565,
0.001525230472907424,
0.4678865075111389,
-0.43089571595191956,
-0.25246116518974304,
-0.6988070607185364,
0.023754799738526344,
0.39402204751968384,
1.4715288877487183,
0.3552362620830536,
-0.07425543665885925,
-0.2546254098415375
] |
Chern-Simons term and Topological Charge on the Lattice
|
In a somewhat overlooked work by Seiberg, a definition of the topological charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and L\"{u}schers charge definition are related up to the section of the bundle. With the continued interest in baryon number violating processes, Seibergs paper is useful since it allows for a Chern-Simons number also.
|
M.L.Laursen
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209015
|
hep-lat/9209016
|
[
0.17813004553318024,
0.6337078809738159,
0.38432684540748596,
-0.13484680652618408,
0.19238480925559998,
-0.36104995012283325,
0.12911978363990784,
-0.22483709454536438,
-0.8405470252037048,
1.3261877298355103,
1.0493756532669067,
-0.24145953357219696,
1.1342498064041138,
-1.4188278913497925,
0.015115584246814251,
0.39037418365478516,
-0.6325616240501404,
-0.7967520356178284,
-0.5364258289337158,
-0.45045995712280273,
0.3370613157749176,
-0.34984561800956726,
-1.5651813745498657,
-0.8271774053573608,
-0.5105569362640381,
0.6256109476089478,
0.3985153138637543,
0.41642093658447266,
1.4482320547103882,
0.4734605550765991,
0.04233741760253906,
-0.4853913486003876,
-0.13718155026435852,
-0.6353361010551453,
-0.10921766608953476,
-0.6792742013931274,
0.32947614789009094,
0.02992500178515911,
0.5821884870529175,
-0.38833653926849365,
0.887142539024353,
0.10004055500030518,
0.5061416029930115,
-0.613592803478241,
-0.7450175285339355,
0.002197388093918562,
-0.15727436542510986,
-0.3686578869819641,
0.11741016805171967,
-1.1082559823989868,
0.5058397054672241,
-0.26156842708587646,
0.558279275894165,
-0.7679643034934998,
-0.21005599200725555,
0.4980602264404297,
-0.6205858588218689,
-0.2828774154186249,
-1.0349637269973755,
-0.4476899206638336,
0.7445507049560547,
0.34548598527908325,
1.3947874307632446,
-0.753122091293335,
0.6294703483581543,
1.0966796875,
0.20164074003696442,
0.37388578057289124,
0.015243948437273502,
0.04952916130423546,
-0.9580623507499695,
-0.8381631970405579,
-0.6470964550971985,
-0.01774418354034424,
-0.6142220497131348,
0.09362244606018066,
-0.5517773628234863,
0.3341641128063202,
-1.2324707508087158,
-0.5695044994354248,
-0.30297723412513733,
-0.32208842039108276,
-0.9061267971992493,
0.9502890706062317,
-0.15337350964546204,
-0.3918139934539795,
0.5472103953361511,
0.10559210926294327,
-0.03435731679201126,
-0.009669219143688679,
-0.17444726824760437,
0.7194664478302002,
0.540439784526825,
-0.3838326334953308,
0.4448058605194092,
0.7359187006950378,
0.02506295219063759,
0.8344686627388,
0.16968487203121185,
0.4671986401081085,
-0.01931101642549038,
1.2565629482269287,
-1.1244040727615356,
0.33806750178337097,
-0.4018520712852478,
-0.2407015711069107,
-0.11560818552970886,
0.039505671709775925,
-0.014897673390805721,
-0.44077178835868835,
-0.3457159101963043,
-0.29311299324035645,
0.23582327365875244,
0.9912645816802979,
-0.20871220529079437,
0.6375325322151184,
-0.012570480816066265,
0.19698920845985413,
-0.5759618878364563,
0.1121748834848404,
-0.06904478371143341,
0.4106229245662689,
0.31691184639930725,
0.19715479016304016,
-0.42212459444999695,
-0.7332130074501038,
0.050927408039569855,
0.9465200304985046,
-0.6882472038269043,
0.0896167978644371,
-0.1919572353363037,
-0.14464105665683746,
-0.26842647790908813,
1.1838161945343018,
-0.06718006730079651,
0.47757020592689514,
0.14198054373264313,
0.5168898701667786,
0.5283043384552002,
-0.16574007272720337,
0.5741821527481079,
-0.1326308399438858,
0.18968559801578522,
1.391078233718872,
0.1800035834312439,
0.34347692131996155,
0.24251501262187958,
-0.9116653203964233,
0.206464484333992,
0.34766221046447754,
-1.393144965171814,
0.26937130093574524,
-0.3505539000034332,
0.15674227476119995,
-0.21109291911125183,
0.45853617787361145,
-0.803554356098175,
1.158087968826294,
-0.7933737635612488,
-0.9031271934509277,
-0.10842953622341156,
-0.5716128349304199,
-0.5287984013557434,
-0.1909632831811905,
-0.277651846408844,
0.08152642846107483,
-0.02293681725859642,
-0.04535747691988945,
0.052655238658189774,
-0.6270985007286072,
-0.043613582849502563,
0.4395679831504822,
0.30784133076667786,
0.8192336559295654,
-0.2142750769853592,
0.828424870967865,
0.17527800798416138,
-0.4359881281852722,
0.15171177685260773,
0.4181258976459503,
-0.5302571058273315,
-0.3789080083370209,
0.711983859539032,
0.12760601937770844,
0.29549238085746765,
0.5051249861717224,
-0.5167618989944458,
-0.3140072226524353,
-0.5150833129882812,
0.5911659002304077,
0.07670410722494125,
0.870294988155365,
-0.05233735591173172,
0.9759907722473145,
-0.340663880109787,
-0.18086445331573486,
-0.017973730340600014,
0.3548387885093689,
-0.7021185755729675,
-0.47190943360328674,
-0.5575882196426392,
0.9368755221366882,
-0.5968880653381348,
0.18192240595817566,
-1.312968373298645,
0.04404248669743538,
0.4303385615348816,
-0.2785048186779022,
-0.9988853335380554,
-0.3194099962711334,
0.5452960133552551,
0.45480453968048096,
0.3748544454574585,
-0.504852294921875,
0.31112542748451233,
0.21778245270252228,
-0.49507445096969604,
-0.4669439494609833,
0.9355190992355347,
-0.5517837405204773,
0.719356119632721,
0.34614694118499756,
-0.7322791218757629,
0.8862532377243042,
-0.26108667254447937,
-0.4014292061328888,
0.3654530644416809,
0.30951669812202454,
0.024466311559081078,
0.13627563416957855,
0.1639849990606308,
1.07866632938385,
-0.20458915829658508,
0.4661073386669159,
1.1681239604949951,
0.6686308979988098,
0.5760408043861389,
0.8961151242256165,
0.29314205050468445,
-0.3123334050178528,
0.18898533284664154,
0.07341255247592926,
0.7012858986854553,
0.7591050863265991,
-0.016443708911538124,
0.20124311745166779,
-0.6024842262268066,
0.2687055766582489,
-0.35978323221206665,
0.08224803954362869,
-0.609516978263855,
1.4017103910446167,
0.17828664183616638,
0.049651797860860825,
-0.7840939164161682,
-0.5499097108840942,
0.3562605381011963,
0.5161666870117188,
-0.32602202892303467,
-0.47383350133895874,
-0.5936377644538879,
0.2590930461883545,
0.18819789588451385,
0.40287962555885315,
-0.6508434414863586,
1.2777754068374634,
0.5725845694541931,
-0.18532535433769226,
0.029441334307193756,
-0.40150925517082214,
-1.287890076637268,
-0.31307175755500793,
-0.7829598784446716,
-0.054549507796764374,
-0.33192211389541626,
-0.21209508180618286,
1.1669477224349976,
-0.7812280654907227,
0.7980350255966187,
-0.32934102416038513,
-0.38075438141822815,
0.8046692609786987,
-0.3332503139972687,
0.5066206455230713,
0.8668696284294128,
-0.5064302086830139,
-0.7352738380432129,
-0.17575755715370178,
-0.32749655842781067,
0.29934173822402954,
-0.11633459478616714,
0.3817148804664612,
0.7420123219490051,
-0.42051243782043457,
0.17140710353851318,
-0.5663313865661621,
-0.922829806804657,
-0.5244665145874023,
0.2860221862792969,
-0.5233011245727539,
-0.06599043309688568,
0.28804469108581543,
-0.07921398431062698,
-0.22444067895412445,
-0.6911843419075012,
0.8842995166778564,
0.48270782828330994,
-0.4160590171813965,
1.320786952972412,
0.579716682434082,
-0.5510303378105164,
0.5270703434944153,
-0.48719877004623413,
-0.40521758794784546,
0.03329528123140335,
0.5915903449058533,
0.7251911163330078,
0.15477629005908966,
0.5137500166893005,
-0.43210074305534363,
-0.5809020400047302,
-0.04166370630264282,
-0.489722341299057,
-0.578288733959198,
-0.4712456166744232,
1.1406145095825195,
-0.12907437980175018,
-1.1699143648147583,
0.2516694664955139,
-0.8790044188499451,
-0.5569667816162109,
0.1146654263138771,
-0.41255080699920654,
0.8559126257896423,
0.13699094951152802,
0.13965964317321777,
-0.6171184182167053,
0.326123982667923,
0.3684576153755188,
0.6155478954315186,
0.2845367193222046,
-0.6351580619812012,
1.240148901939392,
0.22525247931480408,
0.724369466304779,
-0.6584343314170837,
0.7253460884094238,
-0.11144490540027618,
0.20159493386745453,
0.3473776578903198,
-1.0648326873779297,
0.11894544959068298,
0.16625921428203583,
0.47237929701805115,
-0.19054165482521057,
0.4645130932331085,
-0.6588138341903687,
-0.3779432773590088,
-0.8822909593582153,
-0.10849333554506302,
0.2039739489555359,
0.5851291418075562,
-0.5148725509643555,
0.962856650352478,
-0.6565322875976562,
-0.6113510727882385,
0.4932883381843567,
-0.21045035123825073,
1.1527124643325806,
-0.6199808716773987,
0.5190432667732239,
0.4069652557373047,
-0.2050008475780487,
0.06549371778964996,
-0.01815766654908657,
0.20742204785346985,
0.15712149441242218,
0.5874238014221191,
1.1171009540557861,
-0.6018059849739075,
-0.7546277046203613,
0.19460336863994598,
1.6722666025161743,
1.0455553531646729,
1.005488634109497,
0.8105910420417786,
-0.2525333762168884,
0.25520509481430054,
-0.7810909748077393,
-0.16850818693637848,
-0.19518662989139557,
-0.4713849425315857,
-0.6429958343505859,
-0.5691127777099609,
-0.2812845706939697,
-0.34051647782325745,
0.4409618377685547,
0.7604540586471558,
0.5597294569015503,
0.10077421367168427,
1.0061721801757812,
-0.11311965435743332,
0.7195678353309631,
0.7849307060241699,
0.7051551342010498,
-0.3138117492198944,
-1.1397948265075684,
0.5568066835403442,
0.24728736281394958,
-0.16689230501651764,
-0.06505797803401947,
-0.5660585165023804,
-0.46147090196609497,
-0.2208850383758545,
0.9714522361755371,
0.1908617466688156,
-0.5103816390037537,
0.8617581725120544,
-0.6747133731842041,
0.3359069526195526,
0.2896290719509125,
-0.5080918669700623,
0.1900031417608261,
0.47409459948539734,
-0.5076439380645752,
-0.6367347240447998,
0.10353554785251617,
-0.4548025131225586,
0.46857139468193054,
-0.09070788323879242,
-0.48716339468955994,
-1.2352235317230225,
-0.44056081771850586,
0.05782559886574745,
-1.3121957778930664,
0.00989765115082264,
1.1048142910003662,
-0.343810498714447,
-0.39124247431755066,
-1.0650533437728882,
-0.7314929962158203,
-0.026563044637441635,
0.1184646263718605,
-0.40988948941230774,
0.4576445519924164,
-0.09982066601514816,
-0.7002003192901611,
0.858027458190918,
0.2214299887418747,
-0.052376579493284225,
-0.5867435336112976,
0.02950158342719078,
-0.4095698297023773,
-0.29989251494407654,
-0.8273658156394958,
-0.34968557953834534,
-0.6131014823913574,
-0.6140594482421875,
0.5991477966308594,
-0.7312859892845154,
0.33294880390167236,
0.3501199781894684,
0.31637832522392273,
-0.6677531003952026,
-0.7543277144432068,
0.043750062584877014,
0.1522785723209381,
-0.07809550315141678,
0.5418946146965027,
1.204426884651184,
0.06820526719093323,
0.14036458730697632,
0.23916180431842804,
0.3528907001018524,
0.5148113965988159,
0.2707069516181946,
0.335064172744751,
-0.5300493836402893,
-0.12680935859680176,
-0.6007097959518433,
-1.5835566520690918,
0.3329213261604309,
-0.46263033151626587,
1.4284303188323975,
-0.22901196777820587,
-0.47110459208488464,
-0.030178381130099297,
-0.23002026975154877,
-0.478749543428421,
0.2640842795372009,
-0.24412661790847778,
-0.8891161680221558,
0.5594812035560608,
-0.8905431032180786,
0.2835555374622345,
-0.08019126951694489,
0.4955286383628845,
-0.4652394652366638,
0.4767477810382843,
0.5479955077171326,
-0.5149526596069336,
0.7663018703460693,
-0.7684835195541382,
0.18934638798236847,
-0.10463391989469528,
0.056467097252607346,
-0.27396562695503235,
-0.8302506804466248,
-0.12428659200668335,
-0.9286062717437744,
-0.43314945697784424,
-0.7602540254592896,
0.08348522335290909,
-0.17929458618164062,
0.2735077440738678,
0.29441171884536743,
-0.5633866786956787,
0.5644789934158325,
-1.1487431526184082,
1.1879103183746338,
-0.5414208173751831,
-0.8748637437820435,
-0.10664597898721695,
0.9873740077018738,
0.12084493041038513,
0.27852436900138855,
0.2372460514307022,
-0.4809400737285614,
0.3774288296699524,
0.13013137876987457,
0.21096165478229523,
-0.555229663848877,
0.31045660376548767,
-0.5339720845222473,
-0.9737748503684998,
0.009596869349479675,
1.0852341651916504,
0.01824408955872059,
0.0435488224029541,
0.1837434321641922,
-0.7186960577964783,
0.6335930228233337,
0.05757132172584534,
-0.35682082176208496,
-0.6655017733573914,
0.0402037613093853,
-0.4997680187225342,
0.9990609288215637,
0.5261005759239197,
-0.24055898189544678,
0.23819690942764282,
0.22407542169094086,
-0.07004484534263611,
0.38584762811660767,
-0.3699181377887726,
0.1253887116909027,
0.1564822494983673,
0.4231557846069336,
0.1783861517906189,
0.3645552098751068,
-0.8594287633895874,
0.6144979000091553,
-1.0161739587783813,
0.9854641556739807,
-0.8091333508491516,
0.46762850880622864,
0.20517748594284058,
0.06837130337953568,
0.9431778788566589,
-0.6330845952033997,
0.5695223808288574,
0.03018987737596035,
0.2587273120880127,
1.043454647064209,
0.4909047782421112,
-0.17171086370944977,
-0.2901889383792877,
-0.8411819934844971,
-1.4778963327407837,
0.864846408367157,
-0.45555371046066284,
-0.36196649074554443,
-1.184369444847107,
-0.6292169690132141,
0.7243073582649231,
-0.24708962440490723,
0.8745031356811523,
0.3275429308414459,
-0.13139976561069489,
-0.005067949183285236,
0.6463053822517395,
-0.4247739911079407,
-0.3772490322589874,
-0.5154127478599548,
0.8815944790840149,
-0.7822005152702332,
-0.6589646935462952,
-0.03394900634884834,
-1.0134724378585815,
-1.4455500841140747,
0.06999018788337708,
0.654932975769043,
0.5160335302352905,
-0.44233089685440063,
0.5048129558563232,
-0.3616889417171478,
-0.4052186608314514,
-0.4398699402809143,
-0.2766309082508087,
-0.05364082381129265,
0.49876150488853455,
1.1301896572113037,
0.1641489565372467,
0.09559030830860138,
-0.20112277567386627,
0.5155932307243347,
-0.2798691987991333,
-0.11765178292989731,
0.570540726184845,
-0.33856400847435,
-0.4987145662307739,
0.1351427286863327,
0.0025573831517249346,
-1.3269959688186646,
-0.9612333178520203,
-0.15949729084968567,
0.3383146822452545,
-0.24345195293426514,
-0.9166236519813538,
-0.022795366123318672,
-0.562470018863678,
-0.3823336362838745,
0.581853449344635,
0.36084747314453125,
-0.48102930188179016,
0.007187803275883198,
0.16890601813793182,
-0.3106735348701477,
-0.5476759076118469,
0.2893718183040619,
1.1017038822174072,
-0.31524333357810974,
0.04009026288986206,
-0.4500056207180023,
-0.7426748871803284,
-0.0034831922966986895,
0.21133378148078918,
0.2396605908870697,
-0.236712247133255,
0.3718951642513275,
0.6510611772537231,
0.8324346542358398,
0.5218881368637085,
0.39197617769241333,
0.663392961025238,
-0.24056082963943481,
0.18299174308776855,
-1.0817923545837402,
-0.8879154324531555,
-0.381413072347641,
-0.16710816323757172,
0.8325837254524231,
-0.41676434874534607,
0.7105408906936646,
-0.10849834978580475,
-0.36301615834236145,
-0.10165829211473465,
-1.0571051836013794,
0.6221231818199158,
-1.4233261346817017,
-0.3720934987068176,
-0.5726546049118042,
-0.8118073344230652,
0.09192010760307312,
0.49946749210357666,
0.5450074076652527,
-0.3023512065410614,
-0.8895667195320129,
0.533838152885437,
0.41517403721809387,
-0.02029825747013092,
-0.1695205420255661,
-0.47285130620002747,
-0.8481057286262512,
-0.2889541983604431,
-0.8019757866859436,
0.28321054577827454,
0.0564180351793766,
0.3470928370952606,
-0.6030427813529968,
0.4866372346878052,
-0.5267937779426575,
0.4873926043510437,
-0.7449825406074524,
-0.46634534001350403,
0.4810866117477417,
-0.2662059962749481,
-0.3693180978298187,
-0.15867850184440613,
-0.8480852246284485,
-0.0914306715130806,
0.4036096930503845,
-0.004046838264912367,
-0.20758002996444702,
0.2815723121166229,
-1.1195682287216187,
-0.7888606786727905,
-0.29901185631752014,
0.8089621067047119,
-0.3553519546985626,
-0.44767677783966064,
0.4874390661716461,
-0.07524027675390244,
-1.3638802766799927,
0.46723616123199463,
-0.3329497277736664,
-0.549290657043457,
-0.05296740308403969,
0.08017569780349731,
0.2796211838722229,
0.6703997254371643,
-0.6716816425323486,
0.753200113773346,
-0.23194153606891632,
-0.0659313052892685,
-0.02109794318675995,
0.05637039244174957,
-0.8718520402908325,
0.4102352559566498,
0.6717725992202759,
-1.4220668077468872,
0.04286426305770874,
0.6146572232246399,
-0.7112587094306946,
0.3102151155471802,
-0.5456783175468445,
-0.01764576882123947,
-0.5753130912780762,
-0.12568773329257965,
-0.3897738754749298,
0.7727460861206055,
0.271366685628891,
-0.8575872182846069,
0.06780479103326797,
-0.7182772755622864,
-0.12834148108959198,
0.10140418261289597,
-1.1508243083953857,
-0.3185013234615326,
-0.08617479354143143,
-0.5401163697242737,
0.24254870414733887,
-0.4303082823753357,
0.27166640758514404,
0.4290936291217804,
0.32249191403388977,
-0.22774386405944824,
-0.4159010052680969,
0.05556736886501312,
0.03160013630986214,
0.18963943421840668,
-0.482227623462677,
-0.6615874171257019,
0.10339470207691193,
0.6585319638252258,
-0.933776319026947,
-0.963432788848877,
0.18937326967716217,
0.8039980530738831,
0.4619716703891754,
-0.04452945291996002,
-0.6636640429496765,
0.2937549352645874,
0.33004018664360046,
0.24899084866046906,
-0.43558332324028015,
0.029434503987431526,
0.14919129014015198,
0.47160980105400085,
0.17797407507896423,
-0.42817893624305725,
0.31535786390304565,
0.32962268590927124,
0.45811188220977783,
-0.04047538340091705,
-0.7355769276618958,
0.2986697256565094,
0.033757761120796204,
-0.8257635235786438,
1.5035704374313354,
0.03679554909467697,
1.4175515174865723,
0.04441756010055542,
-0.056201476603746414,
0.19373641908168793,
0.07336695492267609,
0.8435834050178528,
0.4015161693096161,
0.6365863084793091,
0.0984746441245079,
0.5830672979354858,
0.26925259828567505,
-0.11967378109693527,
0.394565224647522,
0.5687462687492371,
0.24593499302864075,
0.5043087601661682,
-0.4002039134502411,
0.2567312717437744,
0.049381982535123825,
-0.006546171847730875,
-0.307157427072525,
-0.2285679131746292,
-0.6143909096717834,
-0.7079764008522034,
-0.22116674482822418,
0.010473737493157387,
-0.24511495232582092,
-0.2230915129184723,
-0.20415809750556946,
0.7048155665397644,
-0.06313767284154892,
0.16040053963661194,
0.2511124014854431,
0.48394304513931274,
0.35459306836128235,
0.7860667109489441,
0.3600435256958008,
0.6582286953926086,
0.4262375831604004,
0.1437845230102539,
-0.12052314728498459,
0.9216768741607666,
1.0480520725250244,
0.4924294650554657,
0.41445788741111755,
-1.4576516151428223,
-0.5236855149269104,
0.5953337550163269,
-1.5698540210723877,
-0.015027538873255253,
-0.6994006037712097,
-0.33816689252853394,
-0.36879852414131165,
-0.5893593430519104,
0.33628591895103455,
-0.47467947006225586,
0.4959571063518524,
1.3846957683563232,
0.6413611769676208,
0.6099497675895691,
0.5970353484153748,
-0.4474794864654541,
1.1423531770706177,
1.309107780456543,
-0.6376733183860779,
-0.33450448513031006,
0.6191693544387817,
1.3639026880264282,
0.02250158041715622,
0.06127851828932762,
-0.0334663912653923,
-0.03603507950901985,
0.18437986075878143,
-0.09492318332195282,
-0.005405930336564779,
1.1331802606582642,
-0.9100559949874878,
-0.6451289057731628,
-0.08821670711040497,
0.1367497593164444,
-0.8716179132461548,
-0.00443051103502512,
-0.157937690615654,
0.4468821883201599,
-0.716873288154602,
-0.4630749523639679,
1.243656873703003,
0.17887119948863983,
-0.2645198404788971,
0.18129095435142517,
-0.15198515355587006,
-0.41641318798065186,
0.31430214643478394,
-0.7324671149253845,
0.3354320228099823,
0.6993532180786133,
0.5536173582077026,
-0.2880723774433136,
-0.7836617827415466,
-0.39462965726852417,
-0.524739146232605,
-0.0002523466828279197,
-0.632708728313446,
0.7471527457237244,
0.3104120194911957,
0.5452181100845337,
-0.13426236808300018,
-0.825321614742279,
0.3729073405265808,
0.6396673917770386,
1.476609468460083,
-0.3090377449989319,
0.4791053831577301,
0.7991678714752197,
0.8000385761260986,
-0.3561770021915436,
0.5998013615608215,
0.27798715233802795,
-0.33532676100730896,
0.2991379499435425,
-0.30497559905052185,
0.03317321836948395,
-0.2805948257446289,
-0.3570828437805176,
0.49780160188674927,
-0.2607375979423523,
0.30907583236694336,
-1.2212445735931396,
-0.42237794399261475,
-0.20805256068706512,
-1.056946873664856,
0.17645874619483948,
-1.3355315923690796,
0.27394914627075195,
0.6658205389976501,
0.3465443551540375,
-0.47945961356163025,
0.04982328787446022,
3.461127758026123,
0.9746533036231995,
1.1647655963897705,
-0.40825334191322327,
0.8415347933769226,
0.2465570718050003,
0.009999300353229046,
-0.5859516263008118,
0.55628901720047,
-0.12190312147140503,
0.5172619819641113,
0.4702001214027405,
1.0250829458236694,
0.08543136715888977,
-0.1989220231771469,
0.46054646372795105,
-0.39328452944755554,
0.33569952845573425,
0.6776055693626404,
-0.9238570928573608,
-1.000963807106018,
0.34194469451904297,
0.3403106927871704,
-0.01668393984436989,
0.09640290588140488,
0.021472183987498283,
0.09504660964012146,
-1.1589436531066895,
-0.6227861046791077,
0.2925540506839752,
-0.21926313638687134,
-0.8347963690757751,
-0.17314885556697845,
-0.43385040760040283,
-0.08525162190198898,
1.0493755340576172,
0.7512121200561523,
-0.0753997340798378,
0.09970180690288544,
0.5808189511299133,
-0.5950392484664917,
-0.20038414001464844,
-0.1827610284090042,
0.303449809551239,
-1.0764060020446777,
1.285904049873352,
-0.14528495073318481,
0.8169001340866089,
0.013815431855618954,
-0.4435340166091919,
0.4453112781047821,
-0.4588775634765625,
0.6571145057678223,
-0.6564485430717468,
-1.5760301351547241,
-0.1968812346458435,
-0.7644498944282532,
-1.1476867198944092,
-0.1359301209449768,
0.09667554497718811,
1.161214828491211,
0.2031841278076172,
-0.38123011589050293,
0.4919722378253937,
-0.5769408345222473,
0.40475139021873474,
0.7150124311447144,
-0.29670271277427673,
-0.4390433728694916,
0.45558395981788635,
-0.3187365233898163,
-0.1879454255104065,
-0.6615515351295471,
0.5480066537857056,
-0.12783493101596832,
-0.3364946246147156,
-0.42062491178512573,
1.2453795671463013,
-0.10223669558763504,
0.05360816791653633,
-0.4996761381626129,
-0.23223468661308289,
-0.3996235132217407,
0.46296122670173645,
-0.093605637550354,
0.8562796711921692,
-0.4759329557418823,
-0.507205605506897,
-0.25553441047668457,
0.43863070011138916,
0.12914088368415833,
1.3530209064483643,
0.4296542704105377,
-0.6472551822662354,
-0.7925435304641724
] |
Direct Monte Carlo Measurement of the Surface Tension in Ising Models
|
I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model.
|
Martin Hasenbusch
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209016
|
hep-lat/9209017
|
[
0.5250536203384399,
-0.037577223032712936,
0.5942043662071228,
0.025284085422754288,
0.5691888928413391,
0.2400207817554474,
0.11288806796073914,
-0.6374871730804443,
-0.8949850797653198,
0.9843295216560364,
1.5090608596801758,
-0.13495555520057678,
0.6298776268959045,
-1.1726583242416382,
0.022009791806340218,
-0.07574072480201721,
-0.4109031558036804,
-0.7945617437362671,
-0.9315321445465088,
-0.3160479962825775,
0.013332352973520756,
-0.7918103933334351,
-1.431360125541687,
-0.9392984509468079,
-0.13644014298915863,
0.7942973971366882,
-0.20650462806224823,
0.6494680047035217,
0.9666884541511536,
0.6723969578742981,
0.6718888878822327,
-0.7392832636833191,
0.07132132351398468,
-0.30294859409332275,
-0.5674903988838196,
-0.36560890078544617,
0.07465794682502747,
-0.06704443693161011,
0.47802117466926575,
-0.5281409621238708,
0.6984459757804871,
-0.14883045852184296,
0.7008851170539856,
-0.280322790145874,
-0.4965655505657196,
0.07421089708805084,
-0.336980938911438,
0.07428991794586182,
0.23627182841300964,
-1.0758435726165771,
0.38176074624061584,
0.07610157132148743,
0.5466006994247437,
-0.31613728404045105,
-0.11144662648439407,
-0.1541426032781601,
0.16807124018669128,
0.12452765554189682,
-0.780735433101654,
-0.2796216905117035,
0.805412769317627,
-0.030735494568943977,
1.1140446662902832,
-0.7120873332023621,
0.7748507261276245,
0.9302257895469666,
-0.5881170034408569,
0.03220607340335846,
0.49794256687164307,
-0.5992064476013184,
-0.8493706583976746,
-0.6462206840515137,
0.42562437057495117,
0.2541031539440155,
-0.21856829524040222,
0.3912796378135681,
0.07990924268960953,
-0.16865894198417664,
-1.738594889640808,
-0.4025961756706238,
-0.5057985186576843,
-0.21816304326057434,
-0.291748583316803,
0.4148184061050415,
-0.3566594421863556,
-0.5796694159507751,
0.23095962405204773,
0.30249491333961487,
0.3849814832210541,
0.5869690179824829,
0.29714205861091614,
0.263298898935318,
0.4276929199695587,
-0.12027091532945633,
0.6279991865158081,
0.6927452683448792,
0.05053940787911415,
0.514457106590271,
0.32621628046035767,
0.45361435413360596,
-0.4367767870426178,
0.9529407024383545,
-0.5778415203094482,
0.7207233905792236,
-0.8805707693099976,
0.4241398870944977,
-0.0435856394469738,
0.07751265913248062,
-0.4990002512931824,
-0.5206794738769531,
0.052895437926054,
0.06501021981239319,
0.27255165576934814,
0.6963948011398315,
0.019202038645744324,
0.8835543990135193,
-0.25964105129241943,
0.03847638890147209,
-0.603983998298645,
-0.129961296916008,
0.07965407520532608,
0.06405269354581833,
0.17597052454948425,
0.32810544967651367,
0.14097321033477783,
-0.5636943578720093,
0.8202444314956665,
0.7942734360694885,
-0.7792529463768005,
-0.05248154327273369,
-0.058934930711984634,
-0.2851737439632416,
-0.09850563853979111,
0.5219510197639465,
-0.43695470690727234,
0.17750465869903564,
0.10160078853368759,
0.3558180332183838,
0.2153363674879074,
-0.4258091151714325,
0.5945659875869751,
-0.9561721086502075,
0.4539961814880371,
0.8060281276702881,
0.05351002514362335,
0.108113594353199,
0.3550964295864105,
-0.7696743607521057,
0.45677199959754944,
0.6272202134132385,
-0.6922684907913208,
-0.07286269962787628,
-0.4573996365070343,
0.39598169922828674,
0.4961007833480835,
0.23783203959465027,
-1.0263148546218872,
0.6274232864379883,
-0.9912220239639282,
-0.6174970269203186,
0.5710476636886597,
0.08293775469064713,
-0.6511039733886719,
0.13520677387714386,
-0.5264759063720703,
-0.06679854542016983,
-0.4033258259296417,
-0.32854682207107544,
-0.1674838811159134,
-0.7752809524536133,
0.12563791871070862,
0.6936118602752686,
-0.18126773834228516,
0.34734106063842773,
0.08921017497777939,
0.2991028428077698,
0.8213084936141968,
-0.5415665507316589,
-0.10067351162433624,
0.200731560587883,
-0.5009714365005493,
-0.3226661682128906,
1.0401769876480103,
-0.019622396677732468,
0.033559318631887436,
0.1195615828037262,
-0.5251920819282532,
-0.0013018534518778324,
0.2586919367313385,
0.6360966563224792,
-0.08190370351076126,
0.585209846496582,
-0.12583956122398376,
0.7747151851654053,
-0.5836875438690186,
-0.7176824808120728,
-0.717628002166748,
0.2108456939458847,
-0.6631969809532166,
-0.4048280715942383,
-0.36552488803863525,
0.41205739974975586,
-0.6466901302337646,
0.3411082327365875,
-1.7040351629257202,
0.7644286751747131,
0.5784776210784912,
-0.2554739713668823,
-0.5697149634361267,
-0.442808598279953,
0.4169917404651642,
-0.06908506155014038,
0.4627535343170166,
-0.08231713622808456,
0.10601511597633362,
0.28889796137809753,
-0.7865583300590515,
0.015705568715929985,
1.1690558195114136,
-0.4654863774776459,
0.9523807168006897,
-0.016398107632994652,
-0.5273997783660889,
0.8696979284286499,
-0.02839316613972187,
-0.08790900558233261,
0.26962897181510925,
0.6301577687263489,
0.7263213992118835,
-0.14053097367286682,
-0.09647750854492188,
0.5687920451164246,
-0.37358564138412476,
-0.18972668051719666,
0.6880561113357544,
1.2865346670150757,
0.6605826616287231,
0.8003408312797546,
0.1670718640089035,
0.3342789113521576,
0.04198775440454483,
0.19775056838989258,
0.7787899971008301,
0.575572669506073,
0.29473018646240234,
0.29078108072280884,
-0.2687046527862549,
0.35584598779678345,
-0.5123052000999451,
0.443165123462677,
-0.9652968645095825,
0.7355037331581116,
0.05085603520274162,
0.11796215921640396,
-0.9988789558410645,
-0.2626282572746277,
-0.2756802439689636,
0.32738587260246277,
0.10122773051261902,
-1.046894907951355,
-0.14792874455451965,
0.06298423558473587,
0.23183093965053558,
-0.16437512636184692,
-0.2622596025466919,
0.997262179851532,
0.28235137462615967,
0.23989643156528473,
0.26329877972602844,
-0.12638357281684875,
-1.0071275234222412,
0.09034720063209534,
-0.6935346126556396,
0.028532804921269417,
-0.4071345329284668,
0.1661756932735443,
0.9314515590667725,
-1.0855649709701538,
0.46011123061180115,
0.09842415153980255,
0.013475729152560234,
0.6688127517700195,
-0.0943230614066124,
1.0326290130615234,
0.9323780536651611,
-0.04430106654763222,
-0.6843655109405518,
-0.07420230656862259,
-0.13728612661361694,
0.6553073525428772,
-0.1375814974308014,
0.5656604766845703,
1.1066609621047974,
-0.22138750553131104,
-0.1259220838546753,
-0.5687593817710876,
-0.6601305603981018,
-0.056928589940071106,
-0.05691523477435112,
-0.824985921382904,
0.17456890642642975,
0.690697431564331,
-0.17201334238052368,
-0.18685856461524963,
-0.3722628951072693,
0.9946276545524597,
-0.24869880080223083,
-0.4922238290309906,
0.8345165848731995,
0.3702210485935211,
-0.0507432296872139,
0.32930320501327515,
-0.8084618449211121,
-0.07943733781576157,
-0.061798010021448135,
1.1829935312271118,
0.7088867425918579,
0.25796830654144287,
-0.054467666894197464,
-1.0006096363067627,
0.0034017583820968866,
-0.2627188563346863,
-0.6880199909210205,
-0.9002712368965149,
-0.575283408164978,
1.2179958820343018,
0.14354990422725677,
-0.7869074940681458,
0.09364179521799088,
-1.1964759826660156,
-0.6209593415260315,
-0.0878661647439003,
-0.3139197826385498,
0.9182522296905518,
-0.10892836004495621,
-0.42034101486206055,
-0.18350766599178314,
0.3151904046535492,
-0.005051702726632357,
0.2798480689525604,
0.1979091316461563,
-0.5197688341140747,
0.5683904886245728,
0.6198873519897461,
0.08694551140069962,
0.006075398996472359,
0.18767398595809937,
0.004772835876792669,
-0.4980701804161072,
0.6400695443153381,
-1.0095845460891724,
0.06269285827875137,
0.7170577049255371,
0.15370236337184906,
-0.13301123678684235,
0.2563568353652954,
-0.5303006768226624,
-0.7116424441337585,
-0.5039755702018738,
-0.3482045531272888,
0.8139647245407104,
0.005502767860889435,
-0.424355149269104,
0.4073755145072937,
-0.574288010597229,
-0.10797438770532608,
0.4588886499404907,
-0.2509925663471222,
0.8021719455718994,
-0.7664053440093994,
0.4554339349269867,
0.2997245192527771,
-0.10523238778114319,
0.2635160982608795,
-0.4734365940093994,
0.46511006355285645,
0.01246846653521061,
0.594080924987793,
0.8335351943969727,
-0.6634430289268494,
-0.771824061870575,
-0.17918142676353455,
0.9925920367240906,
0.7118329405784607,
0.6241129040718079,
0.8041666150093079,
-0.31610435247421265,
-0.20483221113681793,
-0.17701242864131927,
-0.04917920380830765,
-0.4445802569389343,
-0.17310361564159393,
-0.7201154232025146,
-0.5807570815086365,
0.08655872941017151,
-0.04258240759372711,
0.5924303531646729,
0.23036718368530273,
0.7379486560821533,
-0.09244000911712646,
0.9675725698471069,
0.3035551905632019,
1.187492847442627,
0.8368094563484192,
0.9369296431541443,
0.2074194997549057,
-1.0030959844589233,
0.4814186990261078,
0.15695397555828094,
0.1893530935049057,
-0.16344097256660461,
-0.5556960701942444,
-0.029122017323970795,
-1.0146297216415405,
0.8512909412384033,
-0.04296213015913963,
-0.5879359841346741,
0.8118545413017273,
-0.5657792687416077,
0.23329022526741028,
-0.3928658366203308,
-0.5283744931221008,
0.49065613746643066,
0.4349825978279114,
-0.11964193731546402,
-0.7885823249816895,
-0.1150563508272171,
-0.18014250695705414,
0.4650666117668152,
0.7043505907058716,
-0.8384764790534973,
-0.9074960947036743,
-0.9542525410652161,
-0.15971805155277252,
-0.4711320996284485,
-0.4114432632923126,
0.6611802577972412,
0.0015510888770222664,
0.3638720214366913,
-0.3911435604095459,
-0.9291843175888062,
0.2784511148929596,
-0.42423540353775024,
-0.5366836786270142,
0.36923232674598694,
0.09091240167617798,
-0.10407900810241699,
0.3755521774291992,
0.4005934000015259,
-0.576851487159729,
-0.19195494055747986,
0.014941640198230743,
0.20159275829792023,
-0.4702596366405487,
-0.2741346061229706,
-0.21960832178592682,
-0.6936204433441162,
-0.7639068365097046,
0.5104191899299622,
-0.09136989712715149,
0.1982300579547882,
0.2519421875476837,
-0.4147297143936157,
-0.515846312046051,
-0.766566276550293,
0.18594691157341003,
0.024448668584227562,
0.6622665524482727,
0.9387600421905518,
0.03955869376659393,
0.0030757125932723284,
0.7562450766563416,
-0.041306283324956894,
0.8077555298805237,
0.3380347490310669,
0.07999040186405182,
-0.48131266236305237,
-0.046439576894044876,
0.31971290707588196,
-0.9520071744918823,
-0.8140435218811035,
0.24411283433437347,
-0.44627904891967773,
1.1850717067718506,
0.14961479604244232,
-0.34412312507629395,
0.06568954885005951,
-0.30596569180488586,
-0.5699970722198486,
0.11384689807891846,
-0.367713063955307,
-0.3943561017513275,
0.405316025018692,
-0.7470073699951172,
-0.28682810068130493,
0.42183616757392883,
0.011978011578321457,
-0.2501051723957062,
0.09995683282613754,
0.48987433314323425,
-0.3709667921066284,
0.42173704504966736,
-0.5510966777801514,
0.5923724174499512,
-0.44412365555763245,
0.5357303619384766,
-0.26155054569244385,
-0.586072564125061,
-0.216819167137146,
0.26826372742652893,
-0.11951758712530136,
-0.9889446496963501,
-0.37106114625930786,
-0.1880573183298111,
0.49104616045951843,
-0.2799258828163147,
-0.15577606856822968,
-0.31486234068870544,
-0.6666628122329712,
1.1612303256988525,
-0.21188968420028687,
-0.9569798111915588,
-0.10661689192056656,
0.7274442911148071,
0.06537675112485886,
0.3310210108757019,
-0.35768502950668335,
-0.45521894097328186,
0.0961117371916771,
0.051455412060022354,
0.10923072695732117,
-0.6471521258354187,
-0.43998458981513977,
-0.4996764659881592,
-0.886627733707428,
0.4679119884967804,
0.5276987552642822,
0.23998460173606873,
0.12876863777637482,
-0.07779263705015182,
-0.5379799008369446,
0.0548737607896328,
-0.6311883926391602,
-0.6282509565353394,
-0.6140995025634766,
-0.36216479539871216,
-0.6920314431190491,
0.18279585242271423,
-0.01376901101320982,
0.14842431247234344,
0.3346365690231323,
0.29658952355384827,
0.2489957958459854,
0.8088391423225403,
-0.2274397760629654,
-0.4354705512523651,
-0.1396580934524536,
0.47991904616355896,
-0.7118919491767883,
0.15556581318378448,
-0.7167434096336365,
0.6476948857307434,
-1.1999564170837402,
0.9063304662704468,
-0.42962974309921265,
-0.15474002063274384,
-0.000965152052231133,
0.3765418827533722,
0.4653318226337433,
-0.5561105608940125,
0.4348639249801636,
0.3403630554676056,
-0.06981119513511658,
0.8334138989448547,
0.1272902488708496,
-0.5829753875732422,
-0.6536539793014526,
-0.10103409737348557,
-1.1163660287857056,
0.5694993734359741,
0.026630591601133347,
-0.07023452967405319,
-0.9108744263648987,
-0.6418118476867676,
0.3790443241596222,
0.22401879727840424,
0.45184656977653503,
0.5588211417198181,
-0.6323437094688416,
0.08881863951683044,
0.20072802901268005,
0.3727867603302002,
-0.13334910571575165,
0.1021619662642479,
0.3305259644985199,
-0.5926160216331482,
-0.24623052775859833,
-0.26442959904670715,
-0.5098696947097778,
-1.4101403951644897,
-0.17954754829406738,
0.3916526734828949,
0.42475977540016174,
-0.07457897812128067,
0.5976592898368835,
-0.5930642485618591,
-0.8510035872459412,
-0.28674253821372986,
-0.03439720720052719,
-0.5613572597503662,
-0.04616443067789078,
0.6754060983657837,
-0.07166740298271179,
0.2435029298067093,
-0.04139791429042816,
0.741551399230957,
-0.5533302426338196,
0.41136637330055237,
0.08870050311088562,
-0.13048680126667023,
-0.4370042681694031,
-0.06893915683031082,
0.14004558324813843,
-0.9223155975341797,
-0.40555137395858765,
-0.815879225730896,
-0.387576162815094,
-0.056073740124702454,
-0.41802841424942017,
0.7492714524269104,
-0.5365983843803406,
-0.3466983437538147,
0.8328182697296143,
0.3907317519187927,
-0.5784881114959717,
-0.7367699146270752,
0.08155757933855057,
-0.514983057975769,
-0.24024395644664764,
-0.12542276084423065,
1.7655479907989502,
-0.5993401408195496,
-0.3222261965274811,
-0.6691917777061462,
-0.766802966594696,
-0.09851237386465073,
0.7757538557052612,
-0.40566956996917725,
-0.18817974627017975,
0.15589198470115662,
0.47077876329421997,
0.5874380469322205,
0.35325706005096436,
0.19811567664146423,
0.6952733993530273,
-0.3705925941467285,
0.6231560707092285,
-1.3060222864151,
-0.722195565700531,
0.004129903391003609,
0.22887131571769714,
0.5285882949829102,
-0.39461055397987366,
0.3652542531490326,
0.2005649209022522,
-0.8332945108413696,
-0.2563837468624115,
-0.7587405443191528,
0.3595011532306671,
-1.2672624588012695,
-0.06726688146591187,
-0.7109314203262329,
-0.8351264595985413,
-0.1280815452337265,
-0.057994451373815536,
0.18067343533039093,
-0.7553921341896057,
-0.8536403775215149,
0.5493466854095459,
0.2312517613172531,
-0.1784384399652481,
0.21298539638519287,
-0.5447134375572205,
-0.866021990776062,
-0.5493081212043762,
-0.01754012145102024,
-0.40367475152015686,
-0.2599966526031494,
0.4263572692871094,
-0.05512353032827377,
-0.11351966857910156,
-0.1517932265996933,
0.4273427128791809,
-0.6377651691436768,
-0.19887395203113556,
0.27052009105682373,
-0.12286093831062317,
-0.3090059757232666,
-0.27640917897224426,
-0.38128843903541565,
0.24666208028793335,
-0.1311141401529312,
-0.2549801766872406,
-0.2777060866355896,
0.1601739227771759,
-0.920110821723938,
-0.08360619843006134,
0.05606086552143097,
0.43427619338035583,
-0.6443619728088379,
-0.8370502591133118,
0.5661992430686951,
0.18954019248485565,
-1.2740235328674316,
0.4896261990070343,
-0.5019218325614929,
0.11081326007843018,
-0.2171856015920639,
0.7741521596908569,
0.18887346982955933,
0.8225609064102173,
-0.6346063017845154,
1.3813949823379517,
-0.5816497802734375,
-0.4205552041530609,
-0.29098761081695557,
0.08171530067920685,
-0.11089400202035904,
0.41859039664268494,
-0.06830128282308578,
-0.6921221613883972,
-0.20000502467155457,
0.23963850736618042,
-0.3508521318435669,
-0.3616954982280731,
-0.4088820815086365,
-0.02707485295832157,
-0.2379993051290512,
-0.5511766076087952,
-0.46866893768310547,
0.38015878200531006,
-0.16344545781612396,
-0.7137428522109985,
-0.33149105310440063,
-0.4310532510280609,
-0.5517498850822449,
0.4249904751777649,
-1.0684621334075928,
-0.5840126872062683,
-0.18778152763843536,
-0.35944199562072754,
0.11105899512767792,
0.1483975350856781,
0.04259544983506203,
0.7329391241073608,
0.04282074421644211,
-0.12373581528663635,
0.07901617884635925,
0.019675493240356445,
-0.14180082082748413,
0.5098753571510315,
-0.635871946811676,
-0.5742781758308411,
-0.34752896428108215,
0.6587250232696533,
-0.46587803959846497,
-0.54765784740448,
-0.6325302720069885,
0.5548250675201416,
0.11861837655305862,
0.37327688932418823,
-0.4404193162918091,
-0.012756267562508583,
0.5044222474098206,
0.3490108549594879,
-0.6428689956665039,
0.23822523653507233,
-0.01448859553784132,
1.1064530611038208,
-0.2832992970943451,
-1.1147370338439941,
0.5585388541221619,
0.6269412040710449,
0.18717798590660095,
0.00469389371573925,
-0.18326367437839508,
0.24707980453968048,
-0.32455095648765564,
-0.9651437997817993,
1.3489971160888672,
0.1476835161447525,
0.7848331928253174,
-0.01258350070565939,
-0.22601094841957092,
0.23921740055084229,
0.27813559770584106,
1.0157448053359985,
0.24548567831516266,
0.6877075433731079,
0.03374447301030159,
0.4834597110748291,
0.1760486215353012,
0.372886598110199,
0.05293422192335129,
0.4046735465526581,
0.191121906042099,
0.5696982145309448,
-0.11258819699287415,
0.05942874774336815,
0.1413871943950653,
0.46855124831199646,
-0.08477012068033218,
0.08391154557466507,
0.11992496997117996,
0.3802340030670166,
-0.08853854984045029,
0.923778772354126,
-0.5852866768836975,
-0.1413825899362564,
-0.2183428406715393,
0.5329229235649109,
0.002580404281616211,
0.5163386464118958,
-0.08385943621397018,
0.502892792224884,
0.45361679792404175,
0.31013253331184387,
-0.23992739617824554,
0.8052430152893066,
0.5836378335952759,
0.23105411231517792,
0.02891952358186245,
0.8672122955322266,
0.6827279329299927,
0.1410558968782425,
0.17200393974781036,
-1.1259909868240356,
-0.009051552973687649,
0.5198710560798645,
-1.6126405000686646,
0.4828682541847229,
-0.5509768128395081,
0.13931436836719513,
-0.42799875140190125,
-0.7236901521682739,
0.193117156624794,
-0.5664066672325134,
0.16377663612365723,
1.1553683280944824,
0.40930065512657166,
0.2076716423034668,
0.7274317145347595,
-0.15512080490589142,
0.5195528268814087,
1.0193148851394653,
-0.05507291853427887,
-0.41978827118873596,
0.7010546922683716,
1.1470205783843994,
-0.2518357038497925,
0.25790509581565857,
-0.041499003767967224,
-0.6256698966026306,
0.5041355490684509,
0.6884577870368958,
-0.230089470744133,
1.2060552835464478,
-0.4935009777545929,
-1.0751709938049316,
0.2678182125091553,
0.6185793280601501,
-0.4192647337913513,
-0.11082608997821808,
-0.10152698308229446,
0.32744288444519043,
-0.010332079604268074,
-0.3943195044994354,
1.3564214706420898,
0.6045989990234375,
0.16726389527320862,
-0.4368707835674286,
-0.0199135709553957,
0.2936186194419861,
-0.20097795128822327,
-0.5973231196403503,
0.09045327454805374,
-0.06726952642202377,
0.4248887002468109,
-0.22618426382541656,
-0.498371422290802,
-0.9906688332557678,
-1.1342461109161377,
-0.032308224588632584,
-0.7407901287078857,
0.7344870567321777,
-0.16920918226242065,
0.6282088160514832,
0.34929704666137695,
-0.7170789837837219,
0.34035879373550415,
-0.15354327857494354,
1.0226374864578247,
0.021401293575763702,
0.29037240147590637,
0.9308707118034363,
1.1259459257125854,
-0.6282637715339661,
0.8485180735588074,
0.45921966433525085,
-0.55217045545578,
0.4361572265625,
-0.42933475971221924,
0.14466318488121033,
0.09115946292877197,
-0.028526540845632553,
0.07774721831083298,
-0.02449444867670536,
0.22789780795574188,
-0.7205843329429626,
0.04112791642546654,
-0.6552480459213257,
-1.0948665142059326,
-0.21867111325263977,
-0.7768791913986206,
0.09210364520549774,
0.1893296241760254,
0.4433550536632538,
0.4048556089401245,
0.12169676274061203,
3.901705741882324,
0.9574218988418579,
0.6792714595794678,
-0.0794636532664299,
0.8666702508926392,
0.6079893708229065,
0.28026917576789856,
-0.6003758907318115,
0.2932475805282593,
-0.4867754578590393,
-0.5324240326881409,
0.684036135673523,
0.5326139330863953,
-0.5409533381462097,
-0.4716798961162567,
0.04063790664076805,
0.031839217990636826,
0.48378700017929077,
0.1138601079583168,
-1.3507630825042725,
-0.3487054109573364,
0.38525983691215515,
0.0668008029460907,
-0.3130442202091217,
0.47649186849594116,
-0.38923147320747375,
0.2172812670469284,
-0.736869215965271,
-0.9088635444641113,
-0.4638863503932953,
-0.508384644985199,
-0.9050504565238953,
-0.27387160062789917,
0.2698987126350403,
-0.5428300499916077,
0.6119454503059387,
0.029259338974952698,
0.03528947755694389,
0.030436914414167404,
0.4177791476249695,
-0.2600531280040741,
0.18652360141277313,
-0.650535523891449,
-0.23784202337265015,
-1.3459516763687134,
1.0729873180389404,
-0.05809371918439865,
0.7967509031295776,
0.34683793783187866,
-0.37537476420402527,
0.7018591165542603,
-0.1809275597333908,
0.5577128529548645,
0.33492910861968994,
-1.5934966802597046,
-0.06933659315109253,
-0.2776099741458893,
-0.698934018611908,
0.2521607577800751,
0.3078480362892151,
0.6199812889099121,
-0.0720752477645874,
-0.2751765549182892,
0.04124211147427559,
-0.6136224269866943,
1.0528855323791504,
0.14751644432544708,
0.10442891716957092,
-0.5536443591117859,
0.24544990062713623,
-0.18963523209095,
-0.6037169098854065,
-0.5339919328689575,
0.5414713025093079,
-0.006178340408951044,
0.17052531242370605,
0.08512750267982483,
0.7722270488739014,
-0.19836607575416565,
0.17611904442310333,
0.11532636731863022,
-0.17347599565982819,
-0.2741392254829407,
0.47027042508125305,
0.20167282223701477,
1.6061736345291138,
0.06474731862545013,
0.07226807624101639,
0.049138959497213364,
0.8268141150474548,
0.3034120500087738,
1.511472463607788,
0.008328261785209179,
-0.379447340965271,
-0.7189154624938965
] |
Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model
|
We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.
|
Christian Holm and Wolfhard Janke
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209017
|
hep-lat/9209018
|
[
-0.16079141199588776,
0.20658574998378754,
0.45806175470352173,
0.36814597249031067,
0.40057528018951416,
-0.34122738242149353,
-0.30666571855545044,
-0.4713829755783081,
-0.4520403742790222,
1.3349156379699707,
0.2494617998600006,
-0.2607656717300415,
-0.3994477689266205,
-0.5115834474563599,
0.1849074363708496,
0.23944510519504547,
-0.6786697506904602,
-0.7148441076278687,
-1.5201786756515503,
0.6088449954986572,
0.7428433895111084,
-0.4480350613594055,
-1.1517655849456787,
-1.1773631572723389,
0.11697302013635635,
1.4307101964950562,
0.3413406312465668,
0.748421311378479,
0.728219211101532,
1.0935912132263184,
0.6554238796234131,
-0.5131980180740356,
-0.6592233180999756,
-0.1771862804889679,
-0.3126560151576996,
0.16158649325370789,
-0.35968443751335144,
0.09388571977615356,
0.3286575973033905,
-0.5874550342559814,
0.43685615062713623,
-0.5006569027900696,
-0.39562973380088806,
-0.020105011761188507,
-0.3499015271663666,
0.3484303653240204,
0.06774435192346573,
0.349030464887619,
0.7369051575660706,
-1.1995689868927002,
0.10963217914104462,
-0.15512874722480774,
0.4165123403072357,
-0.6604567766189575,
-0.36256125569343567,
-0.015627296641469002,
0.4766477942466736,
-0.20323054492473602,
-0.492542028427124,
-0.027837708592414856,
1.0027525424957275,
-0.0023119603283703327,
0.7485400438308716,
-0.8257073760032654,
-0.057293280959129333,
1.1891789436340332,
-0.5496670007705688,
0.6087731122970581,
-0.24380140006542206,
-0.38699567317962646,
-0.6566336154937744,
0.06829147040843964,
-0.48348069190979004,
0.43300774693489075,
-1.544838547706604,
1.2122422456741333,
-0.4191440939903259,
0.2558235228061676,
-0.7999897003173828,
-0.41739317774772644,
0.27858757972717285,
0.5082164406776428,
-0.3532586693763733,
0.357967346906662,
-0.4112723767757416,
-0.5218893885612488,
0.21753861010074615,
-0.4917392432689667,
0.23187187314033508,
0.1269613653421402,
0.6244425773620605,
0.5990083813667297,
-0.052854422479867935,
-0.18673287332057953,
0.4417993724346161,
-0.21694375574588776,
-0.15496224164962769,
0.4232882261276245,
0.31498754024505615,
0.39359599351882935,
0.13113835453987122,
0.4923401176929474,
-0.5198987722396851,
0.09001357853412628,
-0.4746150076389313,
0.650795042514801,
-0.16727110743522644,
-0.061911337077617645,
-0.518845796585083,
-0.9796785712242126,
-0.040274083614349365,
-0.3524472713470459,
0.3528953194618225,
0.9866807460784912,
0.7813628911972046,
0.22530417144298553,
-0.4404066503047943,
-0.196468785405159,
-0.334760844707489,
-0.27702343463897705,
0.6229196786880493,
-0.06307671964168549,
0.36952969431877136,
0.8483628034591675,
0.02551978826522827,
-0.4121904969215393,
-0.084157794713974,
0.6689457297325134,
-0.6912157535552979,
0.6800309419631958,
-0.4722062349319458,
0.2823840379714966,
-0.01913796178996563,
0.587550938129425,
-0.19977742433547974,
0.2504628300666809,
-0.3481927216053009,
0.7340511083602905,
-0.04360217973589897,
-0.8248932361602783,
0.6557822227478027,
-0.8218926787376404,
-0.23628996312618256,
1.0814844369888306,
0.06456220149993896,
-0.05960434675216675,
0.6812832355499268,
0.37380409240722656,
0.29735898971557617,
0.679728090763092,
-0.5544808506965637,
0.10491271317005157,
0.19340184330940247,
0.02083595283329487,
-0.3623597323894501,
0.3626924753189087,
-1.2884702682495117,
0.35001882910728455,
-0.4778270423412323,
0.03792648762464523,
0.017011355608701706,
0.5939884781837463,
0.09801817685365677,
0.4505496025085449,
-0.41350263357162476,
-0.2765052914619446,
-0.6128690242767334,
-0.5936863422393799,
0.09162517637014389,
-0.5630872249603271,
-0.11632795631885529,
0.08089462667703629,
-0.09311728179454803,
0.6626182794570923,
1.1302998065948486,
0.7112007141113281,
-0.04097342863678932,
-0.8539908528327942,
0.673708438873291,
0.6371653079986572,
-0.23428505659103394,
-0.0015876216348260641,
0.09499388933181763,
0.20757798850536346,
-0.466805100440979,
-0.07049030810594559,
0.08056384325027466,
-0.214538112282753,
0.355350524187088,
0.9410895705223083,
-0.32747334241867065,
0.2527572512626648,
-0.4555802643299103,
0.8926653861999512,
-0.4795205295085907,
0.15764838457107544,
-1.0256996154785156,
-0.10663031786680222,
-0.3786602020263672,
-0.267647922039032,
0.3168794810771942,
0.49589866399765015,
-1.2248647212982178,
-0.017282560467720032,
-1.3026196956634521,
-0.17599326372146606,
0.5619468092918396,
0.7330030798912048,
-0.43474048376083374,
0.31456008553504944,
0.15164043009281158,
-0.37888652086257935,
0.2266945242881775,
-0.6385160088539124,
0.5060463547706604,
-0.033952899277210236,
-0.7249270677566528,
0.14282694458961487,
0.05092577636241913,
-0.619027316570282,
0.709357500076294,
0.41548579931259155,
0.19208207726478577,
0.5203008651733398,
0.3598107695579529,
-0.7450193166732788,
0.2115097939968109,
0.7428507804870605,
0.6398754715919495,
0.15078499913215637,
0.456585168838501,
1.1108359098434448,
-0.0478479340672493,
0.626539409160614,
0.5253933072090149,
-0.1609804928302765,
0.18631277978420258,
0.39654698967933655,
0.36064258217811584,
0.36916184425354004,
-0.1517343819141388,
0.28050780296325684,
0.6278497576713562,
0.5485935807228088,
-0.3956111669540405,
0.5917657017707825,
-0.4051959812641144,
0.15522998571395874,
-1.0684939622879028,
0.31357139348983765,
-0.1642029732465744,
0.18246053159236908,
0.1296520233154297,
0.4104776978492737,
-0.766573429107666,
0.06535729765892029,
-0.16821202635765076,
0.13427530229091644,
0.19268816709518433,
-0.37500429153442383,
-0.008328652009367943,
0.2053649127483368,
-0.27714836597442627,
-1.0688554048538208,
-0.03274150937795639,
0.6486034393310547,
-0.8324699401855469,
0.4124176502227783,
0.040489111095666885,
-0.545753002166748,
-0.9157741665840149,
-0.22959749400615692,
-0.34261608123779297,
-0.2387654334306717,
-0.7883898615837097,
-0.19561313092708588,
0.8732019066810608,
-0.8361895084381104,
0.7869397401809692,
0.39124003052711487,
-0.09506410360336304,
0.4908771514892578,
-0.016148701310157776,
0.465607613325119,
0.6946513056755066,
-0.009220573119819164,
-0.40242815017700195,
-0.2397419661283493,
-1.0819876194000244,
-0.24880681931972504,
-0.40663444995880127,
-0.27687424421310425,
0.1323891580104828,
0.292046457529068,
0.394350528717041,
0.037564631551504135,
0.1603255569934845,
0.06521926075220108,
-0.004246266093105078,
-0.7351304292678833,
0.17828845977783203,
0.4592286944389343,
-0.07472246885299683,
0.3723597824573517,
-1.0204955339431763,
0.6380102038383484,
-0.39337408542633057,
-0.5870426893234253,
-0.002889767987653613,
0.1840491145849228,
-0.7842097282409668,
0.5767999291419983,
-0.4512292444705963,
-0.03241913020610809,
-0.058201711624860764,
0.7990530133247375,
-0.03411904349923134,
-0.33219221234321594,
-0.22665584087371826,
-0.06438475847244263,
-0.23377767205238342,
-0.022356688976287842,
-0.041917018592357635,
-1.5216623544692993,
-0.047063954174518585,
0.8087245225906372,
0.4421195685863495,
-0.45179569721221924,
0.7029830813407898,
-1.2226523160934448,
-0.6728433966636658,
-0.06943834573030472,
-0.776486337184906,
0.10955347120761871,
0.9069036841392517,
-0.3469964265823364,
-1.1689624786376953,
-0.02265062741935253,
0.3479316234588623,
0.2935587167739868,
0.2478286325931549,
0.05727376043796539,
0.36683031916618347,
1.0046769380569458,
-0.29503515362739563,
-0.10446768999099731,
0.28128278255462646,
-0.674762487411499,
-0.4278210997581482,
0.10883371531963348,
-0.6810380220413208,
-0.3055960536003113,
-0.07972153276205063,
0.23467154800891876,
0.13103389739990234,
0.24547968804836273,
-0.8668266534805298,
-0.17738838493824005,
-0.5629006624221802,
-0.2742312252521515,
0.5489744544029236,
0.6427749991416931,
0.5133642554283142,
-0.3460957109928131,
-0.8654857873916626,
-0.5493150949478149,
-0.03741283342242241,
0.30461788177490234,
0.8029016256332397,
-0.8006899952888489,
0.3107127249240875,
0.43118175864219666,
-0.24683693051338196,
0.12354080379009247,
-0.31200918555259705,
0.20300137996673584,
0.42229631543159485,
0.24901804327964783,
0.7616820335388184,
-0.4881880283355713,
-0.5667106509208679,
-0.2609466314315796,
1.285779595375061,
0.4208523631095886,
0.729933500289917,
0.4284946024417877,
-0.32152754068374634,
-0.4326176345348358,
-0.6348914504051208,
-0.13417097926139832,
-0.3745906352996826,
-0.46839404106140137,
-0.219643235206604,
-0.32507652044296265,
-0.058732084929943085,
-0.265263170003891,
0.20771895349025726,
1.1397570371627808,
-0.28518572449684143,
-0.14405491948127747,
0.5878701210021973,
-0.43422529101371765,
0.4836708903312683,
0.7937018871307373,
0.7738040089607239,
-0.0060449144802987576,
-0.2957683503627777,
0.7995657324790955,
0.513748288154602,
0.07462115585803986,
0.4444160461425781,
-0.257637619972229,
-0.487219899892807,
-1.050032138824463,
1.035868525505066,
0.09431396424770355,
-0.0068574706092476845,
0.07861484587192535,
0.5467305779457092,
-0.47971221804618835,
-1.0429095029830933,
-0.07223925739526749,
0.8121382594108582,
0.5372128486633301,
0.035744667053222656,
0.0029322279151529074,
0.12234900146722794,
-0.6020857691764832,
-0.04269128292798996,
0.9318534135818481,
-0.24937495589256287,
-0.6482068300247192,
-0.31447741389274597,
0.3633981943130493,
-0.20974986255168915,
0.34780552983283997,
0.8223331570625305,
0.08026090264320374,
0.2738361656665802,
-0.6421818137168884,
0.3961000144481659,
0.9704843163490295,
-0.5626680254936218,
-0.34958431124687195,
0.6810299158096313,
-0.033875998109579086,
-0.09214001893997192,
0.5280113816261292,
-0.6371442079544067,
-0.6087873578071594,
0.009019345045089722,
-0.7637525200843811,
0.8734022378921509,
-0.7640337944030762,
-0.48287850618362427,
-0.25713977217674255,
-0.5148097276687622,
0.3404225707054138,
0.4033917188644409,
0.23442591726779938,
-0.20894472301006317,
-0.35922542214393616,
0.7162551879882812,
0.04230678454041481,
0.33554983139038086,
0.08234106749296188,
0.43558478355407715,
1.1957783699035645,
0.8182255029678345,
0.35543641448020935,
0.0937400683760643,
0.12776991724967957,
0.1173749789595604,
0.1704779714345932,
0.44217801094055176,
-0.3884291648864746,
-0.3299739956855774,
-0.5216983556747437,
-0.3194686770439148,
-0.9231139421463013,
-0.5809131264686584,
0.957223117351532,
-0.21697790920734406,
0.634387731552124,
-0.05828952044248581,
-0.28108465671539307,
-0.7317958474159241,
-0.35027894377708435,
-0.8457475304603577,
0.1744614839553833,
-0.4536336362361908,
-0.6990641951560974,
-0.286978155374527,
-0.6078788042068481,
-0.14903326332569122,
-0.23468917608261108,
-0.03458337113261223,
0.08338001370429993,
-0.14232082664966583,
0.8989438414573669,
-0.23662984371185303,
0.28715839982032776,
-0.8790491819381714,
0.25562354922294617,
-0.8831297159194946,
-0.03119778260588646,
-0.8623884916305542,
-0.5484211444854736,
-0.2977103292942047,
-0.5803232789039612,
0.18545690178871155,
-0.27267906069755554,
-0.07739607989788055,
0.3350302278995514,
0.7337815761566162,
-0.07993076741695404,
-0.16024716198444366,
-0.580781877040863,
-0.005444350186735392,
0.6376777291297913,
0.27047014236450195,
-0.8271774649620056,
-0.4062941372394562,
0.11126818507909775,
-0.1113894060254097,
0.08374711126089096,
0.025406619533896446,
-1.2571038007736206,
-0.6957341432571411,
0.07826969772577286,
0.6688691973686218,
-0.4572196900844574,
-0.39284056425094604,
-0.1258762776851654,
-0.2757530212402344,
0.18592879176139832,
0.12909333407878876,
-0.31491729617118835,
-0.1509198248386383,
-0.791959285736084,
-0.29511916637420654,
-0.093210868537426,
-0.36082327365875244,
0.2819593548774719,
-0.638663649559021,
-0.6171218156814575,
-0.05514984950423241,
0.7254214882850647,
-0.1371985673904419,
0.10933610051870346,
0.37859857082366943,
0.14450019598007202,
0.004746612161397934,
-0.3131665885448456,
-0.20406609773635864,
-0.5087391138076782,
0.18392960727214813,
0.20741765201091766,
-0.4420711398124695,
0.5098305344581604,
-0.46828532218933105,
0.48473140597343445,
-0.7191515564918518,
0.4402692914009094,
-0.3588162064552307,
0.05676618963479996,
0.707026481628418,
0.2081618756055832,
0.9630177021026611,
-1.045062780380249,
0.5184640288352966,
1.0809412002563477,
-0.006080150604248047,
0.6340663433074951,
-0.13446210324764252,
-0.9675069451332092,
-0.12554821372032166,
0.10595357418060303,
-1.0218414068222046,
0.6007227301597595,
-0.03443405404686928,
-0.24779030680656433,
-0.610687792301178,
-0.7389445900917053,
0.45952320098876953,
0.08155813068151474,
0.5010502934455872,
0.3944563567638397,
0.07944948971271515,
0.019774125888943672,
-0.0886819064617157,
-0.20740985870361328,
-0.15050171315670013,
-0.5018267035484314,
0.3600538969039917,
-0.3320988416671753,
-0.07773325592279434,
0.22390861809253693,
-0.5522767305374146,
-0.8763343095779419,
0.2110111117362976,
0.3094150722026825,
0.6797139644622803,
-0.33686506748199463,
0.6400490403175354,
-0.13899418711662292,
-0.5723521113395691,
-0.5285420417785645,
0.29787659645080566,
0.4545571208000183,
0.5531659126281738,
0.6494820713996887,
-0.026052717119455338,
-0.21898530423641205,
-0.12359924614429474,
0.5809932351112366,
-1.3752472400665283,
-0.5245221853256226,
0.524675190448761,
-0.26721587777137756,
-0.23883266746997833,
0.12887123227119446,
-0.2282862663269043,
-0.6277929544448853,
-0.845217227935791,
-1.242190957069397,
-0.2206224501132965,
0.05131741240620613,
-0.36534184217453003,
-0.2850615978240967,
-1.0132907629013062,
0.18019349873065948,
0.7650534510612488,
0.9413008093833923,
-0.05746322497725487,
-0.4322819113731384,
0.2866692543029785,
-0.3982674777507782,
-1.1333670616149902,
0.37351474165916443,
1.3636422157287598,
0.5292046070098877,
-0.3433245122432709,
-0.6455013155937195,
0.02010786347091198,
-0.13808287680149078,
-0.38532331585884094,
0.33701789379119873,
-0.5271655917167664,
-0.11848101019859314,
-0.0606415793299675,
0.07387354969978333,
0.07983937859535217,
0.06517622619867325,
0.31399625539779663,
-0.08416160941123962,
0.19696861505508423,
-0.9019806385040283,
-0.11583657562732697,
-0.19339880347251892,
0.37928277254104614,
0.4871591031551361,
0.20595145225524902,
0.19635377824306488,
-0.5841226577758789,
-0.09867418557405472,
-0.061329178512096405,
-0.8129079937934875,
-0.4979211688041687,
-1.0353418588638306,
-0.04765325039625168,
-0.952820360660553,
-0.14255397021770477,
-0.31861281394958496,
0.31965160369873047,
-0.07896148413419724,
-0.0049814097583293915,
-0.5111706852912903,
-0.4346339702606201,
0.5751193165779114,
0.7256437540054321,
-0.07183535397052765,
-1.0659263134002686,
-0.9727994203567505,
-0.1315677911043167,
-0.6002650856971741,
0.11968154460191727,
-0.2941032946109772,
-0.06318970024585724,
0.41574373841285706,
0.355031818151474,
-0.22029836475849152,
1.4552922248840332,
-0.6371543407440186,
-0.5290813446044922,
0.844792366027832,
0.2103174328804016,
-0.8185505867004395,
0.7624931335449219,
-0.0035840622149407864,
0.852665364742279,
0.5304257869720459,
0.05880776047706604,
-0.4349297285079956,
-0.4317561686038971,
-1.0645928382873535,
-0.17626118659973145,
0.4597057104110718,
0.8251262307167053,
0.011803330853581429,
-0.9009604454040527,
-0.224504292011261,
-0.31916847825050354,
-0.8245779871940613,
0.44410666823387146,
-0.857835590839386,
0.6952311992645264,
-0.9555966854095459,
0.6651897430419922,
0.3117492198944092,
0.23100757598876953,
-0.2058284431695938,
0.9533430933952332,
-0.13397160172462463,
-0.6307655572891235,
0.1240910142660141,
0.27442631125450134,
-0.15099790692329407,
-0.025898993015289307,
0.706346869468689,
-0.08385295420885086,
-0.3419281840324402,
0.03994649276137352,
0.16581837832927704,
0.0041975597850978374,
-0.5278176665306091,
-0.45258745551109314,
-0.7795615196228027,
-0.2629404366016388,
-0.5388203859329224,
0.4384220540523529,
0.2934246063232422,
-0.42212650179862976,
-0.1368933469057083,
-0.7116546630859375,
-0.808285653591156,
-0.23828904330730438,
-0.5531330704689026,
-0.3737810254096985,
0.3085458278656006,
0.10399049520492554,
-0.573727548122406,
0.42745906114578247,
0.13704515993595123,
-0.2590506672859192,
-0.5402659177780151,
1.3949095010757446,
0.5475046038627625,
-0.4278908371925354,
-0.39219269156455994,
0.2056403011083603,
-0.8015686869621277,
-0.40358537435531616,
-0.7202371954917908,
0.7027490735054016,
-0.35385507345199585,
-1.104438066482544,
0.6489477157592773,
0.5901528000831604,
-0.3856373131275177,
0.1283874213695526,
-0.3588101267814636,
0.01538687665015459,
-0.41481465101242065,
-0.061331216245889664,
-0.15241779386997223,
-0.2105979323387146,
-0.30851128697395325,
0.5578817129135132,
-0.09287026524543762,
-0.6037449240684509,
0.007560380734503269,
0.23568475246429443,
0.3062215745449066,
-0.07710301876068115,
-0.024856040254235268,
0.7507138848304749,
0.3519449234008789,
-0.6584942936897278,
0.39880383014678955,
0.6124078631401062,
0.6337772607803345,
0.4269810914993286,
-0.3239671289920807,
0.15233510732650757,
0.25149503350257874,
-0.01858961209654808,
0.40697795152664185,
0.18463465571403503,
0.46334144473075867,
0.6363769173622131,
0.3773539364337921,
0.680980384349823,
-0.05933196842670441,
-0.0368318073451519,
-0.09744303673505783,
0.7567046880722046,
-0.3325069844722748,
0.14452020823955536,
-0.27177098393440247,
0.25128939747810364,
0.41321203112602234,
0.22733168303966522,
-0.2749932110309601,
-0.532181978225708,
-0.26926887035369873,
0.3281986713409424,
-0.9463161826133728,
-0.4682150185108185,
-0.026623554527759552,
-0.25796428322792053,
0.370572954416275,
0.4465457797050476,
-0.3014455735683441,
0.14311586320400238,
0.5598395466804504,
0.11805910617113113,
-0.30198609828948975,
0.36594727635383606,
0.7641926407814026,
0.848879337310791,
-0.04105303809046745,
0.8890636563301086,
0.385975182056427,
0.4631845951080322,
0.6618247628211975,
-0.39765664935112,
0.06972791254520416,
0.26689770817756653,
-1.0905829668045044,
0.3738781213760376,
-0.3216429054737091,
0.20979641377925873,
0.0974062904715538,
-0.7830991744995117,
0.2262689769268036,
0.20366449654102325,
-0.0019478824688121676,
0.5120512247085571,
-0.29357779026031494,
-0.2116054743528366,
0.023271456360816956,
0.24542738497257233,
0.4670504033565521,
0.16889521479606628,
0.14928938448429108,
-0.2662132978439331,
1.1208281517028809,
1.372853398323059,
-0.3698122501373291,
0.389279305934906,
-0.12042184919118881,
-0.06437375396490097,
0.13388724625110626,
0.9564646482467651,
-0.3819761574268341,
0.9533587694168091,
-0.5595460534095764,
-0.2272779494524002,
0.005687696393579245,
0.042918961495161057,
-0.44245463609695435,
-0.14076265692710876,
0.3389400541782379,
-0.047748807817697525,
-0.5777342319488525,
-0.30803099274635315,
1.2135809659957886,
0.9214414954185486,
-0.7590978145599365,
0.2749291956424713,
0.29513126611709595,
-0.6525246500968933,
0.07442251592874527,
-0.8739263415336609,
0.7568984031677246,
-0.827917218208313,
-0.6909967660903931,
-0.6594492197036743,
-0.06732326000928879,
-1.2366955280303955,
-1.4140836000442505,
0.5806010961532593,
-0.6856880187988281,
0.7030974626541138,
0.5001111030578613,
0.4933597147464752,
0.5937901139259338,
-0.29896441102027893,
-0.15887627005577087,
-0.23188939690589905,
0.6914269924163818,
0.33078110218048096,
0.6020956635475159,
1.1654671430587769,
0.24108478426933289,
-0.8380960822105408,
-0.26820677518844604,
0.4703025817871094,
-0.32464051246643066,
0.8049393892288208,
-0.24673481285572052,
-0.27532216906547546,
-0.049688033759593964,
-0.6396172642707825,
0.48185083270072937,
0.42696404457092285,
0.16779033839702606,
0.10619814693927765,
-0.3349520266056061,
-0.044931184500455856,
-0.6577757000923157,
0.18299104273319244,
-0.7407439947128296,
0.4415045976638794,
0.09343218803405762,
0.0021230929996818304,
-0.007473562378436327,
-0.44220808148384094,
4.068967342376709,
0.5275787115097046,
0.4549800455570221,
0.2359275221824646,
1.2660685777664185,
0.8679455518722534,
-0.034328632056713104,
-0.006449074484407902,
0.4183203876018524,
-0.30477458238601685,
-0.12028736621141434,
0.5396539568901062,
0.6673955321311951,
-0.13776728510856628,
0.18321387469768524,
0.5436725616455078,
-0.02897496335208416,
0.3179965615272522,
-0.29200947284698486,
-1.3210033178329468,
-1.1552739143371582,
0.4158477783203125,
0.03946905955672264,
0.0176461823284626,
-0.2669522762298584,
0.017359942197799683,
0.35159674286842346,
-0.20401553809642792,
-0.2398601770401001,
-0.3749139606952667,
-0.5732101202011108,
-0.6431100368499756,
0.23608475923538208,
0.19826394319534302,
-0.8496766090393066,
0.29440945386886597,
0.4596399664878845,
-0.07002908736467361,
0.5653442740440369,
0.05715499445796013,
0.10627847164869308,
-0.32234272360801697,
0.1375778764486313,
-0.43384644389152527,
-0.26006656885147095,
0.9803248047828674,
0.31685295701026917,
0.8970842361450195,
0.7636748552322388,
-0.7073274850845337,
-0.06088902801275253,
-0.051582708954811096,
0.6747295260429382,
-0.6124190092086792,
-0.9157339930534363,
0.0059850760735571384,
-0.6047422289848328,
0.1600370854139328,
0.494886577129364,
0.22144131362438202,
0.18430586159229279,
-0.34839606285095215,
0.09221479296684265,
-0.23610781133174896,
-0.3423445224761963,
0.5447341799736023,
0.12293754518032074,
-0.17577417194843292,
-0.3650023341178894,
0.09410175681114197,
-0.03664092719554901,
-0.15918219089508057,
-0.5717160105705261,
0.09442545473575592,
0.4228828549385071,
0.6710652709007263,
-0.5700598359107971,
0.22375264763832092,
-0.11397092044353485,
0.25388315320014954,
-0.08903006464242935,
-0.6066926121711731,
0.18288755416870117,
-0.0038128430023789406,
0.6977710127830505,
0.6718878149986267,
0.02959594875574112,
0.4465421140193939,
-0.44373130798339844,
0.7612148523330688,
0.5023955702781677,
1.4557677507400513,
0.42384961247444153,
0.005051136948168278,
-0.7293882966041565
] |
Lyapunov Exponent of SU(3) Gauge Theory
|
The classical SU(3) gauge theory is shown to be deterministic chaotic. Its largest Lyapunov exponent is dertermined, from which a short time scale of thermalization of a pure gluon system is estimated. The connection to gluon damping rate is discussed.
|
C. Gong
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209018
|
hep-lat/9209019
|
[
0.4491475522518158,
-0.34582996368408203,
0.22779208421707153,
0.5112080574035645,
-0.8144893646240234,
-0.20927691459655762,
0.027712607756257057,
0.1849021166563034,
-0.2295396327972412,
1.367126226425171,
0.6836775541305542,
-0.41174840927124023,
-0.10425632447004318,
-0.08781785517930984,
-0.301866739988327,
0.4547313153743744,
0.1237621083855629,
-0.3934439718723297,
-1.2727627754211426,
0.6410489678382874,
0.10874083638191223,
0.017193108797073364,
-1.4360995292663574,
-0.6669299602508545,
-0.3672434985637665,
0.28360453248023987,
0.6680821180343628,
0.16705501079559326,
1.2784396409988403,
0.3335753381252289,
0.29235565662384033,
-1.0110901594161987,
0.36991575360298157,
-0.19153012335300446,
-0.475427508354187,
0.02075612172484398,
0.23194794356822968,
-0.15141069889068604,
0.9255768656730652,
-0.3215043842792511,
1.2344259023666382,
-0.10724405199289322,
-0.37590521574020386,
-0.175268292427063,
-0.3062562048435211,
-0.2316417098045349,
-0.480826199054718,
-0.6186062693595886,
-0.2855054438114166,
-1.2321348190307617,
0.16022279858589172,
0.5139961838722229,
0.7396625280380249,
-0.6306419968605042,
-0.6421785950660706,
-0.5586140751838684,
0.0707525834441185,
0.5394905805587769,
-0.26294994354248047,
-0.11164779216051102,
0.5139980912208557,
0.04647158831357956,
0.594732940196991,
-0.1852269172668457,
-0.36392781138420105,
0.8808342814445496,
0.1009330227971077,
0.7087065577507019,
-0.08639328926801682,
-0.24538666009902954,
-0.15167264640331268,
-0.22419355809688568,
-0.8749169707298279,
0.11086295545101166,
-0.9246615767478943,
0.042096592485904694,
0.2373264878988266,
-0.788438081741333,
-0.7837937474250793,
-0.008445999585092068,
-0.023743348196148872,
-0.49026528000831604,
-0.3843809962272644,
0.6200422644615173,
-0.35700830817222595,
-0.04370027780532837,
0.07148638367652893,
-0.1663234978914261,
0.15629464387893677,
0.4680909812450409,
0.2499929964542389,
0.7826871871948242,
-0.5059379935264587,
-0.4621922969818115,
0.5459314584732056,
0.23250840604305267,
0.42335301637649536,
0.14951367676258087,
0.07322061061859131,
0.2420061081647873,
-0.1528281718492508,
0.8283492922782898,
-0.35342100262641907,
0.1126827821135521,
-0.6927750706672668,
0.40841835737228394,
0.061572957783937454,
0.4355338215827942,
0.4267153739929199,
-0.8852868676185608,
0.3193194270133972,
-0.5337446928024292,
0.016772475093603134,
0.7194581627845764,
-0.28247880935668945,
0.34127166867256165,
0.30960577726364136,
0.2407355010509491,
-0.30428484082221985,
-0.1507020741701126,
-0.00574233615770936,
0.206521674990654,
0.25095194578170776,
0.8896310925483704,
0.09301973879337311,
-0.13560950756072998,
-0.2159043401479721,
-0.10308525711297989,
-0.1840037703514099,
-0.09980754554271698,
0.15536561608314514,
0.25447896122932434,
-0.3706083297729492,
0.5670754909515381,
-0.5461487174034119,
-0.07544202357530594,
-0.25716254115104675,
0.5561898946762085,
-0.12246086448431015,
0.0922689139842987,
0.766954779624939,
-0.33397844433784485,
0.06384506076574326,
1.201560616493225,
-0.2950948476791382,
0.7584277391433716,
0.035862550139427185,
0.6138600707054138,
-0.6720616221427917,
0.42571818828582764,
-0.5674404501914978,
-0.4172940254211426,
-0.602223813533783,
0.38717785477638245,
0.07946054637432098,
0.7934572696685791,
0.13715459406375885,
0.09201294928789139,
-0.8354083895683289,
-0.5445092916488647,
0.30895376205444336,
-0.1504443734884262,
0.12818829715251923,
0.5986225605010986,
-0.5153865218162537,
-0.12141476571559906,
-0.7377286553382874,
-0.5269659161567688,
0.6257897019386292,
-0.3764225244522095,
-0.10687922686338425,
0.5070902705192566,
-0.4955066442489624,
1.0059136152267456,
0.07031234353780746,
0.7409395575523376,
0.40117383003234863,
-0.21109069883823395,
-0.48155340552330017,
0.6693248152732849,
0.010367611423134804,
-0.2768884301185608,
0.9202333688735962,
0.2206987738609314,
-0.12474844604730606,
-0.38978704810142517,
-0.4264366328716278,
-0.4550357460975647,
-0.30512261390686035,
0.29233285784721375,
-0.5894275307655334,
0.09304486215114594,
-0.35028010606765747,
0.7989348769187927,
-0.7728129029273987,
-0.039063602685928345,
-0.9929622411727905,
0.7001393437385559,
-0.5456013083457947,
-0.28967875242233276,
0.07621263712644577,
0.16236340999603271,
-0.76216721534729,
-0.003566101426258683,
-1.4944705963134766,
-0.18269678950309753,
0.48963242769241333,
-0.1483737975358963,
-0.4061408042907715,
-0.367877721786499,
-0.3245117962360382,
-0.1174791231751442,
0.28681981563568115,
-0.09085576236248016,
0.4169881045818329,
0.032405056059360504,
0.3159394860267639,
-0.0608389638364315,
0.6893242001533508,
0.7214157581329346,
0.44217655062675476,
0.8717150688171387,
-0.23749949038028717,
0.6393312215805054,
-0.832261323928833,
-0.10323972254991531,
-0.19174258410930634,
0.41680601239204407,
0.10499861091375351,
-0.1865972876548767,
-0.3759009838104248,
0.5000489354133606,
-0.1658923327922821,
0.6760411858558655,
0.4153725206851959,
-0.08749730885028839,
0.5783873796463013,
0.281274676322937,
0.7166743278503418,
0.35351741313934326,
0.17878758907318115,
-0.35518258810043335,
0.5230454206466675,
-0.03007460944354534,
-0.11559615284204483,
0.18668979406356812,
-0.5056052207946777,
0.5009710192680359,
-1.0878468751907349,
0.7875381112098694,
0.2835961878299713,
0.4540883004665375,
-0.15384337306022644,
0.445712149143219,
-0.7370554804801941,
0.09770489484071732,
0.3164824843406677,
-0.07390377670526505,
-0.6292402744293213,
-0.3749361038208008,
0.2451147586107254,
0.13048812747001648,
-0.43623727560043335,
-0.5178513526916504,
0.05243125930428505,
1.274369478225708,
0.16255244612693787,
-0.11642973124980927,
0.8342746496200562,
-0.12537923455238342,
-1.5314195156097412,
-0.007799865212291479,
-1.4778001308441162,
0.1155238226056099,
-0.15312357246875763,
0.32276618480682373,
0.5280444025993347,
-0.04294373840093613,
0.5491800904273987,
-0.23932957649230957,
-0.7189381718635559,
0.138726145029068,
-0.6387442946434021,
-0.045124977827072144,
-0.021693537011742592,
-0.017165925353765488,
-0.32978567481040955,
0.8365733027458191,
-0.5304635167121887,
-0.5953271389007568,
-0.4259484112262726,
0.06547590345144272,
1.0310841798782349,
-0.7511712908744812,
0.2594701051712036,
-0.903978168964386,
-0.4092386066913605,
0.21444480121135712,
0.2674310505390167,
-0.37509462237358093,
-0.03715875744819641,
0.6734674572944641,
0.3153565526008606,
-0.622977614402771,
-0.7697964906692505,
0.3955879211425781,
0.19917641580104828,
-0.20215974748134613,
0.24958688020706177,
-0.26693812012672424,
-0.40271857380867004,
0.4067850112915039,
-0.0031494733411818743,
-0.06576550751924515,
-0.1670694202184677,
0.8181453347206116,
0.645343542098999,
0.5731940269470215,
0.17845749855041504,
-0.27493375539779663,
-0.2657696008682251,
0.3205268383026123,
0.22089605033397675,
-0.4308871626853943,
-0.5438979864120483,
0.7025444507598877,
-0.5183901190757751,
-0.18821629881858826,
0.48558834195137024,
-0.6665381789207458,
-0.5756008625030518,
0.18916089832782745,
-0.4963986575603485,
0.02885480597615242,
-0.8201679587364197,
0.2709237039089203,
-0.7209941744804382,
0.4922301471233368,
0.36022838950157166,
0.11858999729156494,
0.6858804821968079,
-0.440913587808609,
0.28057315945625305,
-0.0005599692231044173,
0.8615142703056335,
-0.3803403675556183,
-0.4555048942565918,
0.03296204283833504,
-0.374612420797348,
0.7444203495979309,
-0.8574608564376831,
0.043096113950014114,
-0.42514732480049133,
0.5290253162384033,
0.22583308815956116,
0.5976390838623047,
-0.14093364775180817,
-0.3750809133052826,
-0.5311024785041809,
-0.4970535635948181,
-0.2990601062774658,
1.29403817653656,
0.1309167891740799,
-0.04680244252085686,
-0.44456273317337036,
-0.4093846380710602,
0.21923398971557617,
0.04081166163086891,
0.14873456954956055,
-0.2449979931116104,
0.0056351665407419205,
0.11020398139953613,
-0.23568867146968842,
0.1597447395324707,
0.4918259084224701,
0.4356856346130371,
0.7035572528839111,
0.38755086064338684,
1.0834925174713135,
-0.24985024333000183,
-0.5973897576332092,
0.2021900713443756,
0.4750933051109314,
0.5583152770996094,
0.9421020746231079,
0.23620212078094482,
0.09902094304561615,
0.31504860520362854,
-0.04708925634622574,
-0.499729186296463,
-0.7717579007148743,
-0.19996172189712524,
-0.06176997348666191,
0.24355824291706085,
0.49734464287757874,
-0.47245028614997864,
-0.07123849540948868,
-0.4028901159763336,
0.5994820594787598,
-0.28371739387512207,
0.1335597038269043,
0.11269694566726685,
0.3262671232223511,
0.46279093623161316,
-0.0981070026755333,
0.0561683289706707,
-0.4824124276638031,
-0.07411286234855652,
0.3824574649333954,
0.4516366720199585,
-0.5345409512519836,
-0.05561702698469162,
0.3195071816444397,
-0.3074384331703186,
0.7013905048370361,
0.10316485166549683,
-1.3527767658233643,
0.18822048604488373,
-0.1420554369688034,
0.8161557912826538,
-0.10790977627038956,
-0.2481551617383957,
0.6623073816299438,
0.22639262676239014,
0.4490201771259308,
-0.37570804357528687,
0.30815455317497253,
-0.4996449649333954,
0.7927536964416504,
-0.06646682322025299,
-1.0291424989700317,
-0.5517232418060303,
-1.0659111738204956,
-0.32244908809661865,
-0.654543936252594,
0.1354677975177765,
1.2578963041305542,
0.25732794404029846,
0.21225231885910034,
-0.6835513710975647,
-0.42162609100341797,
1.0156428813934326,
-0.1402997076511383,
-0.5963250994682312,
0.8158416748046875,
-0.10014085471630096,
-0.4336017370223999,
0.5639442801475525,
-0.2358456701040268,
-0.1735183447599411,
0.060263171792030334,
-0.07843911647796631,
0.9462325572967529,
-0.3241327404975891,
-0.4551847279071808,
-0.656533420085907,
0.03430785983800888,
-0.665034830570221,
0.5363106727600098,
0.2899227738380432,
-0.1726894974708557,
-0.013354476541280746,
0.17960034310817719,
-0.14785850048065186,
-0.18797039985656738,
-0.08545026928186417,
-0.3543250560760498,
0.4658001959323883,
0.5314370393753052,
0.02888951078057289,
0.7083443999290466,
0.47666430473327637,
-0.048226434737443924,
-0.4333251416683197,
0.9458016157150269,
-0.35233643651008606,
-0.04443143308162689,
-0.19621622562408447,
-0.23011216521263123,
-0.721405029296875,
-0.7318224906921387,
0.17209504544734955,
-0.1270446479320526,
0.2627885341644287,
0.36557498574256897,
0.04569021239876747,
-0.3475729823112488,
-0.268148273229599,
-0.8708029985427856,
0.22692684829235077,
-0.561795711517334,
-0.5013566613197327,
0.8028883337974548,
-0.0443144217133522,
0.24077391624450684,
-0.22534790635108948,
-0.3299407660961151,
-0.09765104949474335,
0.3634985685348511,
0.7076018452644348,
0.15919461846351624,
0.6812724471092224,
-1.278701901435852,
0.8258897662162781,
-0.2088860124349594,
0.5163217782974243,
-0.9911665916442871,
-0.6358097195625305,
0.09372518211603165,
-0.19333525002002716,
-0.064094677567482,
0.4552406966686249,
-0.545389711856842,
-0.03742996230721474,
-0.3849588632583618,
0.03396817669272423,
0.7924385666847229,
-0.6206740736961365,
-0.6108613610267639,
0.5204305052757263,
0.1732267290353775,
-0.45115572214126587,
-0.11423049122095108,
0.39984968304634094,
-0.0908157080411911,
0.14598491787910461,
0.30411630868911743,
-0.7773039937019348,
0.1263720840215683,
-0.368894100189209,
-0.0024874333757907152,
-1.3095641136169434,
-0.2736492156982422,
-0.059376318007707596,
-1.1212822198867798,
0.3050156831741333,
0.2557142972946167,
0.17535585165023804,
-0.7193865776062012,
-0.9661657214164734,
-0.5631142854690552,
0.38712894916534424,
0.1633301079273224,
0.10469622910022736,
-0.5893721580505371,
-0.16334687173366547,
-0.39031121134757996,
0.33698439598083496,
-0.2848880887031555,
0.34450045228004456,
0.07451310753822327,
-0.10214253515005112,
0.210490420460701,
0.8809695243835449,
0.24272143840789795,
-0.10097835212945938,
0.007769600488245487,
0.2794208824634552,
-0.009976687841117382,
0.324963241815567,
-0.7191896438598633,
0.18172164261341095,
-0.7023184299468994,
0.9514659643173218,
-0.35372069478034973,
-0.6469950675964355,
0.31883320212364197,
0.043219663202762604,
0.6292595863342285,
0.07198131829500198,
0.15533724427223206,
-0.012920679524540901,
-0.0017896536737680435,
0.8845868706703186,
0.5560123324394226,
-0.948426365852356,
-0.39277052879333496,
-0.7636107802391052,
-0.20530158281326294,
0.5905239582061768,
0.14645002782344818,
0.0025817120913416147,
-1.1150197982788086,
-0.8291177153587341,
0.06423206627368927,
0.27260228991508484,
0.01029282622039318,
0.7638460397720337,
0.1983906328678131,
0.6082903146743774,
-0.022115211933851242,
-0.42261266708374023,
-0.9136294722557068,
0.5538519024848938,
0.015243126079440117,
-0.16994865238666534,
0.459319144487381,
0.22541747987270355,
-0.7179731130599976,
-0.6489232778549194,
-0.39016085863113403,
0.3399030566215515,
-0.21287328004837036,
-0.6941525936126709,
0.6800144910812378,
-0.29002660512924194,
-0.52921062707901,
-0.5692882537841797,
0.25555044412612915,
0.1744186133146286,
0.43507081270217896,
0.37325945496559143,
0.38603997230529785,
0.19595211744308472,
-0.14199776947498322,
0.5719629526138306,
-0.07070848345756531,
-0.5650032162666321,
0.8287748694419861,
-0.8695078492164612,
-0.06894166767597198,
0.5799550414085388,
0.23849013447761536,
-0.9718347191810608,
0.04683400318026543,
-0.5805554986000061,
0.42525139451026917,
-0.3316276967525482,
-0.08717677742242813,
-0.45348215103149414,
-0.26022884249687195,
-0.03670622035861015,
0.7280471920967102,
1.0825166702270508,
0.06473886221647263,
0.3849135935306549,
-0.38252168893814087,
-0.10934867709875107,
-0.1925368309020996,
-0.19647465646266937,
1.2043718099594116,
0.29303401708602905,
-1.2531274557113647,
0.0950753316283226,
0.07333094626665115,
-0.15555092692375183,
-0.15700571238994598,
0.9169780015945435,
0.10613042116165161,
0.3233106732368469,
0.037302978336811066,
-0.00972011499106884,
0.2970159649848938,
0.7416511178016663,
0.2633081376552582,
-0.22623401880264282,
-0.02578897587954998,
-0.49472862482070923,
-0.44183477759361267,
-0.2581920027732849,
-0.020623890683054924,
0.6571717858314514,
0.34097743034362793,
0.17979474365711212,
-0.29282814264297485,
-0.34325993061065674,
-0.12947715818881989,
-0.5667668581008911,
0.6424316167831421,
-0.9072410464286804,
-0.27606257796287537,
-0.4661801755428314,
-0.34241825342178345,
0.5510368347167969,
0.9396240711212158,
-0.45655837655067444,
0.00489287031814456,
-0.6469686031341553,
0.15911446511745453,
-0.007128478493541479,
0.5538640022277832,
-0.27741363644599915,
-0.7173474431037903,
0.07023144513368607,
-0.037970274686813354,
-0.5273922085762024,
-0.19624321162700653,
-0.5108036398887634,
0.17910026013851166,
-0.38847437500953674,
0.28874722123146057,
-0.22402670979499817,
1.027599811553955,
-0.7599359154701233,
-1.1890735626220703,
0.3995956778526306,
-0.40307119488716125,
-1.012603759765625,
0.65614253282547,
-0.40652602910995483,
0.7291943430900574,
0.16032074391841888,
0.202293261885643,
-0.8029447197914124,
-0.3084152638912201,
-0.09725241363048553,
-0.16631124913692474,
0.5339094996452332,
0.3257181644439697,
-0.23653070628643036,
-0.7206761837005615,
-0.04026442766189575,
0.13134698569774628,
-0.8103329539299011,
0.6905151605606079,
-0.2658994793891907,
0.42237725853919983,
-0.16273970901966095,
0.20567800104618073,
0.1999165415763855,
0.49355441331863403,
-0.06762871146202087,
0.8616525530815125,
-0.08509933203458786,
-0.5348397493362427,
-0.1971798837184906,
0.1561981588602066,
-0.7800137996673584,
0.5229151248931885,
-0.06468378007411957,
0.2805042564868927,
-0.6687285900115967,
1.3802422285079956,
-0.41122376918792725,
0.29057836532592773,
-0.13908931612968445,
-0.027985356748104095,
0.028289925307035446,
-0.2628340721130371,
-0.74880051612854,
0.2189633995294571,
0.18022355437278748,
-0.5600913763046265,
-0.21051742136478424,
-0.594742476940155,
-0.5792394280433655,
0.3838713467121124,
-0.9563336372375488,
-1.0207836627960205,
-0.16101601719856262,
-0.16847118735313416,
0.24991293251514435,
0.6877894401550293,
-0.5090416073799133,
0.3560071587562561,
0.19562946259975433,
0.21182604134082794,
-0.150806725025177,
-0.4452689290046692,
-0.776718258857727,
0.13839875161647797,
-1.0165276527404785,
-0.6351135969161987,
-0.8209506869316101,
0.437051385641098,
-1.4126931428909302,
-0.9508842825889587,
-0.04046982526779175,
0.8791550993919373,
0.32408347725868225,
0.05888752639293671,
-0.4941886365413666,
-0.11313626170158386,
-0.05705179646611214,
-0.41467759013175964,
-1.2617498636245728,
-0.392091304063797,
-0.6212266683578491,
0.09756752848625183,
-0.26193758845329285,
-0.11450571566820145,
0.010623406618833542,
0.1803625077009201,
0.5073866248130798,
0.2973242998123169,
-0.03398020192980766,
0.5889076590538025,
0.4877261519432068,
-0.6152421832084656,
0.8255413770675659,
0.20627301931381226,
-0.07758566737174988,
0.19445858895778656,
-0.9417225122451782,
0.8508075475692749,
0.5726947784423828,
0.39260125160217285,
0.7184619903564453,
0.14798177778720856,
0.22210299968719482,
0.2949763536453247,
-0.05965367332100868,
0.0852842703461647,
-0.33983027935028076,
0.12620282173156738,
0.6429861783981323,
0.29498791694641113,
0.21663011610507965,
-0.5258978009223938,
0.11916083097457886,
-0.021711595356464386,
-0.38846510648727417,
-0.5287843942642212,
-0.030351730063557625,
-0.036666709929704666,
0.17810697853565216,
0.44118010997772217,
-0.3382682204246521,
-0.005950332619249821,
-0.2975938320159912,
0.3655087947845459,
0.18016661703586578,
-0.14416837692260742,
-0.1639043539762497,
0.5074172019958496,
1.1007962226867676,
0.3317784368991852,
0.3338566720485687,
0.5949592590332031,
-0.5666812658309937,
1.1608244180679321,
0.6668901443481445,
0.4790549874305725,
0.45286667346954346,
0.6398593783378601,
0.3007736802101135,
-0.4994807839393616,
0.4272024929523468,
0.24979229271411896,
-1.099427580833435,
0.41861748695373535,
-0.638138473033905,
-0.2897106409072876,
-0.5472397804260254,
0.052637241780757904,
0.14243382215499878,
-0.46226197481155396,
0.43879416584968567,
0.6273051500320435,
-0.4432884156703949,
-0.025372648611664772,
0.9469035267829895,
-0.18692119419574738,
0.277634859085083,
0.8315392136573792,
-0.16253502666950226,
0.4865526854991913,
1.143270492553711,
1.7750188112258911,
-0.06104814633727074,
0.03207406401634216,
0.28146401047706604,
-0.36889976263046265,
0.5992446541786194,
-0.33659234642982483,
-0.41955453157424927,
0.3012235462665558,
-0.7065297961235046,
-0.4902205467224121,
0.1825111210346222,
0.07122235745191574,
-0.19614382088184357,
-0.6230564713478088,
0.38329842686653137,
0.059829022735357285,
-0.5311042666435242,
-0.8518195748329163,
1.5122159719467163,
0.29399651288986206,
-0.39172443747520447,
-0.758552610874176,
0.10261689126491547,
-0.17803210020065308,
0.1073051244020462,
-0.9541768431663513,
0.4754406213760376,
-0.18903006613254547,
-0.3668694794178009,
-0.29970481991767883,
-0.7082099914550781,
-0.5164914727210999,
-0.24699611961841583,
0.22619383037090302,
-0.5797223448753357,
0.39085036516189575,
0.29182976484298706,
0.05642644688487053,
0.5877222418785095,
-0.636831521987915,
-0.27046021819114685,
0.15446209907531738,
0.6278619170188904,
0.074382483959198,
-0.11810313910245895,
0.4870520234107971,
0.6210362911224365,
-0.04043753445148468,
0.7029885053634644,
0.845704197883606,
-1.1780086755752563,
1.1203250885009766,
-0.14012287557125092,
0.9952237010002136,
0.3679834306240082,
0.14412090182304382,
0.007978977635502815,
-0.09422726184129715,
-0.0024539621081203222,
-0.058238882571458817,
-0.49654242396354675,
0.04798898845911026,
-1.0185596942901611,
0.18815220892429352,
-0.2582066059112549,
0.24848000705242157,
-0.43556270003318787,
0.24296724796295166,
0.13633927702903748,
-1.161563515663147,
4.20587682723999,
0.4761784076690674,
0.36973482370376587,
0.007084931246936321,
0.09455748647451401,
0.1191755160689354,
-0.6171857714653015,
-0.8083223700523376,
0.12642309069633484,
-0.2769322693347931,
-0.24359866976737976,
-0.19791756570339203,
0.36410561203956604,
-0.5590251684188843,
-0.08455303311347961,
0.8119260668754578,
-0.5735273361206055,
-0.17822745442390442,
0.402728796005249,
-0.8834015130996704,
-0.3251158893108368,
-0.021640455350279808,
0.32504233717918396,
0.003933258820325136,
0.10605674237012863,
0.661141037940979,
0.1758187860250473,
-0.4731126129627228,
-0.3212142586708069,
-0.4267805218696594,
-0.5447710752487183,
-0.872209906578064,
0.16851834952831268,
0.2540093958377838,
-0.42959946393966675,
0.31761276721954346,
0.4544816017150879,
-0.21985405683517456,
-0.3877854347229004,
-0.0458308570086956,
0.07824082672595978,
-0.4425010085105896,
0.14111115038394928,
-0.5934351086616516,
-0.6542946696281433,
1.102814793586731,
-0.5005986094474792,
0.7322694659233093,
0.6233656406402588,
-1.0563253164291382,
0.5246200561523438,
0.0419844351708889,
1.012978196144104,
-0.47393888235092163,
-1.2205243110656738,
0.07979501038789749,
-0.05383850634098053,
0.07793977856636047,
0.33851319551467896,
-0.05868328735232353,
0.3318118155002594,
-0.3842216432094574,
0.06606639176607132,
-0.05363118648529053,
0.15541799366474152,
-0.051497723907232285,
0.5343902111053467,
-0.5231238603591919,
-0.3100622594356537,
0.4415700137615204,
0.15779532492160797,
-0.5438566207885742,
-0.3777112066745758,
0.7991952896118164,
0.15548627078533173,
0.23914285004138947,
-0.11794727295637131,
0.4194127023220062,
0.08400026708841324,
-0.2638496458530426,
0.14872470498085022,
-0.158110111951828,
-0.3634900152683258,
0.10215474665164948,
0.13489794731140137,
1.1532871723175049,
-0.35970860719680786,
0.15352416038513184,
0.15820541977882385,
0.3943757712841034,
0.0011272374540567398,
0.9316720366477966,
0.08991535753011703,
0.19482699036598206,
-0.7655021548271179
] |
Multi-quark energies in QCD
|
Four-quark potentials for $SU(2)$ are evaluated in the static limit with the quenched approximation -- using a lattice of $16^3\times 32$ and $\beta=2.4$. The four quarks are restricted to the corners of rectangles with sides upto seven lattice spacings long. The results are analysed in terms of a strategy based on interquark two-body potentials -- as advocated earlier by the authors. This shows that a standard two-body approach overestimates the four-quark binding energy by upto a factor of about three for the largest rectangles.
|
A.M.Green, C.Michael and J.E.Paton
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209019
|
hep-lat/9209020
|
[
-0.38095027208328247,
0.39912232756614685,
1.170135259628296,
0.3202044367790222,
0.3756338953971863,
0.07700894773006439,
0.05138150230050087,
-0.46211469173431396,
0.16354459524154663,
1.0522679090499878,
0.31825339794158936,
-0.23423397541046143,
0.28100958466529846,
-0.43984454870224,
-0.23125655949115753,
0.5711683034896851,
-0.28828325867652893,
-0.7961503863334656,
-0.9744443893432617,
-0.3289957642555237,
-0.8067920207977295,
-0.37925079464912415,
-1.4453001022338867,
-1.1798702478408813,
-0.38036930561065674,
0.8938990235328674,
0.44350311160087585,
-0.0013496455503627658,
1.2632369995117188,
0.7676950097084045,
0.3820406198501587,
0.26704221963882446,
-0.4118378758430481,
-0.8840843439102173,
-0.24537791311740875,
-0.2537808418273926,
0.42986637353897095,
-0.3170532286167145,
-0.08190499991178513,
-0.6745909452438354,
1.4246406555175781,
-0.3629208505153656,
0.883347749710083,
-0.3580001890659332,
-0.19098512828350067,
0.43414822220802307,
0.2293703407049179,
0.03967883065342903,
-0.03891054168343544,
-1.268937587738037,
-0.0006526388460770249,
0.3012533187866211,
-0.3944573700428009,
-0.5823498964309692,
-0.6743587255477905,
0.016407184302806854,
-0.3163628876209259,
0.0829654112458229,
-0.08100832998752594,
-0.27943146228790283,
0.6188731789588928,
0.42929595708847046,
0.4436284601688385,
-0.8818053603172302,
0.5637606382369995,
1.4809030294418335,
-0.24402374029159546,
0.31787508726119995,
0.20456399023532867,
0.08019636571407318,
-0.700316309928894,
0.0372249037027359,
-0.0180464219301939,
-0.4000988304615021,
-0.6024905443191528,
-0.03276965767145157,
-0.3334963023662567,
0.11635682731866837,
-1.0685722827911377,
-0.3037736713886261,
0.3650600016117096,
0.40222305059432983,
-0.9494946599006653,
0.6399410367012024,
0.035587552934885025,
-0.6311051249504089,
0.39940208196640015,
0.5851722955703735,
0.7777454853057861,
0.6651251912117004,
-0.029285183176398277,
0.6130820512771606,
0.5280572772026062,
-0.3070610761642456,
-0.01765805296599865,
0.7300535440444946,
-0.5988158583641052,
0.6732518076896667,
0.30969080328941345,
0.8016263842582703,
0.47246700525283813,
1.3501238822937012,
-0.5294559001922607,
0.4762801229953766,
-0.8129757642745972,
0.8237262964248657,
0.11580739915370941,
-0.15143007040023804,
-0.7379018664360046,
-0.7463681101799011,
0.13942848145961761,
-0.032599903643131256,
0.4369037449359894,
0.6759301424026489,
-0.07133979350328445,
0.7266342043876648,
0.18097327649593353,
-0.2056717425584793,
-0.8496423959732056,
-0.26487115025520325,
-1.1394697427749634,
0.3406650125980377,
0.06620737910270691,
0.17489515244960785,
0.06035517156124115,
-0.6537003517150879,
0.21939042210578918,
0.8027861714363098,
-0.3718211352825165,
0.37537989020347595,
0.3761797249317169,
-0.6056087613105774,
-0.7936487197875977,
0.9245736598968506,
-0.05802428722381592,
-0.08128456026315689,
0.17784404754638672,
0.6378004550933838,
-0.1390981525182724,
-0.7519709467887878,
0.37798258662223816,
-0.3711109757423401,
0.16053788363933563,
1.1792182922363281,
-0.5894959568977356,
0.5449597835540771,
0.3109096884727478,
-0.3396287262439728,
-0.5879141688346863,
0.0712650716304779,
-0.9441452026367188,
-0.14870496094226837,
0.06181666627526283,
0.01937924511730671,
0.6200981140136719,
0.545211672782898,
-1.439720869064331,
0.28769516944885254,
-0.5180146098136902,
-0.588598370552063,
0.6514276266098022,
0.03163498267531395,
-0.326730877161026,
0.7830525636672974,
-0.749281644821167,
0.2796381115913391,
-0.822234034538269,
-0.1634974330663681,
0.030956946313381195,
-0.28975027799606323,
-0.3100435733795166,
0.19080492854118347,
0.24617008864879608,
0.0244656503200531,
0.7624362707138062,
0.6060488224029541,
0.7070479989051819,
-0.39743199944496155,
0.41802746057510376,
0.49863940477371216,
-0.17421740293502808,
-0.6188902258872986,
0.7085174918174744,
0.6403648257255554,
-0.4974617660045624,
-0.02296324074268341,
-0.1340024620294571,
-0.014869946986436844,
0.6581806540489197,
-0.02291359193623066,
-0.5355053544044495,
0.8434839248657227,
-0.5286558866500854,
0.22452236711978912,
-1.002024531364441,
-0.21301445364952087,
0.10018729418516159,
0.29991623759269714,
-0.41886985301971436,
-1.3131412267684937,
0.1458766758441925,
-0.5303921699523926,
-0.7092933058738708,
-0.09742575138807297,
-1.1159135103225708,
0.24052694439888,
0.6715164184570312,
0.12131239473819733,
-0.8812903761863708,
-0.11150853335857391,
0.5017321109771729,
-0.48473861813545227,
-0.601112425327301,
-0.11922185122966766,
0.10950178653001785,
-0.27559471130371094,
-0.21342059969902039,
0.06928591430187225,
0.7049668431282043,
-0.47839558124542236,
0.5992633104324341,
0.09777472913265228,
-0.32264187932014465,
0.6171960830688477,
-0.12300938367843628,
1.0772035121917725,
-0.13382533192634583,
0.590376615524292,
0.5060893297195435,
-0.2897696793079376,
0.21964333951473236,
0.7520402073860168,
0.0529351644217968,
0.10811600089073181,
1.0294429063796997,
0.35842931270599365,
0.43430009484291077,
0.696378231048584,
-0.2090703845024109,
0.2558595836162567,
0.48448729515075684,
0.767603874206543,
0.6250360608100891,
0.5306057333946228,
0.05880844593048096,
-0.13696226477622986,
0.1033589169383049,
-0.29416102170944214,
-0.5187519788742065,
0.29302436113357544,
-0.6063224673271179,
1.2910972833633423,
0.11454054713249207,
0.048842158168554306,
-0.6825385093688965,
-0.24886761605739594,
-0.48860129714012146,
0.5648727416992188,
-0.02933492697775364,
-0.4574873447418213,
-0.4340265095233917,
0.5369585156440735,
0.0221553985029459,
-0.05315311625599861,
-0.15972797572612762,
1.0873695611953735,
-0.6405736207962036,
0.14678482711315155,
-0.45204830169677734,
-0.5950096249580383,
-1.3429311513900757,
-0.2913942039012909,
-0.6495283842086792,
-0.04547753185033798,
0.29356005787849426,
-0.15096202492713928,
0.7345001101493835,
-0.37047839164733887,
1.0378515720367432,
0.17579300701618195,
-0.10882283002138138,
0.4091120958328247,
0.13740767538547516,
0.02059023082256317,
0.034829281270504,
-0.1853073239326477,
-0.8619681596755981,
0.7919233441352844,
-0.4428519308567047,
0.5382453799247742,
-0.4169732332229614,
-0.13240168988704681,
0.0648040920495987,
0.35341760516166687,
0.07149221748113632,
0.25183945894241333,
-0.17321737110614777,
-0.2078300267457962,
-0.0999385416507721,
-0.454855352640152,
-0.07047893106937408,
-0.016627034172415733,
-0.8070887923240662,
-0.33982688188552856,
-0.6757537722587585,
1.6278425455093384,
0.1133563295006752,
-0.6711937785148621,
0.5376192331314087,
-0.09915953129529953,
-0.38838887214660645,
-0.057304367423057556,
-0.12230441719293594,
-0.006897411774843931,
-0.3346896469593048,
1.3639137744903564,
0.6784217357635498,
-0.1957443207502365,
0.911253809928894,
-0.3359636068344116,
-0.6719214916229248,
-0.40895816683769226,
0.013104870915412903,
-0.7320866584777832,
-0.41350406408309937,
1.5200544595718384,
0.6110666394233704,
-1.0349302291870117,
0.3754524290561676,
-0.7786853909492493,
-0.8052400350570679,
-0.2938883602619171,
-0.49713703989982605,
0.6899592280387878,
0.9602704644203186,
0.10701161623001099,
-0.04334985464811325,
-0.24184724688529968,
-0.6049917936325073,
-0.06351930648088455,
0.5081881880760193,
-0.9412075281143188,
0.657444953918457,
0.7600472569465637,
0.21517503261566162,
0.6889809966087341,
0.28825023770332336,
-0.4292229115962982,
0.5237405300140381,
0.29682761430740356,
-0.5483521223068237,
-0.28958433866500854,
0.5502585768699646,
-0.1694851964712143,
-0.2399112731218338,
0.15908539295196533,
-0.6458722352981567,
-0.20777083933353424,
-0.898613452911377,
-0.6652054786682129,
0.38268718123435974,
-0.19582726061344147,
-0.5544836521148682,
0.22499728202819824,
-0.7840701937675476,
-0.313892662525177,
0.2032136470079422,
0.12665365636348724,
0.6536192297935486,
-0.7243718504905701,
0.34857386350631714,
0.03303591161966324,
-0.19781948626041412,
-0.25778576731681824,
0.33829742670059204,
-0.2891796827316284,
-0.052362363785505295,
0.09547886997461319,
0.7475671172142029,
-0.9998968839645386,
-0.9998269081115723,
-0.3600807785987854,
0.549275279045105,
1.2507362365722656,
0.5070722699165344,
0.49573996663093567,
-0.10249415040016174,
-0.4846517741680145,
-0.13993136584758759,
-0.7006073594093323,
-0.06463123112916946,
-0.3311725854873657,
-0.5869808793067932,
-0.5236920118331909,
-0.2655933201313019,
0.1342722326517105,
0.5746815800666809,
1.0138720273971558,
0.28450441360473633,
0.88346266746521,
0.41740724444389343,
0.007948377169668674,
0.49770835041999817,
0.5747683644294739,
-0.6028552651405334,
0.16773033142089844,
-0.7900665402412415,
0.19272728264331818,
-0.4252822697162628,
-0.4504673480987549,
-0.09652175009250641,
-0.1845840960741043,
-0.16296225786209106,
-0.048730410635471344,
0.6668849587440491,
0.36420419812202454,
-0.5683578252792358,
0.8725035786628723,
-0.18128617107868195,
0.0945592075586319,
-0.04064296931028366,
-0.05182937532663345,
0.31842663884162903,
0.8110536336898804,
0.11939585208892822,
-0.7655352354049683,
-0.2412988841533661,
-0.5747795104980469,
0.3652324676513672,
0.6840999722480774,
-0.29716867208480835,
-0.9544011354446411,
-0.34044501185417175,
-0.09312964230775833,
0.08894691616296768,
0.4705619812011719,
0.8061308860778809,
-0.2102074772119522,
1.0662516355514526,
0.16532404720783234,
-0.28474709391593933,
0.5966360569000244,
-0.4729059636592865,
-0.6639628410339355,
0.5130703449249268,
0.8536897301673889,
-0.32591673731803894,
1.2117427587509155,
-0.07995904982089996,
-0.7087787389755249,
-0.6036427021026611,
-0.12836790084838867,
0.9797265529632568,
-0.6166630983352661,
-0.4133649468421936,
-0.31502723693847656,
-0.000032296826248057187,
-0.15675105154514313,
1.051841139793396,
-0.726425051689148,
0.4778105914592743,
0.17460322380065918,
0.054030273109674454,
-1.2536617517471313,
-0.42674779891967773,
0.14395825564861298,
-0.04572249948978424,
0.2144506424665451,
1.0505070686340332,
0.08998540788888931,
0.3780120015144348,
0.3132142126560211,
-0.0020459031220525503,
0.006761485710740089,
0.7277366518974304,
-0.38067659735679626,
0.5925192832946777,
-0.23442459106445312,
-0.24245774745941162,
-0.20649433135986328,
-0.1879081130027771,
0.660614550113678,
-0.8480047583580017,
0.39886051416397095,
-0.06352130323648453,
-0.3326389491558075,
-0.38357964158058167,
0.26668885350227356,
-0.35312560200691223,
0.4302864670753479,
-0.49866023659706116,
-0.23090054094791412,
0.620402991771698,
-1.0706305503845215,
0.14395537972450256,
0.11989665776491165,
0.2608492374420166,
0.14865349233150482,
-0.20595036447048187,
0.19962824881076813,
-0.5116672515869141,
0.7821286916732788,
-1.4115428924560547,
0.5200269222259521,
-0.6461629867553711,
-0.3588202893733978,
-1.378949761390686,
0.16935661435127258,
-0.3899683356285095,
0.26058441400527954,
-0.07572459429502487,
-0.5127598643302917,
0.14839908480644226,
0.2909221947193146,
0.42155978083610535,
0.6414046883583069,
0.11517927795648575,
-0.6655844449996948,
0.15832878649234772,
0.4214332401752472,
-0.012580737471580505,
-0.7356626987457275,
-0.5042151212692261,
1.1335867643356323,
0.038599781692028046,
0.15900449454784393,
-0.019773036241531372,
0.05062829703092575,
-0.042659759521484375,
-0.7103646993637085,
-0.14312869310379028,
-0.7266790866851807,
-0.8568309545516968,
-0.6492365598678589,
-0.0686521828174591,
0.44404566287994385,
0.07432696968317032,
-0.09625296294689178,
-0.34110501408576965,
0.024874240159988403,
-1.0136114358901978,
0.7661285400390625,
-0.13322290778160095,
-0.2274179458618164,
-0.23754939436912537,
-0.1512126624584198,
-0.96485835313797,
0.9157777428627014,
-0.8892871737480164,
-0.171808123588562,
0.6182339191436768,
0.8949611186981201,
0.1139107421040535,
0.6213762760162354,
0.22837498784065247,
-0.736452579498291,
-0.5000781416893005,
0.221467986702919,
0.5762065052986145,
0.8348876237869263,
-0.5339121222496033,
0.5644832849502563,
-1.1000207662582397,
0.7678262591362,
-0.34781667590141296,
0.47558867931365967,
0.6985270977020264,
-0.50875324010849,
0.6466922760009766,
-0.7085455656051636,
0.35898536443710327,
0.4621644616127014,
0.3325057923793793,
0.7553017735481262,
0.24561046063899994,
-0.6377218961715698,
-0.25934934616088867,
-0.8713960647583008,
-0.7135767340660095,
0.499219685792923,
-0.2046370506286621,
-0.5343665480613708,
-0.8585320711135864,
-1.041645884513855,
0.6173465847969055,
-0.22539785504341125,
0.9666271805763245,
0.5328231453895569,
0.4592893123626709,
0.1939026564359665,
-0.007883509621024132,
-0.11244958639144897,
0.11266257613897324,
-0.18627841770648956,
0.30621227622032166,
-0.2781740128993988,
-0.7472442984580994,
-0.37522682547569275,
-0.7067505121231079,
-0.6402515172958374,
-0.6817337870597839,
0.47806331515312195,
0.2354988306760788,
0.02282862365245819,
0.8535492420196533,
-0.6301432847976685,
-0.6873499751091003,
-0.4291757643222809,
-0.01878085918724537,
0.0274977944791317,
-0.26592352986335754,
0.07501008361577988,
-0.40671494603157043,
0.04331795498728752,
0.24495923519134521,
-0.19002090394496918,
-0.47676900029182434,
-0.30969706177711487,
1.5628607273101807,
-0.42960241436958313,
-1.046453595161438,
-0.14246436953544617,
0.27010905742645264,
-0.8901272416114807,
-0.9492149353027344,
-1.326067566871643,
-0.4868062436580658,
0.08960722386837006,
-1.0211641788482666,
0.15972395241260529,
-0.22102445363998413,
-0.4093194901943207,
0.35712701082229614,
0.8068957924842834,
-0.5012913942337036,
-0.3552594482898712,
0.2986382246017456,
-0.4489701986312866,
-0.4494565725326538,
0.18065650761127472,
1.2474853992462158,
-0.031282562762498856,
-0.6673237085342407,
-0.49334996938705444,
-0.6797412633895874,
-0.3346629738807678,
0.010364942252635956,
-0.16424764692783356,
-0.11747219413518906,
0.08647558838129044,
0.28621307015419006,
0.6660981774330139,
0.16825896501541138,
0.666908323764801,
0.6962478756904602,
-0.20845825970172882,
-0.2763451933860779,
-0.4954693913459778,
-0.6163783073425293,
0.8319222927093506,
0.11288332939147949,
0.9921337962150574,
-0.6802520751953125,
0.24612568318843842,
0.23309655487537384,
-0.4299843907356262,
-0.4915545582771301,
-1.286952018737793,
-0.16505728662014008,
-0.9985706806182861,
-0.28097057342529297,
-0.7455544471740723,
-0.5496562719345093,
-0.4698844254016876,
0.020170388743281364,
0.487513929605484,
0.9070999026298523,
-0.7425544261932373,
0.4240000545978546,
0.1706937551498413,
0.5294930338859558,
0.2825748324394226,
-0.5228267312049866,
-0.3334446847438812,
-0.023654405027627945,
-0.30488306283950806,
-1.02052903175354,
-0.10018642991781235,
0.3573712110519409,
-0.3662084937095642,
0.09076440334320068,
-0.5533179044723511,
0.8502351641654968,
-0.5084048509597778,
0.10327761620283127,
0.21762774884700775,
-0.2761889100074768,
-0.8249915838241577,
0.4125824272632599,
-0.8039884567260742,
0.11203350126743317,
0.39200836420059204,
-0.7203443646430969,
-0.4819764792919159,
1.0338973999023438,
-1.6067861318588257,
0.33429256081581116,
0.5325303673744202,
0.5315310955047607,
0.35160085558891296,
-1.0248973369598389,
0.5280712246894836,
0.06588871777057648,
-0.7607643604278564,
0.0538724847137928,
-0.13773149251937866,
-0.14021189510822296,
-0.03432152792811394,
0.1277376115322113,
0.4034242331981659,
0.9567403793334961,
0.15812580287456512,
0.8409115672111511,
-0.8754346370697021,
-0.5531985759735107,
-0.3327181339263916,
0.27425166964530945,
-0.10023138672113419,
0.03203311935067177,
1.1559195518493652,
-1.19131338596344,
0.5690816044807434,
0.07325570285320282,
-0.27629902958869934,
-0.11941985785961151,
-0.3873070180416107,
0.0037090459372848272,
-0.07097940891981125,
-0.05806402489542961,
-0.4959682524204254,
0.8076971769332886,
-0.6499751210212708,
0.021730370819568634,
0.20152197778224945,
-0.7544867992401123,
-0.5927643775939941,
0.7648858428001404,
-0.14751067757606506,
-0.6159883737564087,
-0.3654906153678894,
-0.15418709814548492,
-0.1418236792087555,
0.2769855260848999,
-0.2643471658229828,
-0.29705798625946045,
-0.52286696434021,
-0.005071514751762152,
0.48056167364120483,
0.2690333127975464,
0.15174204111099243,
0.39139845967292786,
-0.008029907010495663,
0.0570211261510849,
-0.2467399388551712,
0.46278321743011475,
-0.6283072233200073,
-0.7844448089599609,
-0.3082008361816406,
-0.5034666061401367,
-0.30876392126083374,
-0.21946965157985687,
-0.01689683459699154,
0.32784900069236755,
-0.23836159706115723,
-0.38750460743904114,
-0.8445940613746643,
0.3088477551937103,
-0.6655247807502747,
1.0284141302108765,
0.8568326234817505,
-0.3901045322418213,
0.618659257888794,
0.45630553364753723,
0.2496693879365921,
-0.320823073387146,
-0.49911952018737793,
0.8047810196876526,
0.02838493324816227,
-0.2994864284992218,
0.6451876759529114,
-0.4770019054412842,
1.0030410289764404,
-0.3324776887893677,
-0.291756808757782,
-0.18559719622135162,
-0.20974023640155792,
0.5229406952857971,
0.5058456659317017,
0.531010091304779,
0.516456127166748,
0.3082309663295746,
0.1013997346162796,
-0.0634973794221878,
-0.04061869904398918,
-0.10206717252731323,
-0.3572818636894226,
0.2139330357313156,
-0.19158954918384552,
0.40289974212646484,
-0.6321199536323547,
0.29093095660209656,
-0.1313961297273636,
0.11301117390394211,
-0.14087116718292236,
0.35595032572746277,
-0.010866893455386162,
0.7414590120315552,
-0.8127220273017883,
-0.8797569274902344,
-0.5769099593162537,
1.319076657295227,
-0.17416638135910034,
-0.003136074636131525,
-0.11884061992168427,
0.4594375491142273,
0.24791328608989716,
0.4549577534198761,
-0.5614374876022339,
0.710175633430481,
0.6057853698730469,
-0.009627957828342915,
0.2541084885597229,
1.0234323740005493,
0.178947314620018,
-0.1568274348974228,
0.4425904452800751,
-0.23825585842132568,
-0.7149497866630554,
0.851798415184021,
-0.42911702394485474,
0.23482246696949005,
0.19105295836925507,
-0.6325116753578186,
-0.686338484287262,
-1.261474847793579,
-0.05123981833457947,
-0.18990527093410492,
0.13222341239452362,
0.777704119682312,
0.47932112216949463,
-0.03685310110449791,
0.37179890275001526,
-0.1824692189693451,
0.6849127411842346,
0.8085005283355713,
0.42013564705848694,
-0.07255063951015472,
1.5216468572616577,
1.2374475002288818,
0.2659551501274109,
0.38339874148368835,
-0.21069788932800293,
-0.7123110890388489,
0.3129282295703888,
-0.06952091306447983,
-0.4947586953639984,
1.7307498455047607,
-1.1349904537200928,
-0.4285069704055786,
0.30943557620048523,
0.4571412205696106,
-0.004812184255570173,
-0.33214080333709717,
-0.07084038853645325,
0.7721595168113708,
-0.7572954297065735,
-0.42562440037727356,
0.8776932954788208,
0.5522162318229675,
0.22683024406433105,
0.08538619428873062,
0.15071707963943481,
-0.272575318813324,
0.1188553050160408,
-0.5172280073165894,
0.03449787572026253,
0.20413249731063843,
0.19585373997688293,
-0.34379756450653076,
-0.7718004584312439,
-0.6790862679481506,
-0.8759080171585083,
0.17262011766433716,
-0.13365669548511505,
1.052172064781189,
0.41005414724349976,
0.3233318626880646,
0.487309068441391,
-1.100420355796814,
0.19720359146595,
0.6817548871040344,
1.1617282629013062,
1.0474027395248413,
0.6010497212409973,
0.9542402625083923,
0.48699751496315,
-0.6643480062484741,
0.4886215925216675,
0.426967978477478,
-0.1567312777042389,
0.5480766296386719,
-0.1494196653366089,
0.5438087582588196,
0.0994124785065651,
-0.554990291595459,
-0.19495965540409088,
0.42722591757774353,
0.36665260791778564,
-0.9843763113021851,
-0.6354596018791199,
-0.05521224066615105,
-0.6315459609031677,
0.20380821824073792,
-0.8620451092720032,
0.23544131219387054,
1.0704596042633057,
0.31947916746139526,
0.1990376114845276,
-0.6586265563964844,
3.7031781673431396,
0.478597491979599,
0.11764588952064514,
-0.3077823221683502,
0.8525071144104004,
1.006298542022705,
0.8302172422409058,
-0.6117125749588013,
0.22181060910224915,
0.21786285936832428,
0.3431873321533203,
0.9972684383392334,
1.0634888410568237,
0.14026044309139252,
0.5301744937896729,
-0.4445716440677643,
-0.5534195899963379,
0.3052968680858612,
0.33061182498931885,
-1.1318089962005615,
-0.3527299761772156,
0.5890558958053589,
0.5186829566955566,
0.06844455003738403,
0.7943994998931885,
-0.36880141496658325,
0.1712336242198944,
-0.4140353798866272,
-0.9491625428199768,
-0.7765918970108032,
0.06622341275215149,
-0.5552566051483154,
-0.1567424237728119,
-0.603982150554657,
-1.1239383220672607,
0.8080280423164368,
0.46975529193878174,
-0.5170824527740479,
-0.6026594042778015,
0.5708032250404358,
0.07510779798030853,
-0.3858337104320526,
-0.10335341840982437,
-0.07391324639320374,
-0.18026630580425262,
0.45159661769866943,
0.1800885796546936,
0.20787447690963745,
-0.10557771474123001,
-0.7134717702865601,
-0.0908895879983902,
-0.4491954445838928,
0.21959306299686432,
0.12060043215751648,
-1.626041054725647,
-0.8992778062820435,
-0.6007943749427795,
-0.6210811138153076,
0.2590698003768921,
0.26808035373687744,
0.9884448051452637,
-0.07317514717578888,
-0.8515980243682861,
0.06926023960113525,
-0.5893951654434204,
-0.019646188244223595,
-0.019668428227305412,
-0.28098565340042114,
-0.17163607478141785,
-0.7747083306312561,
-0.314130574464798,
-0.21825598180294037,
-0.3418995440006256,
-0.8509756922721863,
0.5055071711540222,
-0.11407988518476486,
-0.24571093916893005,
0.8455796241760254,
-0.0648769959807396,
0.5445690155029297,
-0.16260913014411926,
-0.2981552183628082,
0.0730145201086998,
1.0754961967468262,
-0.07680850476026535,
0.5296773314476013,
-0.6248587965965271,
-0.7795203924179077,
0.46186789870262146,
0.796074628829956,
0.2464100569486618,
1.4903072118759155,
0.24872516095638275,
0.30251044034957886,
-0.4827900826931
] |
The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature
|
We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling analysis to characterize as much as possible the regime of crossover from crumpled to smooth surfaces.
|
Mark Bowick, Paul Coddington, Leping Han, Geoffrey Harris and Enzo Marinari
|
hep-lat hep-th
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209020
|
hep-lat/9209021
|
[
0.3742143213748932,
0.11272520571947098,
-0.6815071702003479,
0.11639145761728287,
0.34821459650993347,
-0.3039356768131256,
-0.513547420501709,
-0.5202670097351074,
-0.26403987407684326,
1.6004672050476074,
1.1743876934051514,
-0.2642279267311096,
0.4123274087905884,
-0.8312214612960815,
-0.2711629271507263,
0.044625185430049896,
-0.5634641647338867,
-0.7277572751045227,
-0.8967529535293579,
-0.04090864956378937,
-0.204567089676857,
-0.08004652708768845,
-1.3212774991989136,
-0.3319239318370819,
-0.8381342887878418,
0.859742283821106,
0.8771573305130005,
-0.027433766052126884,
1.474581003189087,
-0.03766472637653351,
0.46834078431129456,
-0.1706419736146927,
-0.4921419620513916,
-0.5812568664550781,
0.08849508315324783,
0.28278326988220215,
0.40478116273880005,
-0.5866988301277161,
-0.20704378187656403,
-0.5042909979820251,
0.780051052570343,
-0.190035879611969,
0.0291118361055851,
-0.9075526595115662,
-0.703331708908081,
-0.12003564834594727,
0.7826441526412964,
0.5919603705406189,
0.5214154124259949,
-0.9665690064430237,
-0.06204678863286972,
0.23916564881801605,
-0.514624297618866,
-0.5649380683898926,
-0.5342563390731812,
-0.4676475524902344,
0.6479928493499756,
0.517524242401123,
-0.7083429098129272,
-0.9967784285545349,
1.0685123205184937,
0.3074778914451599,
0.278069406747818,
-1.6543306112289429,
0.3424701690673828,
0.8837161660194397,
-0.27659526467323303,
0.06353294849395752,
0.2015417069196701,
0.41890978813171387,
-0.2779057025909424,
-0.282814621925354,
-0.2570359706878662,
0.5950231552124023,
-0.03462805598974228,
0.47093239426612854,
0.22660936415195465,
-0.6449273824691772,
-1.1242002248764038,
-0.6931191086769104,
-0.22122173011302948,
-0.20835064351558685,
-1.114500880241394,
1.108351230621338,
-0.34311655163764954,
-0.16882134974002838,
0.6736161708831787,
-0.22465722262859344,
0.3257215917110443,
0.1284530758857727,
0.06302541494369507,
0.03415756672620773,
0.4396861493587494,
0.20564930140972137,
0.3656919300556183,
0.9811310172080994,
-0.24404601752758026,
0.9247781038284302,
0.14437003433704376,
0.7197268605232239,
0.1619245409965515,
1.9905486106872559,
-1.3524084091186523,
0.722761869430542,
-0.37138330936431885,
0.06255411356687546,
0.2573564350605011,
0.08828626573085785,
-0.06811442971229553,
-0.8513602614402771,
0.3536999225616455,
-0.0668342188000679,
0.5521867871284485,
0.7681592106819153,
0.5272917151451111,
0.46291473507881165,
0.24970979988574982,
0.04051991552114487,
-0.7823590636253357,
-0.48364824056625366,
-0.5350341796875,
0.12225150316953659,
0.5745902061462402,
0.5892754197120667,
0.6669785976409912,
-0.7928252816200256,
0.181386336684227,
0.38775497674942017,
-1.2809478044509888,
0.07933666557073593,
0.33697667717933655,
-0.6556389331817627,
-0.7774670124053955,
0.918510377407074,
-0.10201285779476166,
0.02754194289445877,
-0.023117437958717346,
0.5708508491516113,
-0.24150128662586212,
-0.14509977400302887,
0.1585712730884552,
-1.0543830394744873,
0.8432233333587646,
1.530970573425293,
-0.33485642075538635,
0.17261463403701782,
0.6025726795196533,
-0.585053563117981,
-0.2526184618473053,
0.9824650883674622,
-0.7444721460342407,
-0.31021517515182495,
-0.2080305963754654,
0.3784574866294861,
-0.14898520708084106,
0.2890966236591339,
-0.7935750484466553,
0.5224412679672241,
-0.32994234561920166,
-0.2343776971101761,
-0.5729368925094604,
-0.148927241563797,
-0.507474422454834,
0.19448541104793549,
-0.0936589315533638,
0.3400675654411316,
-0.3763520419597626,
-0.2894071638584137,
0.3406715989112854,
-0.7703446745872498,
-0.08719600737094879,
-0.0007740617147646844,
0.23974736034870148,
0.6224357485771179,
0.6492337584495544,
0.8140532970428467,
0.303301602602005,
-0.03385893255472183,
0.08808275312185287,
-0.0038913381285965443,
0.06586682051420212,
-0.7780472040176392,
0.7251235842704773,
0.19525720179080963,
-0.20410853624343872,
-0.4271308481693268,
-0.31181982159614563,
0.24264290928840637,
-0.3287613093852997,
0.8942046761512756,
0.02631515823304653,
0.7290840148925781,
-0.5921240448951721,
0.7916989326477051,
-0.4710797071456909,
-0.07372520864009857,
-0.38957613706588745,
0.05239366367459297,
-0.6418164372444153,
-0.5217529535293579,
0.5863725543022156,
0.38228821754455566,
-0.590570867061615,
0.41933050751686096,
-1.4137511253356934,
0.3314257860183716,
0.012768641114234924,
0.14623001217842102,
-1.0292562246322632,
-0.14326344430446625,
0.7553796768188477,
-0.32273975014686584,
0.2270292341709137,
-0.12482133507728577,
0.881535530090332,
0.6246140003204346,
-0.5837499499320984,
-0.02296779304742813,
0.6570154428482056,
-0.03013773448765278,
1.1439285278320312,
0.049687642604112625,
-0.3303883671760559,
0.15213598310947418,
-0.7147107124328613,
-0.1715957075357437,
0.5274931192398071,
0.9780071377754211,
0.8436844944953918,
0.027632789686322212,
0.3087533414363861,
0.11046191304922104,
-0.19960381090641022,
0.8815023899078369,
0.88214111328125,
-0.05862627550959587,
0.9089462161064148,
0.7831684947013855,
0.66175776720047,
0.2656800150871277,
-0.17217719554901123,
0.353557288646698,
0.6477451324462891,
1.0793194770812988,
0.31766363978385925,
-0.09271464496850967,
-0.27043917775154114,
0.11867805570363998,
-0.8216328024864197,
-0.12175657600164413,
-0.8572491407394409,
1.1942918300628662,
-0.41064125299453735,
0.21847669780254364,
-1.092256784439087,
-0.16536784172058105,
0.12064138054847717,
0.6145702004432678,
-0.17309939861297607,
-0.729408323764801,
0.10980770736932755,
0.7826754450798035,
-0.5684719085693359,
-0.3563879728317261,
-0.3207332193851471,
0.8062260746955872,
-0.4803219735622406,
0.2477775514125824,
0.6574767231941223,
-0.40380361676216125,
-1.03798508644104,
-0.3912196755409241,
-0.7063360214233398,
-0.3462454676628113,
-0.2063833475112915,
-0.32750433683395386,
0.35069748759269714,
-0.47095251083374023,
0.6481966972351074,
0.06210603937506676,
-0.3465002179145813,
0.4007483124732971,
-0.14411510527133942,
0.5146055221557617,
0.15121611952781677,
-0.5326648354530334,
-1.0323572158813477,
0.2783602774143219,
-0.45659080147743225,
0.37988802790641785,
0.333233118057251,
-0.7121747732162476,
0.4834531545639038,
-0.43143409490585327,
0.33295661211013794,
-0.40355420112609863,
-0.543941855430603,
-0.14017540216445923,
-0.6127179861068726,
-0.9066893458366394,
0.12170147895812988,
-0.041429657489061356,
-0.3491791784763336,
-0.6023622155189514,
-0.4791673719882965,
0.8625996112823486,
0.5081636905670166,
-0.7041822671890259,
0.7911098003387451,
0.15654544532299042,
-0.7449581027030945,
0.3101966381072998,
-0.30077308416366577,
0.5600523352622986,
0.027433855459094048,
1.1237218379974365,
1.067421793937683,
-0.2484770119190216,
-0.12208583205938339,
-0.47551244497299194,
-0.4328475892543793,
-0.5237399339675903,
-0.2620098292827606,
-0.7512336373329163,
-0.5087350010871887,
1.266326904296875,
0.37338122725486755,
-1.007362723350525,
0.6028755903244019,
-0.4360319674015045,
-1.31171452999115,
0.31878045201301575,
-0.22374647855758667,
0.8283447623252869,
0.3660927712917328,
0.28719159960746765,
-0.6592309474945068,
0.1531711220741272,
-0.07752694934606552,
0.22981855273246765,
-0.023538904264569283,
-1.1426907777786255,
0.6892871856689453,
0.4095802903175354,
-0.18185952305793762,
-0.6874497532844543,
1.0666710138320923,
-0.734576404094696,
0.540699303150177,
0.4313563406467438,
-0.46811455488204956,
0.20966796576976776,
0.033464279025793076,
0.03220215439796448,
-0.18489864468574524,
-0.1555776447057724,
-0.6865339875221252,
-0.16642378270626068,
-0.659798264503479,
-0.11393485963344574,
0.7822434306144714,
1.2962976694107056,
-0.022879498079419136,
0.42643025517463684,
-0.5976724028587341,
-0.5384519100189209,
0.3635018467903137,
0.23118701577186584,
1.2243489027023315,
-0.8791994452476501,
0.8553587198257446,
-0.13350000977516174,
-0.9257075786590576,
-0.11347620189189911,
0.11977805197238922,
-0.2872995138168335,
0.10752817988395691,
1.0824493169784546,
1.0754519701004028,
-0.8026810884475708,
-0.4036868214607239,
-0.4036608934402466,
0.8112419247627258,
1.1914093494415283,
0.8673839569091797,
0.626336395740509,
0.2517354488372803,
-0.16872243583202362,
-0.20527029037475586,
0.12657709419727325,
0.17755332589149475,
-0.2841671109199524,
-0.5899538397789001,
-0.4898473620414734,
-0.008936273865401745,
-0.33624085783958435,
0.6457977294921875,
-0.10421242564916611,
-0.1433458775281906,
0.4949715733528137,
0.9741874933242798,
-0.34982138872146606,
0.8110480308532715,
0.8079442977905273,
0.018986107781529427,
0.07976288348436356,
-1.1381510496139526,
-0.31696727871894836,
0.23453940451145172,
-0.5496447086334229,
0.08831004798412323,
-0.4851038455963135,
-0.4073091447353363,
-0.09764768928289413,
0.21529589593410492,
0.5365612506866455,
-0.4141024351119995,
0.15325631201267242,
0.1493518203496933,
0.7244886159896851,
-0.5376811623573303,
0.35140642523765564,
0.6289656162261963,
0.9306546449661255,
-0.10618418455123901,
-1.573368787765503,
0.3933764696121216,
-0.5227272510528564,
1.1587531566619873,
0.8983815312385559,
-0.4078114628791809,
-1.0655633211135864,
-0.606489360332489,
-0.01095178909599781,
-0.4883647859096527,
0.6286953687667847,
0.7144847512245178,
-0.6540665030479431,
0.50961834192276,
-0.5080126523971558,
-0.3867664039134979,
0.5736827850341797,
0.14380574226379395,
0.11857958883047104,
0.4430234730243683,
0.1152527928352356,
-0.6002684235572815,
0.6488258242607117,
0.10774059593677521,
0.08937892317771912,
0.09906689077615738,
0.009763455018401146,
0.3472227454185486,
-0.23227456212043762,
-0.4070532023906708,
-0.4782998561859131,
-0.20768798887729645,
-0.6170158386230469,
0.9794764518737793,
-0.6177393198013306,
0.4440637528896332,
0.09006236493587494,
-0.05477045848965645,
-0.7539858222007751,
-0.345864474773407,
-0.062317658215761185,
0.16035671532154083,
0.18379546701908112,
0.45295456051826477,
0.5462955832481384,
0.1042080968618393,
0.7294550538063049,
0.01889861561357975,
0.36681345105171204,
0.5988680720329285,
-0.3788062036037445,
0.4180663228034973,
-0.8921360969543457,
-0.28001388907432556,
-0.5058818459510803,
-0.5137585997581482,
-0.14220334589481354,
-0.5830203890800476,
0.1859060823917389,
0.5061742067337036,
-0.21502411365509033,
-0.12924204766750336,
-0.8746341466903687,
-0.640557050704956,
0.17679214477539062,
-0.157093808054924,
0.014753368683159351,
0.3332065939903259,
-0.9921362996101379,
0.4222368597984314,
1.158072590827942,
0.42833951115608215,
-0.020142877474427223,
0.5356865525245667,
0.8117212653160095,
-0.5779860615730286,
0.17958129942417145,
-0.7522520422935486,
0.5307358503341675,
-0.3683335483074188,
-0.02694413810968399,
-0.8523369431495667,
-0.712922990322113,
-0.29065564274787903,
0.08971631526947021,
0.04788178578019142,
-0.5897728800773621,
-0.06351741403341293,
0.06192885339260101,
0.4756828546524048,
0.12244993448257446,
-0.5790421366691589,
-1.3620562553405762,
-0.7143506407737732,
0.9991234540939331,
-0.20906461775302887,
-1.0051462650299072,
-0.5676426887512207,
0.29826968908309937,
0.011339031159877777,
-0.030774760991334915,
0.0181280430406332,
-1.136801838874817,
0.3597518503665924,
-0.318157821893692,
0.870731770992279,
-1.2001436948776245,
-0.3575417697429657,
-0.3361937403678894,
-0.49458447098731995,
-0.13125024735927582,
0.7059500217437744,
0.7690595984458923,
-0.5198543667793274,
0.16025805473327637,
-0.8179813623428345,
0.9233872890472412,
-0.4289422929286957,
-0.46153557300567627,
-0.12524284422397614,
0.4979398250579834,
-0.4593738615512848,
0.5807288885116577,
-0.33119916915893555,
-0.4737687408924103,
0.5581939816474915,
0.39637163281440735,
0.5165709257125854,
1.0365442037582397,
-0.07996828109025955,
-0.1327255368232727,
-0.38643601536750793,
0.026961853727698326,
0.5498765110969543,
0.97514408826828,
-0.2486208826303482,
0.50790935754776,
-0.9955933690071106,
0.18522819876670837,
-0.8048429489135742,
0.5282009840011597,
0.3365659713745117,
-0.7016997337341309,
0.5771679282188416,
-1.0050550699234009,
0.2860402762889862,
0.012088984251022339,
0.14091265201568604,
0.9161170721054077,
0.5040234923362732,
-0.6059165596961975,
-0.6599947810173035,
-0.6041064262390137,
-0.7252330183982849,
0.8648464679718018,
-0.4331248998641968,
-0.9574635028839111,
-0.9217872023582458,
-0.2804409861564636,
0.18711905181407928,
-0.12559707462787628,
0.33232206106185913,
0.6933833956718445,
0.4205883741378784,
0.39879530668258667,
-0.28813984990119934,
-0.7950295805931091,
0.30461257696151733,
-0.42779597640037537,
0.16435641050338745,
-0.5574249029159546,
-0.40575116872787476,
-0.6532297134399414,
-1.1483895778656006,
-1.0290095806121826,
-0.22248923778533936,
-0.1910066455602646,
0.44701746106147766,
-0.5346468687057495,
1.2862309217453003,
0.009051713161170483,
0.185671865940094,
-0.6996593475341797,
-0.6417741775512695,
0.047710660845041275,
-0.11232797056436539,
0.7939777970314026,
0.2607785761356354,
0.13257279992103577,
-0.04798063635826111,
0.0042245276272296906,
-0.4691697955131531,
-0.0033592560794204473,
0.7328182458877563,
-0.8292020559310913,
-0.649970293045044,
-0.424221396446228,
0.03364883363246918,
-1.2750368118286133,
-0.2553006708621979,
-0.8466490507125854,
0.6329987645149231,
-0.408397912979126,
-1.1896823644638062,
0.08902620524168015,
-0.4593752920627594,
0.14890605211257935,
0.4425710439682007,
0.7897366285324097,
-0.3022559583187103,
0.10678429156541824,
0.5195977687835693,
-0.34098899364471436,
-0.8487668037414551,
0.7860236763954163,
1.204120397567749,
-0.3318718373775482,
-0.245838925242424,
0.17979153990745544,
-0.14579850435256958,
-0.2867814004421234,
-0.4409688711166382,
0.06263697892427444,
0.10258060693740845,
0.15296027064323425,
0.7675008177757263,
0.1934710443019867,
0.5623591542243958,
0.9090337753295898,
0.1451501101255417,
-0.7195717096328735,
-0.2882026731967926,
-0.9344222545623779,
-0.7703113555908203,
-0.02800801210105419,
-0.041967324912548065,
0.7189823985099792,
0.115868479013443,
0.4908056855201721,
-0.130645751953125,
-0.33982086181640625,
-0.04554007947444916,
-0.980772852897644,
-0.4878828227519989,
-1.1683207750320435,
-0.7891182899475098,
-0.5055286884307861,
-0.5080065131187439,
-0.7322096228599548,
0.14076440036296844,
-0.3390715718269348,
0.4051012098789215,
0.05036270245909691,
-0.3884672224521637,
-0.23803141713142395,
0.03432232141494751,
-0.10295726358890533,
-0.369013249874115,
-1.485276460647583,
0.010963552631437778,
-0.0320952869951725,
-0.846388578414917,
-0.11166305094957352,
0.06729793548583984,
0.33066892623901367,
1.1810945272445679,
-0.6534548997879028,
0.568274199962616,
-0.6696493029594421,
-0.23890471458435059,
0.5465550422668457,
0.07495254278182983,
-0.8997883200645447,
0.17165251076221466,
-0.5263663530349731,
0.4361913204193115,
0.09279132634401321,
-0.17376182973384857,
-0.5202112197875977,
0.336481511592865,
-0.7151711583137512,
-0.07733824849128723,
-0.4171310365200043,
0.5668963193893433,
-0.24715837836265564,
-0.8088981509208679,
0.5042181611061096,
-0.0366603322327137,
-1.1805883646011353,
-0.007505996618419886,
0.14970968663692474,
0.009438857436180115,
-0.8737682700157166,
-0.4884486794471741,
0.5326431393623352,
1.0197725296020508,
0.22089584171772003,
0.6583936810493469,
-0.22500449419021606,
-0.5879905819892883,
-0.7803583741188049,
0.1715978980064392,
0.012504836544394493,
-0.13149848580360413,
-0.04619525000452995,
-1.4618726968765259,
0.4551328420639038,
0.605588972568512,
-0.6428625583648682,
-0.41082268953323364,
-0.1516980677843094,
0.0894337147474289,
-0.8223918080329895,
0.02921559102833271,
-0.24853646755218506,
1.2137480974197388,
-0.01972445659339428,
-0.23110324144363403,
-0.897357702255249,
-0.4532926082611084,
-0.49634769558906555,
0.5540158152580261,
-0.8088176846504211,
-0.3046458959579468,
-0.14096646010875702,
-0.6149083971977234,
-0.35507622361183167,
0.4417405128479004,
-0.3627735674381256,
0.16324937343597412,
-0.28809288144111633,
0.49352389574050903,
-0.5177096128463745,
0.20545057952404022,
-0.02078896015882492,
0.05194544047117233,
-1.2820848226547241,
-0.029267776757478714,
-0.4972451329231262,
0.26331859827041626,
-0.9349752068519592,
-0.01384348887950182,
0.25159239768981934,
0.17851726710796356,
0.22501221299171448,
0.519568920135498,
-0.5615293979644775,
0.270803302526474,
0.05055953934788704,
0.3156055212020874,
-0.7996800541877747,
0.1935129314661026,
-0.4112964868545532,
0.4067826569080353,
0.08050381392240524,
-0.16630242764949799,
0.5073277950286865,
0.7841013669967651,
0.6902501583099365,
0.1817542165517807,
-0.2525799870491028,
1.1503018140792847,
-0.19563478231430054,
-0.8555599451065063,
0.8512805700302124,
0.06190956011414528,
1.1548774242401123,
-0.11561498790979385,
-0.2020043283700943,
0.5765292644500732,
0.0722912847995758,
0.31647321581840515,
0.870367169380188,
0.03828595578670502,
0.6929330825805664,
0.3113129734992981,
0.20481285452842712,
0.37133780121803284,
0.15012338757514954,
0.30025622248649597,
0.3086598813533783,
-0.11324269324541092,
-0.8147409558296204,
0.6475403308868408,
-0.46889522671699524,
0.09079592674970627,
0.024317147210240364,
-0.15544089674949646,
-0.42680487036705017,
-0.2797991633415222,
-0.6468601822853088,
0.7296286821365356,
-0.7270688414573669,
-0.7158558368682861,
-0.622450053691864,
0.7144415974617004,
0.3371886909008026,
0.009473760612308979,
0.18951913714408875,
0.23477865755558014,
0.5666004419326782,
0.13938674330711365,
-0.5702414512634277,
0.29589396715164185,
0.6136105060577393,
0.19960927963256836,
0.001139216823503375,
1.492238998413086,
0.9263308644294739,
0.4774981439113617,
0.14057675004005432,
-0.32612884044647217,
-0.026522377505898476,
0.6660627722740173,
-0.7731117010116577,
-0.3665657937526703,
-0.6851171255111694,
-0.13614144921302795,
-0.21736398339271545,
-1.0253164768218994,
0.3767888844013214,
-0.9592344760894775,
0.09202444553375244,
0.8793749809265137,
-0.07444757223129272,
-0.22999492287635803,
0.12036682665348053,
-0.6915574669837952,
0.6701512336730957,
0.9018440246582031,
0.28692108392715454,
-0.3954707384109497,
1.196953296661377,
1.4833784103393555,
0.07658538222312927,
-0.009332695975899696,
-0.1355263590812683,
-0.2762737274169922,
0.26443687081336975,
0.19703562557697296,
-0.32838183641433716,
0.8350149989128113,
-0.6909899711608887,
-0.4735676050186157,
-0.48415595293045044,
-0.1464584618806839,
-0.22674448788166046,
-0.005224254913628101,
0.42565321922302246,
0.45068714022636414,
-0.9739176034927368,
0.290654718875885,
1.346800446510315,
0.009879239834845066,
-0.0522627979516983,
-0.19300507009029388,
0.03129591420292854,
-0.2595251500606537,
0.14280585944652557,
-1.138176441192627,
0.6071762442588806,
0.1377130150794983,
-0.17398688197135925,
-0.37332308292388916,
-0.4846069812774658,
-0.028782624751329422,
-0.7417624592781067,
-0.0851028636097908,
-0.16564024984836578,
0.8615759015083313,
0.9682113528251648,
0.21842990815639496,
0.4070606231689453,
-0.6716286540031433,
0.18400144577026367,
0.7382630109786987,
0.38952258229255676,
0.1516289860010147,
0.783406138420105,
0.6923795938491821,
0.13934870064258575,
-0.5925818085670471,
0.18809713423252106,
0.6623591780662537,
-0.3411989212036133,
0.25923556089401245,
-0.12269742786884308,
0.08634395152330399,
-0.5047763586044312,
-0.2461467683315277,
0.08663501590490341,
0.4257674515247345,
0.37139445543289185,
-0.7921175956726074,
-0.2136673927307129,
-0.005889603868126869,
-0.6639602780342102,
-0.06978913396596909,
-0.6060290932655334,
0.45305344462394714,
0.5126287341117859,
0.11240110546350479,
-0.11730797588825226,
-0.6081703901290894,
3.580643653869629,
0.6104499697685242,
1.172847867012024,
-0.8334352970123291,
1.2173864841461182,
1.1149492263793945,
0.3935065269470215,
0.26204782724380493,
0.686198353767395,
-0.3620103597640991,
0.32568857073783875,
0.7444180250167847,
-0.02213250659406185,
-0.4746047258377075,
-0.6488919258117676,
0.2818663418292999,
0.1010330393910408,
0.2126433253288269,
-0.24356456100940704,
-0.7508853673934937,
-0.5298032164573669,
0.39429354667663574,
0.5934741497039795,
-0.26088467240333557,
0.5418915748596191,
0.0033350903540849686,
-0.09177057445049286,
-0.5854458212852478,
-0.6278796195983887,
-0.2498360425233841,
-0.32248079776763916,
-0.8007460832595825,
0.21546366810798645,
-0.4795153737068176,
-0.35810673236846924,
0.9246587753295898,
0.2552301287651062,
-0.7583029866218567,
0.38023802638053894,
0.13438940048217773,
-0.04007142782211304,
-0.965645968914032,
-0.19156314432621002,
0.06359707564115524,
-0.14626529812812805,
1.0861716270446777,
0.5127750039100647,
0.6131665706634521,
0.38982951641082764,
-0.8882176876068115,
0.34755250811576843,
-0.5854515433311462,
0.549426794052124,
-0.21224290132522583,
-0.6321645379066467,
0.00844209361821413,
-1.3250527381896973,
-0.7099956274032593,
-0.042723678052425385,
0.19274477660655975,
1.3956830501556396,
-0.21228757500648499,
0.0018751478055492043,
0.7874264717102051,
0.5726557970046997,
0.22602036595344543,
0.74544358253479,
-0.8961932063102722,
-0.057157982140779495,
0.18433140218257904,
-1.002332091331482,
0.35605332255363464,
0.05752473697066307,
0.1290886253118515,
0.28284090757369995,
0.02180718258023262,
0.06981577724218369,
0.318294495344162,
0.5680995583534241,
0.543786346912384,
-0.5262086391448975,
-0.14937692880630493,
0.35349389910697937,
0.2825871706008911,
-0.5439777970314026,
0.41563257575035095,
-0.3173775374889374,
-0.18145576119422913,
0.05039774999022484,
0.23610816895961761,
0.3226577639579773,
1.7932175397872925,
0.5272701978683472,
0.4692850112915039,
-0.31219953298568726
] |
Neural multigrid for gauge theories and other disordered systems
|
We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.
|
M. Baeker, T. Kalkreuter, G. Mack and M. Speh
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209021
|
hep-lat/9209022
|
[
0.3359936773777008,
-0.44203251600265503,
-0.003960264381021261,
-0.02856159582734108,
-0.2010907232761383,
-0.08426426351070404,
-0.4586980640888214,
-0.4434971809387207,
-0.9383442401885986,
1.1501681804656982,
0.6102123856544495,
-0.14450772106647491,
0.2047465592622757,
-0.7742250561714172,
-0.28348320722579956,
0.5007324814796448,
-0.2327900230884552,
-0.38043519854545593,
-1.1986294984817505,
0.6664004921913147,
0.24390044808387756,
0.03750307485461235,
-1.4603897333145142,
-0.544121265411377,
-0.0017874442273750901,
0.7447497844696045,
0.04908508062362671,
-0.2343101054430008,
1.3340123891830444,
0.5392964482307434,
0.26185184717178345,
-0.5330223441123962,
-0.6513671278953552,
-0.1200406551361084,
-0.6280146241188049,
-0.16153770685195923,
-0.009781651198863983,
0.18236064910888672,
0.5345000624656677,
-0.4886948764324188,
0.8584864139556885,
-0.47313717007637024,
-0.006546197924762964,
-0.16639520227909088,
-1.0328686237335205,
0.5296270847320557,
-0.013228392228484154,
-0.6084941029548645,
0.30447307229042053,
-1.4656946659088135,
-0.10252024978399277,
0.5019844174385071,
0.3861836791038513,
-0.6440821886062622,
-0.26554781198501587,
0.3128351867198944,
0.5398886799812317,
-0.16866910457611084,
-0.829734206199646,
-0.25109148025512695,
0.8705610632896423,
-0.3550873398780823,
0.6063245534896851,
-0.9827864766120911,
0.3543608486652374,
0.6953098177909851,
-0.4480854272842407,
0.6564745306968689,
0.11179863661527634,
-0.3944791257381439,
0.010976512916386127,
-0.43375372886657715,
-0.9702293872833252,
0.11237481981515884,
-0.8838011622428894,
-0.3424324691295624,
-0.14124388992786407,
-0.3665945827960968,
-1.1960517168045044,
-0.15118944644927979,
-0.16593290865421295,
-0.08229578286409378,
-0.3422325849533081,
0.2663228213787079,
-0.6771318316459656,
-0.08755109459161758,
-0.26722094416618347,
-0.16662272810935974,
0.04147350788116455,
0.8360851407051086,
0.2808528244495392,
0.8484427332878113,
0.6353293061256409,
-0.35118284821510315,
-0.09460178017616272,
0.4095771610736847,
0.10465550422668457,
0.23365585505962372,
0.018161611631512642,
-0.22626754641532898,
0.08655676245689392,
0.5758119225502014,
-0.7206986546516418,
0.06177208945155144,
-0.5815468430519104,
0.7959110140800476,
0.26228195428848267,
-0.5319216847419739,
0.15869255363941193,
-0.6988263726234436,
0.30310526490211487,
-0.35258546471595764,
-0.01157892495393753,
0.8620496988296509,
-0.13176609575748444,
0.24552945792675018,
0.24625252187252045,
-0.11830834299325943,
-0.29588204622268677,
-0.6629102826118469,
0.19662313163280487,
-0.007100999820977449,
0.39110979437828064,
0.14266645908355713,
0.19533458352088928,
0.37135282158851624,
0.16697119176387787,
0.6499068140983582,
-0.8176698684692383,
-0.016529394313693047,
0.030578678473830223,
-0.04388267919421196,
-0.08884309977293015,
0.9605455994606018,
-0.36388343572616577,
-0.26773396134376526,
-0.2766036093235016,
0.35975322127342224,
-0.43602341413497925,
-0.3879716694355011,
0.8357347249984741,
-0.9825947284698486,
-0.06916292756795883,
1.0789330005645752,
-0.11617790162563324,
0.1977616399526596,
0.23767323791980743,
0.08398008346557617,
-0.025964725762605667,
0.40088438987731934,
-0.4997407793998718,
-0.2342996746301651,
-0.4686804711818695,
0.053369417786598206,
0.24512718617916107,
0.5240305662155151,
-0.5111079216003418,
0.15875448286533356,
-0.3592086434364319,
-0.6716912984848022,
0.8792300224304199,
-0.541410505771637,
-0.8910130262374878,
0.06694990396499634,
-1.016218662261963,
-0.43436020612716675,
-0.6219110488891602,
-0.29250842332839966,
0.2627580463886261,
-0.7398412823677063,
0.21456049382686615,
0.8793796300888062,
-0.18057002127170563,
0.6214691996574402,
0.2771855890750885,
0.3541889190673828,
0.27307242155075073,
-0.3274218738079071,
0.20029063522815704,
0.2604127526283264,
-0.5218011736869812,
-0.1936449259519577,
-0.1701454520225525,
-0.3706776797771454,
-0.2306244671344757,
-0.3019838333129883,
-0.20651091635227203,
0.4791320860385895,
0.03261612355709076,
0.3402054011821747,
0.0023980424739420414,
0.041203755885362625,
-0.2753050625324249,
0.9617376327514648,
-0.8100799918174744,
-0.6963154673576355,
-0.5046470761299133,
0.1339387595653534,
-0.909250020980835,
-0.5325759053230286,
-0.2255919873714447,
-0.11717527359724045,
-0.8105320930480957,
0.32483261823654175,
-1.7360284328460693,
0.5044811964035034,
0.917503297328949,
0.19599424302577972,
-0.9606869220733643,
-0.012177572585642338,
0.1594615876674652,
-0.3368081748485565,
0.19665716588497162,
-0.3328007459640503,
0.605204164981842,
0.264788955450058,
0.3313705027103424,
0.4387059807777405,
0.9999842643737793,
0.46469083428382874,
0.6354629397392273,
0.3376959264278412,
0.14524976909160614,
0.5053482055664062,
-0.10962976515293121,
-0.7776710987091064,
0.06710856407880783,
0.43591606616973877,
0.39431172609329224,
-0.4012966454029083,
-0.05814281105995178,
0.5513240098953247,
-0.47044190764427185,
0.5155604481697083,
0.11082937568426132,
0.22122418880462646,
0.8228715658187866,
-0.04579278454184532,
0.86954665184021,
0.3750673234462738,
-0.1424860656261444,
-0.10060760378837585,
0.22568939626216888,
0.0675048753619194,
-0.07837770134210587,
0.0634942278265953,
-0.41082242131233215,
0.2136388123035431,
-0.6898457407951355,
0.12466830760240555,
0.038217730820178986,
1.1058018207550049,
0.41250357031822205,
0.2961711585521698,
-1.1703906059265137,
0.17404742538928986,
-0.22097419202327728,
0.5863871574401855,
-0.23108221590518951,
-0.18128162622451782,
0.5322546362876892,
-0.30808404088020325,
-0.2454916387796402,
-0.5593021512031555,
-0.020522208884358406,
1.1566084623336792,
-0.3231488764286041,
0.8384674191474915,
0.24359804391860962,
-0.43564939498901367,
-0.6233842372894287,
0.3874284327030182,
-1.0140269994735718,
-0.2394590675830841,
-0.6664489507675171,
-0.08528651297092438,
1.202689290046692,
-0.2002716064453125,
0.08657862991094589,
0.35856831073760986,
-0.44301319122314453,
0.8782206773757935,
-0.6630827784538269,
0.5365496277809143,
0.5486400127410889,
-0.270381361246109,
-0.05383017659187317,
0.32878178358078003,
-0.6976824998855591,
-0.6912934184074402,
0.01911688968539238,
-0.0013271995121613145,
0.6823691129684448,
-0.6223986744880676,
0.1706085056066513,
0.01697654277086258,
-0.4195396900177002,
0.27652525901794434,
0.11441347002983093,
-0.6622530221939087,
-0.04333764687180519,
0.42293375730514526,
-0.04147864505648613,
-0.5376520752906799,
-1.1080468893051147,
0.6129117012023926,
-0.07754984498023987,
0.05588741973042488,
0.16881918907165527,
0.08178441226482391,
-0.2878027856349945,
0.5963008403778076,
-0.08686800301074982,
-0.11055805534124374,
0.38152503967285156,
1.4672707319259644,
0.7403120994567871,
-0.26245930790901184,
-0.3428286015987396,
-0.4177251160144806,
-0.17273341119289398,
0.23638278245925903,
-0.42096370458602905,
-0.6090494394302368,
-0.31886863708496094,
0.8313945531845093,
0.12050119787454605,
-0.7028419375419617,
0.14521242678165436,
-0.53122478723526,
-1.0038063526153564,
0.41994258761405945,
-0.4789814054965973,
0.4156414866447449,
-0.12491632252931595,
0.19663618505001068,
-1.0414777994155884,
0.8344929218292236,
0.2666027843952179,
-0.13818523287773132,
0.4660012423992157,
-0.23375479876995087,
0.48671263456344604,
0.20587365329265594,
0.4712032377719879,
0.2391328513622284,
-0.49665898084640503,
-0.42089247703552246,
-0.3582278788089752,
0.413392037153244,
-1.0129027366638184,
-0.08988440781831741,
-0.1814219057559967,
0.9142326712608337,
-0.26098501682281494,
-0.270393043756485,
-0.5743812322616577,
-0.2824854850769043,
-0.41140952706336975,
-0.6140204071998596,
0.7475489377975464,
0.9715474843978882,
-0.38117921352386475,
-0.005708689335733652,
-0.7556418180465698,
-0.4126337766647339,
0.45990896224975586,
-0.2020334005355835,
0.8154304623603821,
-0.09610255062580109,
0.1417631357908249,
-0.17776769399642944,
-0.3324495553970337,
-0.26805242896080017,
0.10841184854507446,
0.42945510149002075,
0.1525999754667282,
0.3459573984146118,
0.9412959218025208,
-0.46212902665138245,
-1.0438443422317505,
0.339091032743454,
0.9191777110099792,
1.0110574960708618,
0.728084921836853,
-0.09169497340917587,
-0.09809963405132294,
-0.19840696454048157,
-0.5240914821624756,
-0.5550297498703003,
-0.22295436263084412,
0.016706176102161407,
0.05825386568903923,
-0.02680572308599949,
0.3511229455471039,
-0.019343426451086998,
0.8880453109741211,
0.2756108343601227,
0.17939946055412292,
0.3256339132785797,
0.6171649098396301,
-0.16823415458202362,
0.9500225186347961,
0.7773138880729675,
0.6396802663803101,
0.4079078137874603,
-1.1666862964630127,
0.3424687385559082,
-0.2042718529701233,
0.7733638882637024,
-0.366878479719162,
-0.16303284466266632,
0.012577778659760952,
-1.1143838167190552,
0.0332537442445755,
0.7515922784805298,
-0.6593323349952698,
0.16287429630756378,
0.1409880667924881,
0.4651601016521454,
-0.013409440405666828,
0.09819156676530838,
0.9332454204559326,
0.28907448053359985,
0.319540798664093,
-0.9109256267547607,
0.6289873719215393,
-0.5856744647026062,
0.2053028792142868,
0.5172265768051147,
-0.9493483304977417,
-0.5946605205535889,
-0.3993775248527527,
0.031204629689455032,
-0.8134133815765381,
0.44095343351364136,
1.1535106897354126,
-0.22301055490970612,
0.28955399990081787,
-0.2829505205154419,
-0.92686927318573,
0.3817445933818817,
-0.5383285880088806,
-0.33200308680534363,
0.4997304677963257,
-0.06850934028625488,
-0.26919177174568176,
0.4670723080635071,
0.11686911433935165,
-0.3552491068840027,
0.22151562571525574,
-0.7400220036506653,
0.264444500207901,
-0.03655760735273361,
-0.4304047226905823,
-0.1855727732181549,
-0.6019793748855591,
-0.47360843420028687,
0.2598872184753418,
0.28201058506965637,
0.10948587954044342,
-0.07065197825431824,
-0.03058658167719841,
-0.21603189408779144,
0.5458230972290039,
-0.14364074170589447,
0.09200878441333771,
1.162325143814087,
0.9002946615219116,
0.5877683162689209,
0.4680386483669281,
0.4564623236656189,
0.4913630485534668,
0.039638590067625046,
0.2299642264842987,
0.3088809847831726,
-0.13115200400352478,
-0.3505878448486328,
-0.2355586439371109,
-0.8048813343048096,
-1.043344259262085,
0.07701678574085236,
-0.11347700655460358,
0.9168198108673096,
-0.2368517965078354,
-0.5223506093025208,
-0.3746632933616638,
-0.08644041419029236,
-0.6543775200843811,
0.9444958567619324,
-0.18091951310634613,
-0.3054283559322357,
1.157705307006836,
-0.817607581615448,
0.01242766436189413,
-0.24475952982902527,
0.05308132246136665,
-0.1931651085615158,
0.3887150287628174,
0.5612403750419617,
0.46273672580718994,
0.2840001881122589,
-1.1302424669265747,
-0.0907062515616417,
-0.46932241320610046,
-0.22438213229179382,
-0.3857124149799347,
-0.13606137037277222,
0.34304243326187134,
-0.36358642578125,
0.16518352925777435,
-0.36279892921447754,
0.06499933451414108,
0.5340799689292908,
-0.3329789638519287,
-0.3527347445487976,
0.058486394584178925,
-0.537294328212738,
0.11213012784719467,
0.6508240103721619,
0.116240493953228,
-0.9444117546081543,
-0.34517017006874084,
0.2979704439640045,
-0.6401034593582153,
0.1840837299823761,
-0.35713258385658264,
-0.268454909324646,
0.10710105299949646,
0.09983820468187332,
0.5825564861297607,
-0.7273691296577454,
-0.8873851299285889,
-0.11326548457145691,
-0.7777755856513977,
0.4147949814796448,
0.4996594488620758,
-0.06360726803541183,
0.1995813101530075,
-0.8063192367553711,
-0.07333936542272568,
0.29724013805389404,
-0.2847382128238678,
-0.1399715095758438,
-0.161864772439003,
-0.2806369662284851,
0.0290038101375103,
0.34314993023872375,
-0.37066879868507385,
0.41134214401245117,
0.3883330821990967,
0.17170216143131256,
0.5221222639083862,
0.5851894021034241,
0.20652860403060913,
-0.34640178084373474,
0.3093835711479187,
0.4139041304588318,
-0.05034445971250534,
0.47297734022140503,
-0.45477932691574097,
0.7513639330863953,
-0.7589266896247864,
1.4686917066574097,
-0.4701511859893799,
0.036425650119781494,
-0.13051410019397736,
-0.17992658913135529,
0.2879863381385803,
-0.7091159820556641,
0.37202274799346924,
0.7194973826408386,
-0.1838676482439041,
-0.059206198900938034,
0.475843608379364,
-0.5807815790176392,
0.10290151834487915,
-0.6797032952308655,
-0.8404644727706909,
0.5710951685905457,
0.08224957436323166,
-0.16332410275936127,
-0.8542241454124451,
-0.9012758731842041,
0.5612608790397644,
-0.14471909403800964,
0.3056991696357727,
0.43338635563850403,
-0.3019363284111023,
0.3801306486129761,
-0.1539691984653473,
-0.014421007595956326,
-0.2839481830596924,
0.348891019821167,
0.1860811859369278,
-0.2702588737010956,
0.1469305008649826,
-0.0012006034376099706,
-0.5845175981521606,
-0.8452077507972717,
-0.06154431775212288,
0.30770331621170044,
-0.16888833045959473,
-0.2190517634153366,
0.5941691994667053,
-0.430412620306015,
-0.6397391557693481,
-0.014418703503906727,
0.1773584485054016,
0.2728849947452545,
0.337317556142807,
-0.3819141685962677,
-0.02240031212568283,
0.5218316912651062,
-0.1104993149638176,
0.5072034001350403,
-0.03922157362103462,
0.10193104296922684,
0.2990363836288452,
-0.5342755317687988,
-0.4673762321472168,
0.2945604622364044,
-0.2949530780315399,
-0.5151773691177368,
-0.2846381366252899,
-0.8517431020736694,
0.17517094314098358,
-0.5497371554374695,
-0.7980170845985413,
-0.6469064354896545,
-0.07904516160488129,
0.28695157170295715,
0.7596449851989746,
0.6797327399253845,
-0.36632245779037476,
-0.4649491608142853,
0.0527895949780941,
-1.0870181322097778,
-0.9566317200660706,
-0.5962119102478027,
1.4469773769378662,
0.3218172490596771,
-0.5445876121520996,
0.10975608974695206,
0.1889123171567917,
-0.16539542376995087,
0.012372974306344986,
0.6523091197013855,
-0.37773650884628296,
0.17588753998279572,
0.42992570996284485,
0.21030418574810028,
-0.006334231235086918,
0.69029301404953,
1.0587153434753418,
0.11035263538360596,
0.039544690400362015,
-0.7498283386230469,
-0.5815445780754089,
-0.23712821304798126,
0.3401138186454773,
0.8338342905044556,
0.40398484468460083,
0.2390110045671463,
0.16592663526535034,
-0.45901256799697876,
-0.24791975319385529,
-0.5047594308853149,
0.22126701474189758,
-1.1113919019699097,
-0.1115662157535553,
0.03224871680140495,
-0.6873711347579956,
0.5521844029426575,
1.0227770805358887,
0.1494155079126358,
-0.26575934886932373,
-1.109487533569336,
0.0673462375998497,
0.2745856046676636,
-0.16642683744430542,
-0.18939627707004547,
-0.9983922839164734,
0.020554689690470695,
-0.6600210666656494,
0.08905009180307388,
-0.17351526021957397,
0.023587476462125778,
-0.07198764383792877,
-0.012258422560989857,
0.378773033618927,
-0.17832116782665253,
0.6003859043121338,
-1.1043667793273926,
-1.1432548761367798,
0.05880628526210785,
-0.0662992000579834,
-0.38685959577560425,
0.42067384719848633,
-0.12759025394916534,
0.7428621649742126,
0.07776942104101181,
-0.020399656146764755,
-0.656475305557251,
0.08095835149288177,
-0.8910791277885437,
0.07131282240152359,
0.3264048099517822,
0.21435238420963287,
-0.13653291761875153,
-0.5887866616249084,
0.06716993451118469,
0.0581987239420414,
-1.2196173667907715,
0.18351151049137115,
-0.7750827074050903,
0.10878828912973404,
-0.6151407957077026,
0.42468616366386414,
0.6529580354690552,
0.5365729928016663,
0.2605668902397156,
0.9993004202842712,
-0.07874029874801636,
0.007700301706790924,
0.6390969157218933,
0.0033933056984096766,
-0.06261076033115387,
-0.001486580353230238,
-0.10365845263004303,
-0.47429385781288147,
-0.17429186403751373,
0.4655875265598297,
-0.04326445609331131,
0.025996197015047073,
-0.3340507447719574,
-0.43086323142051697,
-0.053922757506370544,
-0.49023517966270447,
-0.5054061412811279,
0.5593579411506653,
0.17426231503486633,
-0.6375941634178162,
-0.391082763671875,
-0.533257007598877,
-0.32805195450782776,
0.5566619634628296,
-0.755547285079956,
-0.2593320608139038,
0.539844810962677,
-0.22600078582763672,
-0.3910466730594635,
0.07255972921848297,
0.004921126179397106,
0.016423750668764114,
0.030174609273672104,
0.034346770495176315,
-0.24916604161262512,
0.19650256633758545,
-0.1698823869228363,
-0.07524506002664566,
-0.6896446943283081,
-0.49333426356315613,
-0.387966513633728,
0.44962212443351746,
-0.9855875968933105,
-0.7413560152053833,
-0.26845136284828186,
0.21748948097229004,
0.6547148823738098,
-0.20930586755275726,
-0.48205795884132385,
-0.07203466445207596,
-0.21789498627185822,
0.21362189948558807,
-0.7954035997390747,
-0.18218231201171875,
-0.27518942952156067,
0.7880557179450989,
-0.30427542328834534,
-0.5543910264968872,
0.1876889020204544,
0.4378010034561157,
0.21806700527668,
-0.06868815422058105,
-0.15943528711795807,
1.04800283908844,
0.5701733827590942,
-0.8183805346488953,
0.9854771494865417,
0.06462832540273666,
0.3434351980686188,
0.37604546546936035,
-0.3366897702217102,
-0.05234391242265701,
-0.31819838285446167,
0.42380601167678833,
0.6405647993087769,
0.8515699505805969,
0.11264688521623611,
0.11206179857254028,
0.19605527818202972,
0.190934956073761,
-0.3449430465698242,
0.9465795755386353,
-0.048173751682043076,
0.6201010942459106,
-0.18337476253509521,
0.06267722696065903,
0.1850704699754715,
-0.0529739148914814,
-0.7191126942634583,
-0.3920571208000183,
-0.024837719276547432,
-0.16458778083324432,
0.41914618015289307,
0.06027243658900261,
-0.4156680107116699,
-0.5837271213531494,
0.0018205058295279741,
0.1129402369260788,
0.7088853120803833,
-0.1122763529419899,
0.4346158802509308,
0.5589931607246399,
0.575088381767273,
0.2653421461582184,
-0.20961733162403107,
0.5462925434112549,
0.39866530895233154,
0.7687950134277344,
0.8386449813842773,
0.9218674898147583,
0.5627273917198181,
0.6977423429489136,
0.8120810985565186,
-1.3316149711608887,
0.13969847559928894,
0.5687116980552673,
-0.9326134324073792,
0.16267362236976624,
-0.4627912938594818,
0.492291122674942,
-0.33422866463661194,
-0.5568808913230896,
0.39998769760131836,
-1.3016833066940308,
-0.30387797951698303,
0.6694906949996948,
-0.1120622456073761,
0.3321853578090668,
0.8064178824424744,
0.32538923621177673,
0.4224429428577423,
0.6924524307250977,
-0.2981904149055481,
-0.399673193693161,
1.4236878156661987,
1.6516293287277222,
0.2796330153942108,
-0.26723968982696533,
0.5499342679977417,
-0.4840346574783325,
0.14363451302051544,
-0.05065623298287392,
-0.35922279953956604,
1.0873045921325684,
-0.6342421174049377,
-0.4071075916290283,
0.24237079918384552,
0.0512939989566803,
0.12212085723876953,
-0.36487993597984314,
0.2666071951389313,
0.3956042230129242,
-0.6075201630592346,
-0.8982931971549988,
1.7668378353118896,
0.7468644380569458,
-0.790802001953125,
-0.4601965546607971,
0.414131224155426,
-0.0433376170694828,
-0.10669010877609253,
-0.7157151699066162,
0.407021164894104,
-0.02356087416410446,
-0.03143211454153061,
-0.09638402611017227,
-0.0714501217007637,
-0.42560654878616333,
-0.388963907957077,
0.35083726048469543,
-0.26698216795921326,
0.8128196001052856,
0.08680292963981628,
0.37977394461631775,
0.4590742886066437,
-0.5242412686347961,
0.02883976139128208,
-0.1396476775407791,
0.6907352209091187,
-0.09724360704421997,
-0.03477700427174568,
1.0616966485977173,
0.6980410218238831,
-1.1188734769821167,
0.5397355556488037,
1.05141019821167,
-0.5243462920188904,
0.4379255175590515,
-0.21737928688526154,
0.13344557583332062,
0.7434101700782776,
0.4164317846298218,
0.4001055955886841,
0.16468483209609985,
-0.11596670001745224,
0.01881955936551094,
-0.6349014043807983,
-0.08165090531110764,
-0.7715224623680115,
0.06384916603565216,
-0.3681824505329132,
0.043632570654153824,
-0.20000313222408295,
0.43513888120651245,
0.7496389150619507,
-0.5124452114105225,
4.136526107788086,
0.6978892683982849,
0.19913260638713837,
0.03388863056898117,
1.013933777809143,
0.6260560154914856,
-0.5797706842422485,
-0.6379372477531433,
0.5853801369667053,
-0.7467056512832642,
-0.6837546825408936,
-0.11037132143974304,
-0.14645680785179138,
-0.09593746066093445,
0.4531519114971161,
0.5505377054214478,
-0.3396036624908447,
-0.6624511480331421,
0.25423818826675415,
-0.7016889452934265,
-0.48132824897766113,
0.08197389543056488,
0.17144005000591278,
0.11924627423286438,
0.09291244298219681,
-0.2877809405326843,
-0.24617518484592438,
-0.16894860565662384,
0.2149035781621933,
-0.1976671665906906,
-0.7102010250091553,
-1.2238179445266724,
0.20138296484947205,
-0.025018909946084023,
-0.6462253928184509,
0.49923914670944214,
-0.062246210873126984,
-0.8194612860679626,
-0.096442312002182,
0.1050177663564682,
-0.2662263810634613,
-0.2664741277694702,
-0.3661755919456482,
0.07298707962036133,
-1.2248748540878296,
1.2196805477142334,
-0.18871985375881195,
0.5451961159706116,
0.07627275586128235,
-0.6031904220581055,
0.8405315279960632,
-0.3204053044319153,
0.6707891821861267,
-0.22175149619579315,
-0.7628800272941589,
0.3421960771083832,
-0.4723620116710663,
-0.37832316756248474,
0.10814332962036133,
0.8175823092460632,
0.2100885957479477,
-0.38860225677490234,
-0.43630722165107727,
0.4506601095199585,
0.36318308115005493,
0.5186351537704468,
-0.3692311644554138,
0.3383317291736603,
-0.36742013692855835,
0.11005955189466476,
-0.3373228907585144,
-0.7887036204338074,
-0.21099498867988586,
0.20009708404541016,
0.5332177877426147,
0.026199761778116226,
0.02120630070567131,
0.5123546123504639,
0.19000470638275146,
-0.11026381701231003,
0.5725470781326294,
-0.7054700255393982,
-0.09928668290376663,
-0.3803533613681793,
0.5404447913169861,
0.34712234139442444,
-0.5011470913887024,
0.26976272463798523,
0.0707603320479393,
0.3309333920478821,
0.25844213366508484,
1.243617057800293,
0.08751115202903748,
-0.5591356158256531,
-0.9713073968887329
] |
On the Viability of Lattice Perturbation Theory
|
In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using instead ``renormalized'' coupling constants defined in terms of physical quantities, like the heavy-quark potential, greatly enhances the predictive power of lattice perturbation theory. The quality of these predictions is further enhanced by a method for automatically determining the coupling-constant scale most appropriate to a particular quantity. We present a mean-field analysis that explains the large renormalizations relating lattice quantities, like the coupling constant, to their continuum analogues. This suggests a new prescription for designing lattice operators that are more continuum-like than conventional operators. Finally, we provide evidence that the scaling of physical quantities is asymptotic or perturbative already at $\beta$'s as low as 5.7, provided the evolution from scale to scale is analyzed using renormalized perturbation theory. This result indicates that reliable simulations of (quenched) QCD are possible at these same low $\beta$'s.
|
G.P.Lepage and P.B.Mackenzie
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209022
|
hep-lat/9209023
|
[
-0.15115061402320862,
-1.0696738958358765,
-0.10891450941562653,
0.41065001487731934,
0.4082779288291931,
-0.552829384803772,
-0.5004580020904541,
-0.36861076951026917,
-0.7223986983299255,
1.2498383522033691,
0.6102492213249207,
-0.34870851039886475,
0.3454431891441345,
-0.6958855390548706,
-0.24791544675827026,
0.18642954528331757,
0.027118023484945297,
-0.7636551260948181,
-1.5201219320297241,
0.7274353504180908,
-0.08830902725458145,
-0.4805834889411926,
-1.2232980728149414,
-0.5434426069259644,
-0.1913577914237976,
1.0790491104125977,
-0.2871197760105133,
0.3631516098976135,
0.8988454341888428,
0.8081817626953125,
0.5047628879547119,
-0.49044036865234375,
-0.7674199342727661,
-0.36938798427581787,
-0.13135214149951935,
0.30404847860336304,
-0.21014361083507538,
-0.06659708172082901,
0.438873291015625,
-0.20744077861309052,
0.6194475889205933,
-0.5019406676292419,
-0.2746660113334656,
-0.2821367383003235,
-0.8490657806396484,
0.3216298520565033,
0.02854754775762558,
0.12658962607383728,
0.6590233445167542,
-1.192173719406128,
0.24609820544719696,
0.052268024533987045,
0.6110266447067261,
-0.4724622964859009,
-0.4362139105796814,
-0.5408363342285156,
0.34927237033843994,
0.5468260049819946,
-0.5667517185211182,
-0.15671215951442719,
0.6095930933952332,
-0.17893700301647186,
0.553292989730835,
-1.0193966627120972,
0.13920077681541443,
0.8538671731948853,
-0.16427995264530182,
0.7288381457328796,
0.1121726855635643,
-0.4292032718658447,
-0.25958728790283203,
-0.4741913080215454,
-1.0958009958267212,
0.4358278214931488,
-0.5221667289733887,
0.3290350139141083,
-0.3987749516963959,
-0.4065188765525818,
-0.931552529335022,
-0.14185893535614014,
-0.13511788845062256,
-0.20816273987293243,
-0.42735472321510315,
0.4273422956466675,
-0.21589264273643494,
-0.6412494778633118,
-0.3626890778541565,
-0.36773034930229187,
0.4001328945159912,
0.3828834295272827,
0.3634847402572632,
0.5653849244117737,
-0.28196007013320923,
-0.1429518312215805,
0.4899558126926422,
0.7925921082496643,
0.10553113371133804,
0.7052975296974182,
0.5659031867980957,
0.14349359273910522,
0.11422658711671829,
0.3783460259437561,
-0.823661744594574,
0.18777215480804443,
-0.16792424023151398,
0.5923309922218323,
-0.9085195660591125,
-0.17455126345157623,
-0.341838538646698,
-0.48391851782798767,
0.2677723169326782,
-0.043233588337898254,
0.5679240226745605,
0.8780099749565125,
0.06126406788825989,
0.8492059111595154,
-0.49462035298347473,
-0.25979214906692505,
-0.40851089358329773,
-0.7372758984565735,
0.43730515241622925,
-0.05524490401148796,
0.10847579687833786,
0.26496464014053345,
0.044809963554143906,
-0.3180491626262665,
0.6974506974220276,
0.6490886807441711,
-0.2044793665409088,
0.2942732572555542,
0.4732876420021057,
0.20972149074077606,
-0.2951571047306061,
0.18891993165016174,
-0.5471078157424927,
-0.0702233836054802,
-0.22497950494289398,
0.04543406143784523,
0.5170938372612,
-0.3040773570537567,
0.8291540145874023,
-0.7436069250106812,
0.023392613977193832,
0.6114033460617065,
0.23584440350532532,
0.12282475084066391,
0.06997975707054138,
0.3614307940006256,
-0.6349659562110901,
0.34374722838401794,
-0.6693056225776672,
0.35161736607551575,
0.37979286909103394,
0.3207333981990814,
-0.1589658260345459,
0.7276032567024231,
-0.9439192414283752,
0.1416412889957428,
-0.5699038505554199,
-0.6407938599586487,
0.24758970737457275,
-0.04736648499965668,
-0.9217672944068909,
0.41825470328330994,
-0.4202219247817993,
-0.03729499876499176,
-0.6970720887184143,
-0.39271828532218933,
0.10502709448337555,
-0.5090115070343018,
-0.08235890418291092,
0.42837801575660706,
-0.6610816121101379,
1.2110698223114014,
0.7036144733428955,
0.04961080476641655,
0.4197400212287903,
-0.5426512956619263,
-0.007080047391355038,
-0.022539151832461357,
-0.179090678691864,
-0.5260525345802307,
0.06426547467708588,
0.029159704223275185,
-0.33740729093551636,
-0.017122140154242516,
-0.24245001375675201,
-0.338302344083786,
0.5391270518302917,
0.2175847887992859,
0.09673064947128296,
0.27699974179267883,
-0.2819203734397888,
0.6986952424049377,
-0.48396360874176025,
-0.018885908648371696,
-1.0702223777770996,
0.3380465507507324,
-0.9215670228004456,
-0.140614852309227,
0.023168126121163368,
0.3995378315448761,
-1.3412235975265503,
0.2838926911354065,
-1.4424662590026855,
-0.4334140419960022,
1.0609378814697266,
0.017238041386008263,
-0.48781001567840576,
-0.16931509971618652,
0.16861887276172638,
-0.5508688688278198,
0.29445016384124756,
-0.7751887440681458,
0.7778589129447937,
0.41552701592445374,
-0.013102906756103039,
0.4228581190109253,
0.12077877670526505,
0.10234694927930832,
0.35996949672698975,
0.2605117857456207,
-0.30093714594841003,
0.1411927193403244,
-0.8004215955734253,
-0.5838561058044434,
0.2054770290851593,
0.5401747226715088,
0.07433484494686127,
0.1047663688659668,
0.06622638553380966,
0.2787831723690033,
-0.21614262461662292,
0.5171355605125427,
0.7827267050743103,
0.7292649149894714,
0.6244800090789795,
0.2930811047554016,
0.4228760302066803,
0.27592945098876953,
-0.5225846171379089,
0.04054299369454384,
0.4226318895816803,
-0.2716301381587982,
-0.2602381110191345,
-0.09645865112543106,
-0.4762023985385895,
0.4316861927509308,
-0.8406814336776733,
0.11205615103244781,
-0.5072562098503113,
0.4975664019584656,
-0.1016736850142479,
0.7701790928840637,
-1.0903658866882324,
-0.052852388471364975,
-0.22196200489997864,
0.10915717482566833,
-0.418125182390213,
-0.04506529122591019,
0.25167813897132874,
0.45388543605804443,
-0.01798909343779087,
-0.7686694264411926,
-0.3794390857219696,
0.9785853028297424,
-0.016711082309484482,
-0.05328774452209473,
0.909304678440094,
-0.5819515585899353,
-1.0012996196746826,
-0.12431029975414276,
-0.5741678476333618,
-0.1266658902168274,
-0.4986872375011444,
0.012738893739879131,
0.5246291160583496,
-0.9666244983673096,
0.980931282043457,
0.42147794365882874,
-0.04648568481206894,
0.8414847254753113,
-0.01765756495296955,
0.3051920235157013,
0.16219037771224976,
-0.40846335887908936,
-0.8299041986465454,
0.24398565292358398,
-0.4850001335144043,
-0.1196848526597023,
-0.5122532248497009,
0.06930438429117203,
0.4598143696784973,
-0.289712131023407,
0.04473792016506195,
-0.21872499585151672,
-0.056139592081308365,
0.46583092212677,
-0.11739134043455124,
-0.6561278104782104,
0.4904384911060333,
0.785977840423584,
0.3694593012332916,
-0.026828771457076073,
-0.6467798948287964,
0.5790711045265198,
0.09487903118133545,
-0.1533368080854416,
0.2624833881855011,
0.19579260051250458,
-0.9076591730117798,
0.7377487421035767,
0.18408121168613434,
0.087489053606987,
0.39592865109443665,
0.896876335144043,
0.9134966135025024,
-0.11242962628602982,
-0.4129534065723419,
-0.23419544100761414,
-0.4849848747253418,
0.2288745492696762,
0.1242329552769661,
-0.4128578007221222,
0.48948732018470764,
0.2676965892314911,
-0.11634530127048492,
-0.44431382417678833,
0.7352169156074524,
-0.8776814937591553,
-0.7450552582740784,
0.18623769283294678,
-0.974361002445221,
0.44982045888900757,
-0.029956843703985214,
-0.07819454371929169,
-0.6449575424194336,
-0.0013513072626665235,
0.7508875131607056,
0.1700647622346878,
0.3426811695098877,
-0.3122834861278534,
0.7191845178604126,
0.13131743669509888,
0.6257216930389404,
-0.13408447802066803,
-0.1703309267759323,
-0.3011167347431183,
-0.2715795338153839,
0.21473418176174164,
-0.5508722066879272,
0.3005293309688568,
-0.2684844434261322,
-0.17819924652576447,
-0.13701403141021729,
-0.038886964321136475,
-0.30935943126678467,
-0.6937736868858337,
-0.19280365109443665,
-0.3786119222640991,
0.3166104555130005,
0.6830249428749084,
-0.27019184827804565,
-0.2945142984390259,
-0.7378295063972473,
-0.3320557773113251,
0.3563356101512909,
0.034691084176301956,
0.6450031399726868,
-1.1542783975601196,
0.3425105810165405,
-0.31127217411994934,
-0.48212066292762756,
-0.26329711079597473,
-0.3962011933326721,
0.3473130762577057,
0.4492622911930084,
0.057563651353120804,
0.27542996406555176,
-0.3008691370487213,
-0.6129177808761597,
-0.19030141830444336,
1.059191107749939,
0.6721207499504089,
1.013039231300354,
0.16482305526733398,
0.3595900237560272,
0.1545800119638443,
-0.27471160888671875,
-0.760566234588623,
-0.18459737300872803,
-0.5062961578369141,
-0.05490288883447647,
0.11595468968153,
0.6566807627677917,
0.5050340890884399,
0.28334227204322815,
0.6483616828918457,
0.49148276448249817,
0.35071489214897156,
0.47651034593582153,
-0.1185055524110794,
0.42671865224838257,
0.9894241094589233,
-0.3136833608150482,
0.5104448795318604,
-0.5617276430130005,
0.30548322200775146,
-0.10579363256692886,
0.43705666065216064,
-0.2759082317352295,
-0.609110414981842,
-0.4485544264316559,
-1.0424740314483643,
0.327888548374176,
0.22124013304710388,
-0.6030399799346924,
0.32965195178985596,
0.5507340431213379,
0.6504960060119629,
-0.2682882249355316,
0.4821140468120575,
1.0435287952423096,
0.6927347183227539,
-0.3251596987247467,
-0.8107824325561523,
0.06383968889713287,
-0.45049577951431274,
-0.02541208826005459,
0.1258854866027832,
-0.6987999677658081,
-0.5497553944587708,
-1.2228301763534546,
-0.22763687372207642,
-0.265022337436676,
0.07798374444246292,
1.3423060178756714,
0.377309113740921,
0.09318992495536804,
-0.6090027689933777,
-0.4019812047481537,
0.9377861618995667,
-0.27982744574546814,
-0.7273106575012207,
-0.025868194177746773,
-0.31019189953804016,
-0.04472087323665619,
0.6221548914909363,
-0.26469025015830994,
-0.5733715891838074,
-0.18789738416671753,
-0.5484787225723267,
-0.02307039499282837,
-0.8000301122665405,
-0.5867687463760376,
-0.3376888930797577,
-0.3944014310836792,
-0.641452968120575,
0.8988118767738342,
0.20902171730995178,
-0.25123515725135803,
0.25756797194480896,
-0.10920952260494232,
0.22678357362747192,
0.6110377907752991,
-0.10614784806966782,
-0.17801730334758759,
0.9847174882888794,
0.7748755216598511,
0.34056293964385986,
0.15518024563789368,
0.34249642491340637,
0.16860026121139526,
0.03582746908068657,
0.2852981984615326,
0.25219395756721497,
-0.5203255414962769,
-0.6017405986785889,
-0.05540667101740837,
-0.5018613338470459,
-0.2637951970100403,
-0.24416351318359375,
-0.11864550411701202,
1.07157301902771,
0.2283238172531128,
-0.7104682922363281,
-0.49890899658203125,
-0.39856165647506714,
-0.404894083738327,
0.5593180060386658,
-0.20942431688308716,
0.1924239546060562,
0.6863821744918823,
-0.39369767904281616,
-0.31546130776405334,
-0.21264119446277618,
0.16509315371513367,
-0.21274292469024658,
0.2730758786201477,
0.9433193802833557,
-0.13090772926807404,
0.6801533699035645,
-1.212725043296814,
0.0988299623131752,
-0.16096507012844086,
0.43299126625061035,
-0.1558368057012558,
-0.1612933874130249,
-0.4987350106239319,
-0.6252803206443787,
0.4240836203098297,
0.1916961967945099,
-0.6074414253234863,
-0.042818810790777206,
0.38667726516723633,
-0.24111197888851166,
-0.39436328411102295,
-0.12632976472377777,
-0.17756327986717224,
0.4309152364730835,
0.11128173023462296,
-0.4876774549484253,
-0.14972041547298431,
0.27680090069770813,
0.1689528077840805,
0.7343177199363708,
0.14126823842525482,
-0.8085630536079407,
0.06827089935541153,
-0.47921767830848694,
0.1380864977836609,
-0.9030007719993591,
-0.9657371044158936,
-0.0481019951403141,
-0.18922793865203857,
0.3914187550544739,
1.070825457572937,
-0.165277898311615,
-0.527560830116272,
-0.23719587922096252,
-0.2757670283317566,
0.2059403359889984,
-1.017509937286377,
-0.03909480944275856,
-0.15176603198051453,
-0.3880077600479126,
-0.539219081401825,
0.5823183655738831,
-0.28039443492889404,
0.24183927476406097,
0.4409988522529602,
-0.291703999042511,
-0.28798601031303406,
0.335020512342453,
0.3595356047153473,
-0.08998173475265503,
-0.34034496545791626,
-0.18992118537425995,
-0.384721577167511,
0.6711954474449158,
-0.17195633053779602,
0.38013333082199097,
-0.6806627511978149,
0.962422251701355,
-0.268071711063385,
-0.45906054973602295,
-0.21817122399806976,
0.24253912270069122,
0.8829178214073181,
-1.1314916610717773,
0.30888447165489197,
0.2831983268260956,
-0.11361769586801529,
0.45979833602905273,
0.04024622216820717,
-0.9871469140052795,
-0.6207115650177002,
-0.24559208750724792,
-0.663528323173523,
0.49828678369522095,
0.2126590609550476,
-0.512184739112854,
-0.7091081738471985,
-1.0189766883850098,
0.13119161128997803,
0.06140244007110596,
0.4690091609954834,
0.2680164873600006,
-0.47810736298561096,
-0.035209670662879944,
0.27847883105278015,
-0.1324583888053894,
-0.6626891493797302,
0.19006036221981049,
-0.05605898052453995,
0.2063690721988678,
0.3012174665927887,
0.002245816867798567,
-1.0961889028549194,
-0.3280496299266815,
-0.06682534515857697,
0.3740660548210144,
-0.18571987748146057,
-0.13502077758312225,
0.585299015045166,
-0.06640282273292542,
0.036814913153648376,
-0.44357943534851074,
-0.17746542394161224,
0.26828834414482117,
-0.13086725771427155,
0.4578527510166168,
0.6033562421798706,
0.5732465386390686,
0.23178201913833618,
0.5145549774169922,
-0.25517135858535767,
-0.17675849795341492,
0.5649069547653198,
-0.6587281227111816,
-0.5017204880714417,
0.39212676882743835,
-0.1876077502965927,
-0.7595692276954651,
-0.06990568339824677,
-1.2798787355422974,
-0.4716154634952545,
-0.6221921443939209,
-0.2738077640533447,
-0.18070586025714874,
-0.08239970356225967,
-0.21264393627643585,
0.853045642375946,
0.9230136275291443,
0.08778652548789978,
-0.3619333505630493,
0.2128189504146576,
-0.24171526730060577,
-0.4925885498523712,
-0.010681265965104103,
1.3043122291564941,
-0.3528539538383484,
-0.7715451717376709,
0.2582147717475891,
-0.11970388889312744,
-0.33349499106407166,
0.10308904200792313,
0.36653417348861694,
-0.4140123128890991,
0.7103248834609985,
0.2384059578180313,
0.1454126387834549,
0.479574590921402,
0.7463740110397339,
-0.26299309730529785,
-0.03250734880566597,
-0.4688824415206909,
-0.3666824698448181,
-0.31437328457832336,
-0.6842800974845886,
0.24945318698883057,
0.9139571785926819,
0.20224635303020477,
0.19442600011825562,
0.03896934166550636,
-0.5080088376998901,
-0.0812947005033493,
-0.5734333395957947,
-0.4690325856208801,
-0.6553276777267456,
-0.18052387237548828,
-1.0989075899124146,
-0.38192018866539,
-0.33780890703201294,
0.4851635694503784,
-0.11166378855705261,
0.31963178515434265,
-0.6139851212501526,
-0.08215489983558655,
0.6747860312461853,
0.4912075400352478,
0.27457207441329956,
-0.9863916039466858,
-0.6207997798919678,
-0.28255724906921387,
0.12953394651412964,
-0.2034260630607605,
-0.08641323447227478,
-0.11608228832483292,
-0.24033129215240479,
0.5703179240226746,
-0.248741015791893,
0.9781891703605652,
-0.9410807490348816,
-0.9194936752319336,
0.20484386384487152,
0.10843397676944733,
-1.2812106609344482,
0.68092942237854,
0.7263315916061401,
0.6692528128623962,
0.5662765502929688,
0.15709488093852997,
-0.49823251366615295,
-0.017171990126371384,
-0.8170955181121826,
0.045031044632196426,
-0.18856453895568848,
0.522795557975769,
0.13877038657665253,
-0.840844988822937,
0.09030304104089737,
0.6593016982078552,
-0.8449018001556396,
0.40864744782447815,
-0.3192501366138458,
0.3733515739440918,
-0.6051412224769592,
0.30040156841278076,
0.6176272630691528,
0.008658365346491337,
-0.380312979221344,
0.7012139558792114,
-0.17526958882808685,
-0.11645923554897308,
-0.28798654675483704,
0.16838671267032623,
-0.5200267434120178,
-0.10020049661397934,
0.2541995048522949,
-0.10307073593139648,
0.059232257306575775,
0.7487300038337708,
-0.36161381006240845,
0.08708109706640244,
0.06928157061338425,
-0.3020521104335785,
-0.014190440997481346,
0.045042794197797775,
-0.48124638199806213,
0.8968068361282349,
0.29148679971694946,
-0.46179094910621643,
0.07388793677091599,
-0.4257461428642273,
-0.29354554414749146,
0.4565967321395874,
-0.6419202089309692,
-0.31745487451553345,
0.2822459638118744,
-0.23419000208377838,
0.10101425647735596,
0.16337184607982635,
-0.018098510801792145,
-0.1447000801563263,
-0.006096923723816872,
0.680500328540802,
0.4026617407798767,
-0.17897872626781464,
-0.41075047850608826,
0.26040127873420715,
-0.8297109603881836,
-0.2753883898258209,
-0.13502180576324463,
0.43468889594078064,
-0.6880977749824524,
-1.171898603439331,
-0.006098675541579723,
0.16888846457004547,
0.0026340072508901358,
-0.08110564947128296,
-0.29589682817459106,
-0.44860923290252686,
-0.029900483787059784,
0.30113011598587036,
0.022294949740171432,
0.07938762754201889,
-0.9232556819915771,
0.5003034472465515,
-0.1361594796180725,
-0.6138906478881836,
0.4212031662464142,
-0.020007334649562836,
0.3413410484790802,
-0.3666347861289978,
-0.04657517746090889,
1.0993766784667969,
0.09378351271152496,
-0.8319946527481079,
0.5587462782859802,
-0.19309072196483612,
0.543981671333313,
0.2994215488433838,
-0.5321783423423767,
0.26937854290008545,
0.6890342235565186,
0.015130341053009033,
0.8666740655899048,
0.20183910429477692,
0.2821179926395416,
0.20721054077148438,
0.5189168453216553,
0.19557008147239685,
-0.09070143103599548,
0.15510113537311554,
0.656921923160553,
0.4088100790977478,
0.4450746774673462,
0.212584987282753,
-0.1297493875026703,
0.19667665660381317,
0.3571142554283142,
-0.06298059225082397,
-0.48448318243026733,
-0.4263579249382019,
0.285227507352829,
0.2778257429599762,
-0.6357238292694092,
-0.16067568957805634,
-0.4079728424549103,
0.03782200440764427,
0.25336119532585144,
0.46411392092704773,
-0.522812008857727,
0.12001802027225494,
0.8108513355255127,
-0.22143037617206573,
-0.6135777235031128,
0.592125654220581,
0.24336999654769897,
0.9465147256851196,
0.7490634322166443,
0.41108083724975586,
0.43044570088386536,
0.6167328357696533,
0.32582056522369385,
-1.1090891361236572,
0.390551894903183,
0.3522930443286896,
-1.0180909633636475,
0.2447693943977356,
-0.6311221122741699,
-0.3492744565010071,
-0.7019897699356079,
-0.41993600130081177,
0.017537489533424377,
-0.7034242153167725,
0.02399769425392151,
0.3218468725681305,
-0.6534268856048584,
0.32118159532546997,
0.8419237732887268,
0.09496168047189713,
0.2142828106880188,
0.5316311717033386,
-0.5650773048400879,
0.17377054691314697,
1.4038383960723877,
1.0930705070495605,
-0.10365619510412216,
0.2070658951997757,
0.1587502807378769,
-0.5102302432060242,
0.7377840876579285,
0.6061471700668335,
-0.10963491350412369,
0.7576244473457336,
-0.7132855653762817,
-0.5370993614196777,
0.13329310715198517,
0.23603583872318268,
0.044391047209501266,
-0.14955076575279236,
0.4430105686187744,
0.22328220307826996,
-0.33302047848701477,
-0.672137975692749,
1.4641239643096924,
0.7681878805160522,
-0.7665493488311768,
-0.646550178527832,
0.21187946200370789,
-0.465817391872406,
-0.15579834580421448,
-0.9352675080299377,
0.2734545171260834,
-0.18692654371261597,
0.3528011739253998,
-0.36729705333709717,
-0.49269115924835205,
-0.6006520390510559,
-0.6780932545661926,
0.3492140769958496,
-0.44667500257492065,
0.47973039746284485,
0.3640277087688446,
0.042938295751810074,
0.008575571700930595,
-0.38417521119117737,
-0.27729249000549316,
-0.26372700929641724,
1.2581418752670288,
0.24712848663330078,
0.14850550889968872,
0.8590012192726135,
0.6413297057151794,
-0.3620040714740753,
0.7014497518539429,
1.013440728187561,
-0.7984549403190613,
0.8235217332839966,
-0.15558898448944092,
0.2592715919017792,
0.5415412187576294,
0.13292072713375092,
0.2534751892089844,
-0.16458630561828613,
0.36083799600601196,
0.5070630311965942,
-0.24907676875591278,
-0.4066276252269745,
-0.6176320314407349,
0.14380399882793427,
-0.2923514246940613,
0.5894224643707275,
0.3071434497833252,
0.04616638273000717,
0.5308459997177124,
-0.6668713688850403,
4.260544776916504,
0.9426672458648682,
0.6266146302223206,
0.30468830466270447,
0.8930820822715759,
0.7794063091278076,
-0.20042335987091064,
0.04421953484416008,
0.38895994424819946,
-0.6604002714157104,
-0.016258172690868378,
-0.277924120426178,
0.42056435346603394,
-0.21881677210330963,
-0.3999737799167633,
0.36043205857276917,
0.352522611618042,
-0.6327757835388184,
-0.2662855088710785,
-0.9472285509109497,
-0.7803260684013367,
-0.021577859297394753,
0.5379409193992615,
0.550072431564331,
0.5545875430107117,
-0.23883242905139923,
0.0449787899851799,
-0.26904064416885376,
-0.9139503836631775,
-0.5164497494697571,
-0.6352736353874207,
-0.9565108418464661,
-0.21612773835659027,
-0.2896188795566559,
-0.9267911314964294,
0.023219671100378036,
0.20492184162139893,
-0.4062505066394806,
0.035604607313871384,
-0.3356369435787201,
-0.23883427679538727,
-0.37376663088798523,
0.2709265351295471,
-0.3117624819278717,
-0.525270938873291,
1.1629666090011597,
0.0914575383067131,
0.7865560054779053,
0.6454409956932068,
-0.49706119298934937,
0.414572149515152,
0.2565232217311859,
0.997900664806366,
-0.47920945286750793,
-0.9210150241851807,
-0.025575941428542137,
-0.3301287591457367,
0.23907309770584106,
0.7759395241737366,
0.04948375001549721,
0.30919143557548523,
-0.24969923496246338,
-0.027083100751042366,
0.2913409471511841,
-0.19669018685817719,
0.3603435456752777,
-0.08486776798963547,
0.5960116386413574,
-0.08022697269916534,
-0.012949162162840366,
0.0170348659157753,
-0.05159592255949974,
-0.37039753794670105,
0.3253631591796875,
0.1405029594898224,
0.2637421786785126,
0.129970982670784,
0.5927683711051941,
0.08690676838159561,
0.33171606063842773,
-0.2639385163784027,
-0.28545257449150085,
-0.028497591614723206,
0.13780690729618073,
-0.09352032840251923,
0.8370952606201172,
-0.4974295198917389,
0.12357344478368759,
-0.21831238269805908,
0.42752522230148315,
0.47679850459098816,
1.2383476495742798,
0.2910574674606323,
0.3706137239933014,
-0.8548116683959961
] |
Modified $U(1)$ lattice gauge theory: towards realistic lattice QED
|
We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with monopoles {\it removed}. Employing Monte Carlo simulations we calculate correlators of scalar, vector and tensor operators at zero and nonzero momenta $~\vec{p}~$. We confirm that the theory without monopoles has no phase transition, at least, in the interval $~0 < \beta \leq 2~$. There the photon becomes massless and fits the lattice free field theory dispersion relation very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states show a rather weak dependence on the coupling in the interval of $~\beta~$ investigated, and their ratios are practically constant. We show also a further modification of the theory suppressing the negative plaquettes to improve drastically the overlap with the lowest states (at least, for $~J=1$).
|
V.G. Bornyakov, V.K. Mitrjushkin and M. M\"uller-Preussker
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209023
|
hep-lat/9209024
|
[
0.15028275549411774,
0.12257542461156845,
0.45250019431114197,
-0.10033872723579407,
0.23054447770118713,
-0.20610995590686798,
0.1904594749212265,
-0.430485337972641,
-0.941413164138794,
1.456748127937317,
1.1564255952835083,
-0.34281063079833984,
0.34129008650779724,
-1.4294400215148926,
-0.2493770271539688,
-0.1543750911951065,
-0.36962640285491943,
-0.7527323365211487,
-0.6883413791656494,
-0.35004112124443054,
0.6519306302070618,
-0.3233788013458252,
-1.2508600950241089,
-0.4643245339393616,
-0.4804669916629791,
0.3518264591693878,
0.747159481048584,
0.2683884799480438,
1.6489015817642212,
0.8212494850158691,
0.14572803676128387,
-1.01808500289917,
0.20556774735450745,
-0.6022201776504517,
-0.3300398588180542,
-0.1667172908782959,
0.16418375074863434,
0.1592167466878891,
0.6118851900100708,
0.1196904107928276,
1.2177268266677856,
-0.061260730028152466,
0.585575520992279,
-0.0012777788797393441,
-0.39017829298973083,
-0.16675010323524475,
-0.2477641999721527,
0.0963578000664711,
-0.04312887042760849,
-1.1881335973739624,
-0.07125192880630493,
-0.20772141218185425,
0.2972424328327179,
-0.4557889401912689,
0.17658860981464386,
-0.04795185849070549,
-0.07389411330223083,
0.36913472414016724,
-0.09228546172380447,
-0.02827819250524044,
0.9181522727012634,
0.19904163479804993,
0.9386657476425171,
-0.633427083492279,
0.6174564957618713,
1.1549255847930908,
-0.6617755889892578,
0.44146081805229187,
-0.21074283123016357,
-0.74554443359375,
-0.7767473459243774,
-0.38129109144210815,
-0.07892817258834839,
-0.24347200989723206,
-0.7109188437461853,
0.7530930042266846,
0.18569952249526978,
-0.470408171415329,
-1.0333540439605713,
-0.5987257957458496,
-0.044525887817144394,
-0.3994888961315155,
-0.25670915842056274,
0.7494051456451416,
-0.12300573289394379,
-0.4051550626754761,
0.43241116404533386,
-0.3242706060409546,
-0.2711348831653595,
0.10926766693592072,
0.48473218083381653,
0.6814690232276917,
0.7336108684539795,
-0.5207913517951965,
0.547201931476593,
0.4820137023925781,
-0.29586711525917053,
0.3622771203517914,
0.3938668668270111,
0.09994737803936005,
-0.4777733385562897,
0.8089004158973694,
-0.09733213484287262,
0.37556371092796326,
-0.4752136766910553,
0.21247290074825287,
-0.07614725083112717,
-0.24198025465011597,
0.11688114702701569,
-0.8793699145317078,
-0.07735202461481094,
0.19444072246551514,
-0.1319652944803238,
0.5595924258232117,
0.04301583394408226,
0.4224155843257904,
-0.3621089458465576,
-0.26385292410850525,
-0.8265285491943359,
-0.006331142038106918,
0.45030704140663147,
-0.11158077418804169,
0.34559863805770874,
0.5175660848617554,
-0.14583592116832733,
-1.1493138074874878,
0.04277466982603073,
0.7607123255729675,
-0.9986138343811035,
-0.1898038685321808,
-0.8072571158409119,
0.23500902950763702,
-0.029020199552178383,
0.5937984585762024,
-0.08629235625267029,
0.10916461795568466,
0.3058450222015381,
0.1504269540309906,
-0.006233152933418751,
-0.7368708252906799,
0.9423844814300537,
-0.546952486038208,
0.6907783150672913,
1.2112959623336792,
-0.3060188889503479,
0.6773505806922913,
0.10246232151985168,
-0.6684133410453796,
-0.11188352853059769,
0.8114064931869507,
-0.5176627039909363,
-0.4758274555206299,
-0.2674103379249573,
0.3697702884674072,
-0.20574645698070526,
0.1971595585346222,
-0.6592916250228882,
0.8695837259292603,
-0.7323803901672363,
0.09005957841873169,
-0.07539094984531403,
0.3648192882537842,
-0.19468310475349426,
0.3781311810016632,
-0.004935381934046745,
-0.2202664166688919,
-0.3558993339538574,
-0.3363613486289978,
-0.2869361937046051,
-0.8017990589141846,
-0.25667843222618103,
-0.552598237991333,
0.04718269035220146,
0.38962841033935547,
0.5053897500038147,
0.8827202916145325,
0.2322206199169159,
-0.395171582698822,
0.15538041293621063,
0.311278373003006,
-0.4738963842391968,
-0.47404801845550537,
0.7365023493766785,
0.2467486560344696,
-0.09357146918773651,
0.13749626278877258,
-0.2860885560512543,
-0.06604672223329544,
-0.10644662380218506,
0.5905053615570068,
0.07405301928520203,
0.3070125877857208,
-0.6391574144363403,
0.5851078033447266,
-0.2938620448112488,
-0.46007975935935974,
-0.8604974150657654,
0.033857543021440506,
-0.34476470947265625,
-0.42394348978996277,
-0.7196433544158936,
0.8180698156356812,
-1.0031675100326538,
-0.007277787197381258,
-1.602384328842163,
-0.31628847122192383,
-0.06972100585699081,
0.19705964624881744,
0.04739953204989433,
-0.13597983121871948,
0.5689845681190491,
0.27460557222366333,
0.2696586847305298,
0.0650939792394638,
-0.18433254957199097,
0.47199133038520813,
0.08332836627960205,
-0.05652252584695816,
0.9318206906318665,
-0.4956527650356293,
0.8218797445297241,
-0.04104332998394966,
-0.31814029812812805,
0.6783103942871094,
0.02142149955034256,
0.13130220770835876,
0.43415567278862,
0.8211423754692078,
-0.0105583555996418,
0.2955268621444702,
-0.40027645230293274,
1.037432074546814,
0.060860224068164825,
0.39035651087760925,
0.6853039264678955,
0.5187918543815613,
0.5788435935974121,
0.28796109557151794,
0.13136732578277588,
-0.2766325771808624,
0.19663815200328827,
0.1251857578754425,
0.6551511883735657,
0.27881869673728943,
0.5380244851112366,
0.5344849824905396,
-0.4516657590866089,
0.0889710932970047,
-0.40364325046539307,
0.5514273047447205,
-0.5491355657577515,
0.9829383492469788,
-0.14008207619190216,
-0.6045193672180176,
-0.6494114995002747,
0.474317729473114,
0.596578061580658,
0.4495985805988312,
-0.12889184057712555,
-0.18746723234653473,
-0.18679620325565338,
0.0699770525097847,
-0.5684748291969299,
-0.6194949746131897,
-0.2529653310775757,
1.5574125051498413,
0.005279409699141979,
0.23061460256576538,
0.14259351789951324,
-0.34178584814071655,
-0.7176509499549866,
-0.7285398244857788,
-1.001461386680603,
-0.6507099270820618,
-0.5271549820899963,
0.23260821402072906,
1.113884687423706,
-0.5668166279792786,
0.7130240797996521,
-0.3201315999031067,
0.06979749351739883,
0.22881275415420532,
0.7818977236747742,
0.9177915453910828,
0.7241560816764832,
0.12149787694215775,
-0.9745349287986755,
0.11378534138202667,
-0.802699089050293,
0.47521525621414185,
-0.4901791512966156,
-0.11631401628255844,
0.4445893466472626,
-0.3329869210720062,
0.09324640035629272,
-0.14621402323246002,
-0.1200680285692215,
-0.6800980567932129,
-0.15344403684139252,
-0.28211739659309387,
0.11855878680944443,
0.44772136211395264,
-0.2596087157726288,
-0.019483471289277077,
-0.0010300741996616125,
0.7110784649848938,
0.12280505150556564,
-0.34358033537864685,
1.3266490697860718,
0.32367995381355286,
-0.10956429690122604,
0.22898508608341217,
-0.5071824193000793,
0.047715362161397934,
0.08310618996620178,
0.8123153448104858,
0.5457205176353455,
0.20670509338378906,
-0.32952380180358887,
-0.3552677631378174,
-0.17530405521392822,
0.07266778498888016,
0.09189344197511673,
-0.8416988253593445,
-0.51642906665802,
0.5365320444107056,
0.38913944363594055,
-0.9736281633377075,
0.4509599506855011,
-0.9116140604019165,
-0.49896302819252014,
0.03146011382341385,
-0.024346085265278816,
0.4000529944896698,
-0.4062889814376831,
0.32017046213150024,
-0.8558934926986694,
0.650070071220398,
0.4701957702636719,
0.7288558483123779,
0.1779269576072693,
-0.4942858815193176,
0.4421137571334839,
-0.00965702161192894,
0.3036010265350342,
-0.4933086931705475,
0.3184145987033844,
-0.23998723924160004,
-0.7716923952102661,
0.361385315656662,
-0.9418473243713379,
-0.07796134054660797,
0.6017664670944214,
0.3053685128688812,
0.6033411026000977,
0.43337973952293396,
-0.5079706311225891,
-0.24141950905323029,
-0.2978532910346985,
0.20664390921592712,
0.4188936948776245,
0.43159645795822144,
-0.33383747935295105,
0.22458122670650482,
-0.5225841403007507,
-0.11574885994195938,
0.8394656181335449,
0.45487332344055176,
0.9070619940757751,
-0.4563726782798767,
0.5021697878837585,
0.058221690356731415,
-0.8185986280441284,
0.26668402552604675,
0.04410215839743614,
-0.11062486469745636,
-0.21553939580917358,
0.13777029514312744,
1.1512564420700073,
-0.3466126024723053,
-0.8787067532539368,
-0.6499541997909546,
1.1696687936782837,
0.6974159479141235,
1.0239731073379517,
0.42160964012145996,
-0.7376786470413208,
0.006414486560970545,
-0.5773932933807373,
-0.6819971799850464,
-0.18198376893997192,
-0.0628567636013031,
-0.5110871195793152,
-0.6131371855735779,
-0.33763885498046875,
-0.6464481353759766,
0.9045460224151611,
0.41537541151046753,
0.3604903221130371,
-0.21994325518608093,
0.8565957546234131,
-0.07656263560056686,
0.08077273517847061,
1.053692102432251,
0.4648926258087158,
0.2831847071647644,
-1.1755194664001465,
0.6575788855552673,
0.46922194957733154,
0.06822244077920914,
0.1394389122724533,
-0.3865605890750885,
-0.6625192165374756,
-0.27592259645462036,
0.4255351722240448,
0.24221567809581757,
-0.10006489604711533,
0.18475647270679474,
-0.27129417657852173,
0.483416348695755,
-0.8080321550369263,
-0.27835813164711,
0.24672377109527588,
0.12710964679718018,
-0.298443466424942,
-1.1252261400222778,
0.3836841881275177,
-0.5422237515449524,
0.5823113322257996,
0.761547863483429,
-0.3808172345161438,
-1.1579216718673706,
-0.40058696269989014,
0.17592579126358032,
-1.064650297164917,
0.27508220076560974,
0.6730246543884277,
-0.16938191652297974,
-0.20371247828006744,
-0.37895721197128296,
-0.29035815596580505,
0.7841689586639404,
-0.8104984760284424,
-0.6294530034065247,
0.7129225730895996,
0.37171679735183716,
-0.41875946521759033,
0.1297818422317505,
0.31952184438705444,
-0.26513534784317017,
-0.16957199573516846,
-0.3802601397037506,
0.4477913975715637,
-0.7243938446044922,
-0.5017717480659485,
-0.18086902797222137,
-0.4663255214691162,
-0.29938024282455444,
0.5235031843185425,
-0.27541384100914,
0.5699607133865356,
-0.5131176114082336,
0.42936840653419495,
-0.7538343667984009,
-0.5488428473472595,
0.3149304687976837,
0.3321133852005005,
0.702515184879303,
0.43208423256874084,
0.31859728693962097,
-0.1846333146095276,
0.3925447463989258,
0.42452651262283325,
0.49377039074897766,
0.7917101383209229,
0.12298361957073212,
0.5756499767303467,
-0.040767766535282135,
0.09679966419935226,
-0.7143694758415222,
-0.4716300070285797,
0.4836920201778412,
-0.8648303747177124,
0.7374862432479858,
0.7536830306053162,
-0.5864377617835999,
-0.20936493575572968,
-0.2834562063217163,
-0.6355948448181152,
0.2729870080947876,
-0.24921144545078278,
-0.791245698928833,
0.057742640376091,
0.2681659162044525,
0.1583712249994278,
0.3914039134979248,
-0.3065434992313385,
-0.4254099428653717,
0.3845241963863373,
0.8546826839447021,
-0.5687353610992432,
0.46356451511383057,
-0.5890816450119019,
0.6549223065376282,
-0.7260603904724121,
0.19592337310314178,
-0.31982722878456116,
-0.8938970565795898,
-0.7206616997718811,
-0.1734885722398758,
-0.6181885600090027,
-0.6915608048439026,
-0.011297764256596565,
-0.2721368670463562,
0.10133283585309982,
0.20021182298660278,
0.03969306871294975,
0.2033967524766922,
-1.0731643438339233,
0.7419939041137695,
-0.09156147390604019,
-1.086957335472107,
0.1606304794549942,
0.6490504741668701,
-0.22843705117702484,
0.3738934099674225,
-0.043575648218393326,
-0.9080169200897217,
-0.013329423032701015,
0.0900830551981926,
0.9133625030517578,
-0.717089831829071,
0.007301419973373413,
-0.11590240150690079,
-1.4527980089187622,
-0.18338242173194885,
0.5027791857719421,
0.6039435267448425,
0.19607532024383545,
-0.03161008283495903,
-0.30050528049468994,
-0.498525470495224,
-0.34531429409980774,
-0.25196486711502075,
-0.9190762639045715,
-0.5368965268135071,
-0.6564351916313171,
0.5318007469177246,
-0.5413152575492859,
0.03515104576945305,
-0.02375521883368492,
0.21804594993591309,
-0.6253174543380737,
0.7974227666854858,
0.03902067989110947,
-0.06406012922525406,
0.1152196153998375,
0.5817049741744995,
-0.1403527557849884,
0.46498194336891174,
-0.33042335510253906,
0.3435342609882355,
-1.0008609294891357,
1.1542772054672241,
-0.49124184250831604,
0.13085351884365082,
0.12258225679397583,
0.17673344910144806,
0.5072849988937378,
-0.661537766456604,
0.1956394463777542,
0.21793398261070251,
0.1815119981765747,
0.7528833746910095,
0.6049944162368774,
-0.8055649995803833,
-0.3434852361679077,
-0.8686323761940002,
-1.6687208414077759,
1.0845646858215332,
-0.11878137290477753,
0.10144694894552231,
0.005239193327724934,
0.06777477264404297,
-0.00008274352148873731,
-0.31348511576652527,
-0.04414944723248482,
0.08504891395568848,
0.22516150772571564,
0.28623756766319275,
-0.1523694545030594,
-0.276925653219223,
-0.31202059984207153,
0.03129646182060242,
0.46401074528694153,
-0.44436246156692505,
-0.7374654412269592,
-0.22830656170845032,
-0.3082450330257416,
-0.9885313510894775,
-0.38242077827453613,
0.5511859059333801,
0.17751355469226837,
0.08197548985481262,
0.8905988931655884,
-0.1609455943107605,
-0.24882367253303528,
-0.16269023716449738,
-0.7356218695640564,
0.06159235164523125,
0.4256127178668976,
0.6435366272926331,
-0.42415326833724976,
0.12493709474802017,
-0.5262702703475952,
0.8505153059959412,
-0.7032703757286072,
-0.3215881586074829,
0.2184554934501648,
0.22746986150741577,
-0.49779441952705383,
0.4482109546661377,
0.004010951146483421,
-0.701749861240387,
-0.5515919327735901,
-0.03150827810168266,
-0.07339713722467422,
-0.04686201736330986,
-0.567727267742157,
0.2146269530057907,
-0.15735244750976562,
-0.45882371068000793,
0.22841596603393555,
0.7210166454315186,
-0.6941391825675964,
0.10505867749452591,
0.19200962781906128,
-0.23717111349105835,
-0.7697983384132385,
-0.15953074395656586,
0.8638019561767578,
-0.42118027806282043,
-0.584138035774231,
-0.9956939816474915,
-0.8874210715293884,
0.03527895361185074,
0.20156913995742798,
-0.17500150203704834,
-0.007716858293861151,
0.7797254920005798,
0.38340261578559875,
1.122944951057434,
0.19659501314163208,
0.12530264258384705,
0.4277328550815582,
-0.11511915922164917,
0.2595791816711426,
-0.6055610179901123,
-0.7570485472679138,
-0.7416478991508484,
0.4715936481952667,
0.3777015507221222,
-0.4911125898361206,
0.36800628900527954,
-0.05695977061986923,
-0.5227711796760559,
-0.3053964674472809,
-1.2642630338668823,
0.5227646827697754,
-1.6504642963409424,
-0.7591155171394348,
-0.535293698310852,
-0.5581405758857727,
-0.48604679107666016,
0.4159209430217743,
0.12979552149772644,
-0.4377036392688751,
-0.7837026715278625,
-0.19527526199817657,
0.16110248863697052,
-0.34104403853416443,
-0.13888777792453766,
-0.3805243968963623,
-0.6620578169822693,
-0.22407424449920654,
-0.6821082234382629,
-0.06363832950592041,
-0.008931982330977917,
0.15465891361236572,
-0.1970095932483673,
0.3162183463573456,
-0.43433326482772827,
0.23567791283130646,
-0.808292031288147,
-0.5518938302993774,
-0.15848582983016968,
-0.15914800763130188,
-0.581817626953125,
-0.10897292196750641,
-0.3780272901058197,
-0.029991086572408676,
0.5268746614456177,
0.23866255581378937,
0.3149401843547821,
-0.04316709563136101,
-0.6249620318412781,
-0.4033701717853546,
0.31238797307014465,
0.34755706787109375,
-0.11404640227556229,
-0.4941618740558624,
0.6542118191719055,
-0.11807972192764282,
-0.9565467238426208,
0.5352861285209656,
-0.2802414298057556,
0.3734835684299469,
-0.43919703364372253,
0.03050209768116474,
0.19596388936042786,
0.8473505973815918,
0.2436460256576538,
0.5668509602546692,
0.018826322630047798,
0.30214765667915344,
-0.027863433584570885,
0.20625291764736176,
-0.2896559536457062,
0.8558791875839233,
-0.04013996198773384,
-0.7588887214660645,
-0.4432566165924072,
0.5064646601676941,
-0.10884629935026169,
0.3649947941303253,
-0.29814234375953674,
-0.2087249606847763,
-0.2658432722091675,
0.37467414140701294,
-0.3142302334308624,
0.4192039668560028,
0.1413697600364685,
-0.8243286609649658,
-0.7865867018699646,
-0.41482460498809814,
-0.8675788044929504,
0.22347919642925262,
-1.0041934251785278,
-0.3032297194004059,
-0.7086365818977356,
-0.2545526921749115,
0.09511725604534149,
-0.035289570689201355,
-0.0922875925898552,
0.2435958832502365,
0.33669140934944153,
0.7398564219474792,
-0.29045164585113525,
0.05146472528576851,
0.21831223368644714,
0.7129358649253845,
-0.9412563443183899,
-0.20669898390769958,
-0.3959422707557678,
0.21177183091640472,
-0.39291948080062866,
-0.3006930649280548,
-0.048452574759721756,
0.8674752116203308,
0.04536116123199463,
0.06613511592149734,
-0.5790124535560608,
0.4549780786037445,
0.7549912929534912,
0.37366151809692383,
-0.26398396492004395,
0.3810611963272095,
-0.11725031584501266,
0.4561287760734558,
-0.1252213567495346,
-0.35911378264427185,
0.014030673541128635,
0.25003764033317566,
0.2980216443538666,
0.4914296865463257,
-0.11425776779651642,
0.8681497573852539,
-0.5414903163909912,
-1.0102202892303467,
1.3513591289520264,
0.06742073595523834,
1.2069190740585327,
-0.03644855320453644,
0.29829472303390503,
0.5198123455047607,
0.47667786478996277,
0.24499130249023438,
0.6415651440620422,
0.38019755482673645,
0.1843026727437973,
0.7920410633087158,
0.024177631363272667,
0.32631027698516846,
0.597125232219696,
0.8188670873641968,
0.34435898065567017,
0.3740827441215515,
-0.4346950948238373,
0.10735122114419937,
0.11293592303991318,
0.6980536580085754,
0.3690510094165802,
0.02301625721156597,
-0.03731769695878029,
0.02619246393442154,
-0.10252658277750015,
0.4450523555278778,
-0.39675790071487427,
-0.2443392276763916,
-0.21483159065246582,
0.11975086480379105,
0.3727802634239197,
-0.20841968059539795,
-0.07376599311828613,
0.42945396900177,
0.3233330547809601,
0.45234033465385437,
0.3369252383708954,
0.7799988985061646,
0.2625974416732788,
0.2831001579761505,
0.1902950555086136,
0.6943046450614929,
0.4541075527667999,
0.6212587952613831,
-0.049036044627428055,
-1.007951259613037,
0.25108253955841064,
0.8201523423194885,
-1.5705584287643433,
-0.34036946296691895,
-1.0918290615081787,
0.25922226905822754,
0.27934467792510986,
-0.8971447348594666,
0.5959340333938599,
-0.5898409485816956,
0.490882933139801,
0.6093384623527527,
0.13264502584934235,
0.14135153591632843,
0.2822687029838562,
-0.6221946477890015,
0.8185085654258728,
0.5828153491020203,
-0.19509127736091614,
-0.34299585223197937,
0.9088055491447449,
1.2088861465454102,
-0.3358789086341858,
0.6662144660949707,
0.005333960056304932,
-0.7698773741722107,
0.628778338432312,
-0.09177835285663605,
-0.10645035654306412,
1.047057867050171,
-0.6863176226615906,
-0.78383469581604,
0.037159599363803864,
0.09550876170396805,
-0.6038157939910889,
-0.177438884973526,
0.297672837972641,
0.4876645803451538,
-0.5743565559387207,
-0.11970841139554977,
1.0660662651062012,
0.19555416703224182,
-0.020032916218042374,
-0.32601314783096313,
0.03910500928759575,
-0.2697077989578247,
-0.14672638475894928,
-0.676758348941803,
0.509571373462677,
0.055597398430109024,
0.11871062219142914,
-0.3690258860588074,
-1.0463100671768188,
-0.4417950510978699,
-1.262459635734558,
-0.25045329332351685,
-0.2971796989440918,
0.8555548787117004,
0.30112606287002563,
0.5190230011940002,
0.14981092512607574,
-0.6277923583984375,
0.2806931436061859,
0.266834020614624,
0.9526209831237793,
-0.06386908888816833,
0.7829564213752747,
0.9044619798660278,
0.663109302520752,
-0.5563097596168518,
0.2444356083869934,
0.9735759496688843,
-0.33362168073654175,
0.36285871267318726,
-0.14117346704006195,
0.02431301958858967,
-0.2709929049015045,
-0.3505626916885376,
0.4812510907649994,
0.3684914708137512,
0.44719478487968445,
-0.9320006966590881,
-0.1287502944469452,
0.12420740723609924,
-1.2270694971084595,
-0.17442020773887634,
-1.0583614110946655,
-0.011482138186693192,
-0.30720263719558716,
-0.2744147777557373,
-0.2500517964363098,
0.3810386657714844,
4.017606258392334,
1.2134233713150024,
0.8896886706352234,
-0.2946775555610657,
0.8395751118659973,
0.7583285570144653,
-0.20581498742103577,
-0.21814587712287903,
0.09309060126543045,
-0.5858654379844666,
-0.04693785682320595,
0.9259983897209167,
0.7179629802703857,
-0.6444016695022583,
0.10408806800842285,
0.5827279686927795,
-0.493097186088562,
0.5027384757995605,
0.7096667885780334,
-1.1054434776306152,
-0.595370888710022,
0.42019107937812805,
-0.45219850540161133,
-0.2516813576221466,
-0.1407403200864792,
0.47109803557395935,
0.359959214925766,
-1.1687521934509277,
-0.42796581983566284,
-0.38836216926574707,
-0.7582212090492249,
-0.8120679259300232,
0.18188978731632233,
-0.2974604666233063,
-0.7404723763465881,
0.5590803027153015,
0.2681530714035034,
-0.44463151693344116,
0.22097450494766235,
0.09947862476110458,
-0.12793651223182678,
0.08367764204740524,
-0.24971571564674377,
0.2242104560136795,
-0.6481742858886719,
0.7649701833724976,
-0.10653647035360336,
0.9874465465545654,
0.4109443426132202,
-0.19047468900680542,
0.5926793813705444,
-1.3048789501190186,
0.438551664352417,
-0.21715621650218964,
-1.0606045722961426,
-0.06668418645858765,
-0.9907841086387634,
-0.8451610207557678,
0.3719857931137085,
0.27171486616134644,
1.060098648071289,
0.4073978662490845,
-0.17402243614196777,
-0.05206942558288574,
-0.3572295308113098,
0.53631991147995,
0.14532752335071564,
-0.04055327922105789,
-0.27709847688674927,
-0.0666688084602356,
-0.25737684965133667,
-0.2797512114048004,
-0.29249095916748047,
0.11408258974552155,
0.14934611320495605,
-0.33960598707199097,
-0.8752066493034363,
0.5051549077033997,
-0.22930027544498444,
-0.16346290707588196,
-0.052631862461566925,
0.17686130106449127,
0.18967457115650177,
-0.2374522089958191,
0.21474017202854156,
0.9554516077041626,
-0.28123053908348083,
-0.02632533572614193,
-0.4548909068107605,
0.30714455246925354,
0.7595804333686829,
1.2772183418273926,
0.0038849851116538048,
-0.09145446121692657,
-0.5857428908348083
] |
Multicanonical Cluster Algorithm and the 2-D 7-State Potts Model
|
I present a hybrid-like two-step algorithm, which combines a microcanonical update of a spin system using demons, with a multicanonical demon refresh. The algorithm is free from the supercritical slowing down that burdens the canonical methods: the exponential increase of the tunnelling time between the metastable states in the first-order phase transitions, when the volume of the system is increased. The demons act as a buffer between the multicanonical heat bath and the spin system, allowing the spin system to be updated with any microcanonical demon procedure, including cluster methods. The cluster algorithm is demonstrated with the 2-dimensional 7-state Potts model, using volumes up to $128^2$. The tunnelling time is found to increase as $L^{1.82}$, where $L$ is the linear dimension of the system.
|
K. Rummukainen
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209024
|
hep-lat/9209025
|
[
0.41705745458602905,
-0.2540658712387085,
0.2076530158519745,
0.6620989441871643,
0.49961626529693604,
-0.07792927324771881,
0.03641699254512787,
-0.9347350001335144,
-0.28943800926208496,
1.9439548254013062,
0.9992416501045227,
-0.4667940139770508,
0.0287075974047184,
-1.030656337738037,
-0.2528127431869507,
0.5583562254905701,
-0.14070937037467957,
-0.8317854404449463,
-1.0258681774139404,
0.013408352620899677,
0.1512133926153183,
-0.45425957441329956,
-0.9380553960800171,
-0.8453304171562195,
-0.4522232115268707,
0.7410537600517273,
-0.11505530029535294,
-0.023988449946045876,
0.9909890294075012,
0.5646194815635681,
0.5660580396652222,
-0.6424039602279663,
-0.3878342807292938,
-0.18513402342796326,
-0.6853953003883362,
-0.1250440925359726,
0.06573280692100525,
0.2883099317550659,
0.584204375743866,
-0.2830575704574585,
0.8426455855369568,
-0.8150736093521118,
0.4781285524368286,
-0.15163089334964752,
-0.5105586647987366,
0.23333591222763062,
-0.31055667996406555,
-0.12621824443340302,
-0.08288177847862244,
-1.4345799684524536,
0.2909581959247589,
0.08460527658462524,
0.40411508083343506,
-0.8137528300285339,
-0.05657695233821869,
-0.03064362145960331,
0.18880455195903778,
0.39027532935142517,
-0.473809152841568,
-0.4460708200931549,
1.098413109779358,
0.11404053866863251,
0.49233731627464294,
-1.1819233894348145,
-0.026034755632281303,
0.3240971863269806,
-0.5499241948127747,
0.7390759587287903,
0.14519746601581573,
-0.6056246161460876,
-0.5780540704727173,
-0.0825357735157013,
-0.5338417887687683,
0.25355416536331177,
-0.35743603110313416,
0.5500245094299316,
0.29374101758003235,
-0.5961659550666809,
-1.2945092916488647,
-0.2801794707775116,
-0.43261393904685974,
-0.20356538891792297,
-0.5000373721122742,
0.33720627427101135,
-0.61185622215271,
-0.8595420718193054,
-0.030817145481705666,
-0.2781645357608795,
0.11186297982931137,
0.6977094411849976,
0.33377474546432495,
0.751564085483551,
-0.08320801705121994,
-0.13723698258399963,
0.5162497162818909,
0.4590291380882263,
0.34414181113243103,
0.47953730821609497,
-0.02948048524558544,
0.2828892767429352,
0.04158046096563339,
0.3823082149028778,
-0.28496938943862915,
0.5897604823112488,
-0.9944776296615601,
0.7240715622901917,
0.4073106646537781,
0.05951029434800148,
-0.01108446903526783,
-0.7970312833786011,
0.5868268013000488,
-0.166570782661438,
0.20177598297595978,
0.7081999778747559,
-0.13095740973949432,
0.5939304232597351,
0.008207245729863644,
-0.4186357855796814,
-0.6453547477722168,
-0.20304276049137115,
0.15931446850299835,
-0.21485254168510437,
0.34486669301986694,
0.8991029262542725,
-0.36115410923957825,
-0.4253275394439697,
0.2528066635131836,
0.8087317943572998,
-0.5362902879714966,
-0.17303507030010223,
0.08187738060951233,
0.5232460498809814,
-0.12374278903007507,
0.6822001338005066,
0.2267152965068817,
0.17982284724712372,
-0.19468051195144653,
0.35952499508857727,
0.5222635865211487,
-0.49414390325546265,
0.7329502105712891,
-0.6934945583343506,
-0.014373833313584328,
1.2214027643203735,
0.064323790371418,
0.3419782817363739,
0.2548353374004364,
0.013565026223659515,
0.3603084981441498,
0.5695747137069702,
-1.106339931488037,
0.36529621481895447,
-0.21465268731117249,
0.2844564616680145,
0.3602774441242218,
0.5119120478630066,
-0.5247939229011536,
0.3311336040496826,
-0.9313053488731384,
-1.054044485092163,
0.846506655216217,
-0.2576151192188263,
-0.6006091833114624,
0.033112313598394394,
-0.8090958595275879,
0.0904320776462555,
-0.4720272123813629,
-0.14540329575538635,
0.7754349112510681,
-0.7964935302734375,
-0.10492049902677536,
0.3640511631965637,
-0.4492659270763397,
0.6803198456764221,
0.14512692391872406,
0.542069137096405,
0.4757666289806366,
-0.8126325607299805,
0.7946174144744873,
-0.18423299491405487,
-0.07927680015563965,
-0.455992728471756,
0.5540315508842468,
0.19547982513904572,
-0.15813538432121277,
0.2556515634059906,
-0.14701060950756073,
-0.34872251749038696,
0.14608325064182281,
0.3100719749927521,
-0.44796013832092285,
0.10800517350435257,
-0.3000890016555786,
0.4521499574184418,
-0.8330327868461609,
-0.23223747313022614,
-1.1548676490783691,
0.24325238168239594,
-0.9574410319328308,
-0.6782519817352295,
0.22064663469791412,
0.3262878954410553,
-1.1522692441940308,
0.5077574849128723,
-1.2300082445144653,
0.29065582156181335,
0.5131686329841614,
-0.1022222489118576,
-0.5327028036117554,
-0.5431841611862183,
0.7556160688400269,
-0.10750657320022583,
0.806085467338562,
-0.46210530400276184,
0.09319628030061722,
0.08313829451799393,
-0.23987586796283722,
0.3678642511367798,
1.0470210313796997,
-0.05682354420423508,
0.8952608108520508,
0.34832173585891724,
-0.2420182079076767,
0.8971091508865356,
-0.3613958954811096,
-0.29261577129364014,
0.5543698072433472,
0.566645085811615,
0.23893532156944275,
0.30333054065704346,
0.047911740839481354,
0.3125245273113251,
-0.09441909939050674,
-0.16812406480312347,
1.160557746887207,
0.3227481245994568,
0.35572168231010437,
0.3662523925304413,
-0.14072886109352112,
0.3852531611919403,
-0.45124635100364685,
0.4911738932132721,
0.39758411049842834,
0.47072988748550415,
0.17236824333667755,
0.3163154423236847,
-0.5796127319335938,
0.24953658878803253,
-0.6412636041641235,
0.32911863923072815,
-0.8949858546257019,
0.7928128838539124,
-0.08985123038291931,
0.11415405571460724,
-1.2824498414993286,
0.26082903146743774,
-0.0066868821159005165,
0.3671190142631531,
-0.16616520285606384,
-0.632446825504303,
0.07597529143095016,
-0.11439377814531326,
-0.17791447043418884,
-0.7921712398529053,
-0.3093285858631134,
0.7015295624732971,
0.31062546372413635,
0.47957512736320496,
0.3110082149505615,
-0.023242350667715073,
-1.3836995363235474,
0.2462882697582245,
-1.1464755535125732,
-0.23871856927871704,
-0.468336284160614,
-0.31421366333961487,
0.5646311044692993,
-0.8502696752548218,
0.2714020013809204,
0.03217202425003052,
-0.42296305298805237,
0.45408886671066284,
-0.10266203433275223,
0.5455739498138428,
0.14050745964050293,
-0.14331476390361786,
-0.9637035131454468,
0.3959030508995056,
-0.7912065982818604,
0.12234216183423996,
-0.0678606778383255,
0.6399893760681152,
0.7983818650245667,
-0.398966521024704,
0.21867777407169342,
-0.2450922429561615,
-0.493721604347229,
0.16815203428268433,
0.44109442830085754,
-0.4714769423007965,
-0.13326452672481537,
-0.02967485599219799,
-0.27484130859375,
-0.6699420809745789,
-1.1421599388122559,
1.0088192224502563,
0.4258454442024231,
-0.36582744121551514,
0.32900410890579224,
0.2530469596385956,
-0.3082026243209839,
0.18326836824417114,
0.47282853722572327,
-0.18911582231521606,
0.2856009900569916,
1.0685006380081177,
0.7030970454216003,
0.4438648819923401,
-0.19831174612045288,
-0.7832440733909607,
0.07248156517744064,
0.30505016446113586,
-0.14621102809906006,
-0.30508527159690857,
-0.25155872106552124,
1.127672553062439,
0.13485820591449738,
-0.5874176621437073,
0.018453190103173256,
-0.7214099764823914,
-0.6514580249786377,
0.3695416748523712,
-0.8918294310569763,
0.7637627720832825,
0.022131087258458138,
0.0060102627612650394,
-0.9034419059753418,
-0.04408301040530205,
-0.40323102474212646,
0.1382424235343933,
0.5073993802070618,
-0.3688572645187378,
0.274100661277771,
0.597650945186615,
0.25611668825149536,
-0.34536805748939514,
0.2953832447528839,
-0.21556107699871063,
0.05685308203101158,
0.5802642703056335,
-0.8139132857322693,
0.06746542453765869,
0.6031147837638855,
0.3941078782081604,
0.4171564280986786,
0.4745776057243347,
-0.475524365901947,
-0.7575762867927551,
-0.45467159152030945,
-0.25119760632514954,
0.2583862543106079,
0.07932516932487488,
-0.20157776772975922,
0.3157323896884918,
-0.8164564967155457,
-0.0967986136674881,
0.24505101144313812,
-0.4802422821521759,
0.866432249546051,
-0.8149197697639465,
0.1601637452840805,
0.1392189860343933,
-0.23823946714401245,
0.24666531383991241,
0.1425868719816208,
0.3780859410762787,
-0.13667833805084229,
0.023542141541838646,
0.8015905022621155,
-0.35920000076293945,
-0.5427669286727905,
-0.3749677836894989,
1.274092674255371,
0.7842368483543396,
0.7688528299331665,
0.4146907925605774,
-0.400580495595932,
-0.4654838442802429,
-0.2946973145008087,
-0.1942039579153061,
-0.17790144681930542,
-0.29501309990882874,
-0.30816739797592163,
-0.2891075909137726,
-0.12849704921245575,
-0.11704368889331818,
0.4879688322544098,
0.7117900848388672,
0.5872885584831238,
0.44764164090156555,
0.3448926508426666,
0.3037528693675995,
0.6964283585548401,
0.419180303812027,
0.4670705199241638,
-0.03090064600110054,
-1.3727120161056519,
0.47443798184394836,
0.021849319338798523,
0.35043781995773315,
-0.1477910578250885,
-0.3159962594509125,
-0.4356640875339508,
-1.01197350025177,
0.2214730978012085,
0.049237340688705444,
-0.24191313982009888,
0.19228163361549377,
-0.48574307560920715,
0.6004058122634888,
-0.2986067533493042,
-0.26997363567352295,
0.6468600630760193,
0.520189106464386,
-0.11780369281768799,
-0.9599271416664124,
0.42008262872695923,
-0.19241636991500854,
0.7195392847061157,
0.3556627035140991,
-0.5508952736854553,
-0.9790300726890564,
-0.620802104473114,
-0.018475404009222984,
-0.16829946637153625,
-0.17796513438224792,
1.199619174003601,
-0.2674255669116974,
0.15298739075660706,
-0.8299345374107361,
-0.46360355615615845,
0.6147894263267517,
-0.8795803189277649,
-0.508952260017395,
0.1827283650636673,
0.01235735323280096,
-0.12821891903877258,
0.7676820158958435,
0.03457183763384819,
-0.4366745352745056,
-0.23599711060523987,
-0.11430395394563675,
-0.0735199972987175,
-0.49960851669311523,
-0.2749575674533844,
-0.06544229388237,
-0.6223576068878174,
-0.0433678925037384,
0.6963086724281311,
0.3895825147628784,
0.47490590810775757,
-0.2362033724784851,
-0.07599765062332153,
-0.09268583357334137,
-0.29913902282714844,
0.19684280455112457,
0.16961517930030823,
0.56656414270401,
1.0834009647369385,
0.38358211517333984,
0.3476603627204895,
-0.31328707933425903,
0.060945071280002594,
0.3407481610774994,
0.1581370234489441,
0.3151557743549347,
-0.11865615844726562,
-0.3463135063648224,
0.3460342586040497,
-1.0535955429077148,
-0.5975068211555481,
0.4012041389942169,
-0.038271550089120865,
0.4847997725009918,
0.019595971331000328,
-0.20009252429008484,
-0.4984503388404846,
-0.37402182817459106,
-0.821571409702301,
0.8310864567756653,
-0.1141224130988121,
-0.4409045875072479,
0.6943656802177429,
-0.6754908561706543,
-0.2563677132129669,
-0.06563729792833328,
-0.2275821417570114,
-0.3397257626056671,
0.06598753482103348,
0.4397449791431427,
0.29360637068748474,
0.842475175857544,
-0.4779569208621979,
0.14075630903244019,
-0.4736010432243347,
0.3098245859146118,
-0.7149232029914856,
0.021621819585561752,
-0.26533395051956177,
-0.19463564455509186,
0.18246158957481384,
-0.613351047039032,
-0.1307380348443985,
0.0643080547451973,
0.1321566104888916,
-0.05323980376124382,
-0.06938812881708145,
0.08875969052314758,
-0.6259883046150208,
0.411334365606308,
0.5740005373954773,
-0.5781723856925964,
0.24473196268081665,
1.2940515279769897,
0.12412051856517792,
0.31605491042137146,
-0.2103886902332306,
-0.5652697682380676,
0.5464612245559692,
-0.3791831135749817,
0.2261381894350052,
-1.109540581703186,
-0.44142746925354004,
-0.19419534504413605,
-0.3311028480529785,
0.5387656092643738,
0.5549861788749695,
-0.21108663082122803,
0.13181957602500916,
0.06298207491636276,
-0.34763339161872864,
0.7294743657112122,
-0.8443456888198853,
-0.22612062096595764,
-0.26076266169548035,
-0.37521231174468994,
-0.5228529572486877,
0.5575597882270813,
0.21562053263187408,
0.23232877254486084,
0.4478554427623749,
-0.199795663356781,
-0.02105247974395752,
0.09895768761634827,
-0.2599983811378479,
-0.5647833943367004,
0.34176772832870483,
0.7573392987251282,
0.24012590944766998,
0.10752865672111511,
-0.5001749396324158,
0.608970582485199,
-0.7314938306808472,
0.8237289786338806,
0.18005353212356567,
-0.7346561551094055,
0.031145624816417694,
0.38567855954170227,
0.6755658984184265,
-0.6736518144607544,
0.369514524936676,
0.45612630248069763,
-0.28128373622894287,
0.7182243466377258,
0.12013816088438034,
-0.4862753748893738,
-0.24155576527118683,
-0.4705149829387665,
-1.0622358322143555,
0.242509126663208,
0.058641813695430756,
-0.561930239200592,
-0.8344707489013672,
-0.39302462339401245,
0.1673814058303833,
0.08003528416156769,
0.4925619959831238,
0.2600117027759552,
-0.06538530439138412,
0.5486571192741394,
0.12365152686834335,
0.11880533397197723,
-0.5535506010055542,
-0.4852246046066284,
0.3944719135761261,
0.07957219332456589,
-0.35850197076797485,
0.1214630976319313,
-0.5263540148735046,
-1.1713491678237915,
-0.2974993586540222,
0.4821108877658844,
-0.016780037432909012,
-0.13524912297725677,
0.43855878710746765,
-0.22108517587184906,
-0.4282401204109192,
-0.4141717255115509,
0.11656762659549713,
-0.17615348100662231,
0.12311308085918427,
0.46086961030960083,
0.23496270179748535,
0.23590172827243805,
-0.1425742208957672,
0.7197399139404297,
-0.19015894830226898,
0.05764155834913254,
0.20168368518352509,
-0.46424469351768494,
-0.45078882575035095,
0.31391823291778564,
-0.1535063534975052,
-0.3006173372268677,
-0.41475775837898254,
-0.8283008337020874,
-0.42790359258651733,
-0.09906692057847977,
-0.6418846249580383,
0.42746058106422424,
0.060673996806144714,
-0.4165956377983093,
0.8140996098518372,
0.6985379457473755,
-0.35850340127944946,
0.1350104808807373,
0.0035910008009523153,
-0.44195687770843506,
-0.25320008397102356,
0.25688064098358154,
1.5354220867156982,
-0.23210576176643372,
-0.2884811758995056,
-0.1594608575105667,
-0.384117990732193,
-0.404533714056015,
0.045319635421037674,
0.5100023746490479,
-0.5980051755905151,
0.6517852544784546,
0.3744363486766815,
0.5407582521438599,
0.010759486816823483,
0.502346932888031,
0.16716675460338593,
0.31612059473991394,
0.10662131011486053,
-0.38263025879859924,
-0.5203250050544739,
-0.41618379950523376,
-0.5886204242706299,
1.3847932815551758,
-0.09068332612514496,
0.41047683358192444,
-0.4244375228881836,
-0.8297501802444458,
-0.45305320620536804,
-0.9741464257240295,
0.2090931236743927,
-0.8027963638305664,
-0.17068421840667725,
-0.3360944390296936,
-0.6071041822433472,
0.24519070982933044,
0.1781352162361145,
0.36097994446754456,
-0.2697175443172455,
-0.9293844699859619,
0.28531911969184875,
0.26534223556518555,
-0.2990925908088684,
-0.2858439087867737,
-0.4281749725341797,
-0.3397034704685211,
-0.15422025322914124,
-0.29492369294166565,
-0.2909528613090515,
-0.09727369248867035,
-0.4173043370246887,
0.08281931281089783,
0.16177411377429962,
-0.4829311966896057,
0.4748568832874298,
-0.7860202789306641,
-0.8398749828338623,
-0.39580756425857544,
-0.5749512314796448,
-0.912955105304718,
-0.1383465975522995,
0.14013440907001495,
0.2605104148387909,
0.3727061152458191,
-0.040361933410167694,
-0.18839170038700104,
0.2937657833099365,
-0.9315780401229858,
-0.10347866266965866,
0.614011824131012,
0.13090389966964722,
-0.4728907644748688,
-0.6218904256820679,
0.003517219563946128,
0.034425199031829834,
-0.8874414563179016,
0.330089807510376,
-0.5573516488075256,
0.11269877105951309,
-0.24729381501674652,
0.37821105122566223,
0.37121105194091797,
0.897175133228302,
-0.7371474504470825,
0.3107697069644928,
-0.09371131658554077,
-0.12750455737113953,
0.10829952359199524,
0.33549928665161133,
-0.29133352637290955,
0.57790207862854,
0.5612077713012695,
-0.7488998770713806,
0.2612443268299103,
0.1408078521490097,
-0.4622206687927246,
0.25579026341438293,
0.10182095319032669,
-0.26920199394226074,
-0.05347403138875961,
-0.04170110821723938,
-1.0652897357940674,
0.4613388478755951,
0.00042764045065268874,
-0.37120863795280457,
-0.7885106205940247,
-0.3374159634113312,
-1.0149445533752441,
0.41556811332702637,
-0.7691009640693665,
-0.37552452087402344,
-0.22950729727745056,
-0.5296846032142639,
-0.20718078315258026,
-0.20233187079429626,
-0.10497403889894485,
0.6833478212356567,
-0.06660003960132599,
-0.05538908764719963,
-0.2322734296321869,
0.016415171325206757,
-0.08869367837905884,
0.35933223366737366,
-0.8145183324813843,
-0.5388143062591553,
-0.4748392403125763,
0.2641483545303345,
-0.4709804654121399,
-0.753930926322937,
-0.4002934396266937,
0.4390576183795929,
0.2509661018848419,
0.17745079100131989,
-0.316593199968338,
-0.1197524294257164,
0.3685081899166107,
0.2058044672012329,
-0.2554472088813782,
0.31647631525993347,
-0.27553996443748474,
0.8213234543800354,
-0.23278142511844635,
-1.0676870346069336,
0.5092035531997681,
0.3711898624897003,
0.3355821669101715,
-0.139151930809021,
-0.563065230846405,
0.9698214530944824,
0.16392336785793304,
-0.5567078590393066,
1.0212985277175903,
-0.01215942483395338,
0.3075055480003357,
0.04873008280992508,
-0.1904139667749405,
0.3441593647003174,
-0.08878057450056076,
0.3085004985332489,
0.7463813424110413,
0.6200994253158569,
0.2655212879180908,
0.6990185976028442,
0.18894775211811066,
0.1204722449183464,
-0.053176771849393845,
0.2604748606681824,
0.6637420058250427,
0.43128660321235657,
-0.08251329511404037,
0.20478972792625427,
0.1898096352815628,
0.211391881108284,
0.08275091648101807,
-0.4982394576072693,
-0.03040958195924759,
-0.1448003500699997,
0.0039016720838844776,
0.4121464490890503,
-0.67042475938797,
-0.4409770965576172,
-0.5574848651885986,
0.2602953016757965,
0.11168155819177628,
0.04958153888583183,
-0.0628766268491745,
0.6559372544288635,
0.7004600167274475,
-0.10251765698194504,
-0.07062249630689621,
0.5447748899459839,
0.3603014349937439,
0.9014949202537537,
0.19204828143119812,
0.46009349822998047,
0.5158399939537048,
0.12342704087495804,
0.6437250375747681,
-0.8969578146934509,
-0.07963171601295471,
1.002306342124939,
-1.1250313520431519,
0.35330918431282043,
-0.5049628615379333,
-0.08871199935674667,
-0.11386918276548386,
-0.742141604423523,
0.4079500138759613,
-0.6990299820899963,
0.031486500054597855,
0.9810152649879456,
-0.36746686697006226,
0.2107776254415512,
0.9120054244995117,
-0.12845738232135773,
-0.09771319478750229,
0.5779542922973633,
0.027119308710098267,
0.27287188172340393,
1.3698588609695435,
1.2211915254592896,
0.07340176403522491,
0.27179381251335144,
0.07926374673843384,
-0.5146363377571106,
0.10795958340167999,
0.3519206643104553,
-0.2832920253276825,
1.1111024618148804,
-0.8702014684677124,
-0.35583940148353577,
0.48854687809944153,
0.4495851397514343,
-0.08160362392663956,
-0.20895959436893463,
0.003592581022530794,
0.06336800754070282,
-0.30943089723587036,
-0.8770866394042969,
1.433537244796753,
0.8224811553955078,
-0.3890405595302582,
-0.5231176614761353,
0.0370335578918457,
-0.28199318051338196,
-0.2582756280899048,
-0.4604797065258026,
-0.17276015877723694,
0.33639729022979736,
0.2561856806278229,
0.07017098367214203,
-1.094848871231079,
-0.4099380075931549,
-1.1653765439987183,
0.32101964950561523,
-0.8193404078483582,
0.20211787521839142,
-0.06656782329082489,
0.5941320657730103,
0.34949928522109985,
-0.5861106514930725,
0.1473788321018219,
0.21390633285045624,
1.0240601301193237,
-0.1838301569223404,
0.06227327510714531,
0.3483867943286896,
0.5624404549598694,
-0.43266943097114563,
1.0785523653030396,
0.3214845061302185,
-0.45057767629623413,
0.8253675103187561,
-0.5906662344932556,
0.2273784577846527,
0.11678634583950043,
-0.019950106739997864,
0.6550999879837036,
0.07523985207080841,
0.5777612924575806,
-0.42916399240493774,
-0.1680348664522171,
-0.6246996521949768,
-0.814073383808136,
0.2784089744091034,
-0.7738978266716003,
0.0703137144446373,
-0.24424012005329132,
0.45050323009490967,
0.30759045481681824,
-0.5591185688972473,
4.2184247970581055,
0.7598780393600464,
0.4942188262939453,
0.29697185754776,
0.5090803503990173,
0.6986364126205444,
-0.03579181432723999,
-0.2557430565357208,
0.2508191764354706,
-0.798258364200592,
-0.44190919399261475,
0.45923253893852234,
0.39357858896255493,
-0.3261640667915344,
-0.5138159990310669,
0.5022605061531067,
-0.3185711205005646,
-0.12762252986431122,
0.15425053238868713,
-0.7617140412330627,
-0.6101930141448975,
0.6020780205726624,
-0.12800025939941406,
-0.2928171455860138,
0.0508480966091156,
-0.36974841356277466,
0.33891627192497253,
-0.4486302137374878,
-0.6936778426170349,
-0.6143507361412048,
-0.22016756236553192,
-1.0148905515670776,
-0.0827891007065773,
-0.5633569955825806,
-0.6145931482315063,
0.25765180587768555,
0.44743648171424866,
-0.23159325122833252,
0.3721751272678375,
0.3039005696773529,
0.19588015973567963,
0.4722713232040405,
-0.13838563859462738,
-0.20834468305110931,
-0.9097810387611389,
0.7196403741836548,
-0.1646781861782074,
0.8660762310028076,
0.25735870003700256,
-0.6535781621932983,
0.4635946750640869,
-0.21258442103862762,
0.7813836336135864,
-0.3254479467868805,
-1.038581371307373,
-0.09128288179636002,
-0.7055395841598511,
-0.09501205384731293,
0.1490054577589035,
0.726398229598999,
0.38011541962623596,
-0.41919463872909546,
-0.09219297766685486,
-0.22541452944278717,
-0.26746341586112976,
0.2394397109746933,
-0.019420532509684563,
0.5075098276138306,
0.0610995888710022,
0.0088790412992239,
0.08788991719484329,
-0.5296709537506104,
-0.21428066492080688,
0.6006024479866028,
0.456092894077301,
0.10984476655721664,
-0.3178722560405731,
0.883802056312561,
0.24070893228054047,
0.18141479790210724,
-0.1466224044561386,
-0.1504492461681366,
-0.2798691689968109,
0.3960995376110077,
-0.20908385515213013,
1.3901479244232178,
-0.56411212682724,
-0.1096891239285469,
0.1277267038822174,
0.5756759643554688,
0.3283987045288086,
1.4331661462783813,
-0.15746451914310455,
-0.06052299588918686,
-1.0262700319290161
] |
Monte Carlo simulation of lattice ${\rm CP}^{N-1}$ models at large N
|
In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative agreement with the large-N predictions is found for the correlation length defined by the second moment of the correlation function, the topological susceptibility and the string tension. On the other hand, quantities involving the mass gap are still far from the large-$N$ results showing a very slow approach to the asymptotic regime. To overcome the problems coming from the severe form of critical slowing down observed at large N in the measurement of the topological susceptibility by using standard local algorithms, we performed our simulations implementing the Simulated Tempering method.
|
Ettore Vicari (Dipartimento di Fisica dell'Universita`, I-56126 Pisa, Italy)
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209025
|
hep-lat/9209026
|
[
0.13280421495437622,
-0.5454808473587036,
0.415427029132843,
0.8208613395690918,
-0.18412946164608002,
-0.8064489364624023,
-0.03323526680469513,
-0.42640435695648193,
-0.5923001170158386,
1.615679383277893,
0.6846756339073181,
-0.11467001587152481,
0.559801459312439,
-0.4456391930580139,
-0.21863503754138947,
0.6578125357627869,
-0.04166220873594284,
-0.6978557109832764,
-1.6233478784561157,
0.5428743958473206,
0.358818918466568,
-0.4037722945213318,
-1.112587571144104,
-0.5242603421211243,
-0.1699875295162201,
0.905663788318634,
0.13011959195137024,
0.3087413012981415,
0.710501492023468,
0.2648661732673645,
0.32608485221862793,
-0.7104572653770447,
-0.1354924887418747,
-0.4138977825641632,
-0.755919337272644,
0.08096688985824585,
-0.4537805914878845,
0.027750933542847633,
0.5010021328926086,
0.06585002690553665,
0.5020147562026978,
-0.6500731110572815,
0.009370087645947933,
-0.1140207052230835,
-0.6944794654846191,
0.3196638226509094,
-0.4266873598098755,
-0.21506233513355255,
0.009113709442317486,
-0.8613886833190918,
-0.08990940451622009,
0.23858392238616943,
0.3947221636772156,
-0.4156910479068756,
0.10195937752723694,
-0.6377564668655396,
-0.02583133429288864,
0.4425002336502075,
-0.37367457151412964,
-0.4776407778263092,
0.4610443413257599,
0.08639595657587051,
0.6987054347991943,
-0.7562593817710876,
-0.00699417432770133,
0.8426311016082764,
-0.6424586772918701,
0.945562481880188,
0.15234437584877014,
-0.4405648112297058,
-0.30087950825691223,
-0.5391836166381836,
-0.8341755867004395,
0.24173061549663544,
-0.8396149277687073,
0.051509059965610504,
-0.04994300380349159,
-0.40232235193252563,
-0.8629931807518005,
-0.39702656865119934,
0.04157981649041176,
-0.15526649355888367,
-0.17254909873008728,
-0.3113081455230713,
-0.2534843981266022,
-0.33905062079429626,
-0.40835896134376526,
-0.22880694270133972,
-0.5909861326217651,
0.47373297810554504,
0.21563464403152466,
0.5601602792739868,
-0.1714552491903305,
0.18389955163002014,
-0.08565603196620941,
0.4088152348995209,
0.24269847571849823,
0.4760485291481018,
0.14079110324382782,
0.19563956558704376,
-0.053294211626052856,
0.5320484638214111,
-0.3319369852542877,
0.1566719263792038,
-0.3115397095680237,
0.5659533143043518,
-0.7833847999572754,
0.6098915934562683,
0.23761095106601715,
-0.6046046018600464,
0.061131350696086884,
-0.6653015613555908,
0.389398992061615,
0.7710728049278259,
0.2608993947505951,
0.7939862608909607,
-0.23160788416862488,
0.7919827699661255,
-0.9490253925323486,
-0.7684655785560608,
0.6382675766944885,
0.9443886876106262,
0.37555158138275146,
0.5679498910903931,
0.3111439049243927,
-0.2626784145832062,
0.49978020787239075,
0.5875670909881592,
-0.7768816351890564,
0.2444821000099182,
0.4338373839855194,
-0.26759445667266846,
-0.5514830946922302,
0.44675418734550476,
-0.3767138123512268,
-0.22425630688667297,
-0.3587161600589752,
0.17192520201206207,
0.09623699635267258,
0.1819707602262497,
1.1361825466156006,
-0.3150150775909424,
0.08696180582046509,
1.0077208280563354,
0.2322080433368683,
-0.2024201899766922,
0.32290661334991455,
0.5821475982666016,
-0.13262999057769775,
0.4389691650867462,
-0.93773353099823,
0.18557392060756683,
0.1256864219903946,
0.5060774683952332,
-0.2959415316581726,
0.4578886032104492,
-0.7322582006454468,
0.03678850457072258,
-0.7061039805412292,
-0.16329221427440643,
0.409985214471817,
0.02249329909682274,
-0.6291264891624451,
0.3274538516998291,
-0.4169146716594696,
0.015973616391420364,
-0.45885539054870605,
-0.26993709802627563,
0.19613225758075714,
-0.7390238642692566,
-0.16313540935516357,
0.9335933327674866,
-0.30847010016441345,
0.7590582370758057,
0.8189531564712524,
0.3817662298679352,
0.5801436901092529,
-1.120664119720459,
-0.07009638845920563,
0.22511912882328033,
-0.5975123643875122,
-0.19327618181705475,
0.060158051550388336,
-0.11448495090007782,
-0.20851057767868042,
-0.20535023510456085,
-0.39242061972618103,
-0.023597437888383865,
-0.2113656997680664,
0.44532477855682373,
0.1010981947183609,
0.38272371888160706,
-0.8068170547485352,
0.6812061071395874,
-0.5926856398582458,
0.27634239196777344,
-1.312355399131775,
-0.05586579069495201,
-0.41638028621673584,
-0.42230454087257385,
-0.0919799730181694,
0.21424758434295654,
-1.0616602897644043,
0.41922274231910706,
-1.233655333518982,
0.21087244153022766,
0.49503082036972046,
0.2600095272064209,
-0.538182258605957,
-0.15690118074417114,
0.1487560123205185,
-0.06198303401470184,
0.5270006060600281,
-0.3384908139705658,
0.08292289078235626,
-0.11054948717355728,
-0.38235795497894287,
0.09981506317853928,
0.68381667137146,
0.46255651116371155,
0.5316634178161621,
0.4405945837497711,
-0.09398995339870453,
1.07162344455719,
-0.20303469896316528,
-0.5255049467086792,
-0.002784203505143523,
0.40560638904571533,
0.2666166126728058,
-0.06512867659330368,
0.12499912083148956,
0.388056218624115,
-0.0688551813364029,
0.37773385643959045,
0.32653605937957764,
0.16445790231227875,
-0.07199680805206299,
0.5982115268707275,
0.18795746564865112,
0.47522878646850586,
-0.4474625587463379,
0.4392293393611908,
0.28208282589912415,
-0.24473746120929718,
-0.7522086501121521,
0.5303126573562622,
-0.80003422498703,
0.1881938874721527,
-1.1333212852478027,
0.4305385947227478,
0.5642319321632385,
0.30262139439582825,
0.31935688853263855,
0.5027306079864502,
-1.3601644039154053,
0.22197727859020233,
-0.08670835196971893,
0.13926167786121368,
0.06929083913564682,
-0.5882337689399719,
0.20675446093082428,
-0.3057222068309784,
-0.27890729904174805,
-0.576752245426178,
-0.1534922569990158,
0.9938481450080872,
-0.2754752039909363,
-0.2632453143596649,
0.23312686383724213,
0.1415124088525772,
-0.8963569402694702,
0.07473260909318924,
-0.8355253338813782,
0.025546157732605934,
-0.8009394407272339,
0.48252612352371216,
0.6342450976371765,
-0.7235387563705444,
0.7063490152359009,
0.6816071271896362,
-0.5106149911880493,
0.8123525977134705,
-0.6934430599212646,
0.35397177934646606,
0.34384965896606445,
0.7128437757492065,
-0.8392327427864075,
0.2385735958814621,
-0.835207462310791,
-0.5110118985176086,
0.29337579011917114,
0.016903679817914963,
1.0684250593185425,
-0.1112806648015976,
0.6598930358886719,
0.31932246685028076,
-0.7586107850074768,
0.008285812102258205,
-0.09878847002983093,
-0.6170125007629395,
0.7356683611869812,
0.8101112246513367,
0.30129122734069824,
-0.13462112843990326,
-0.8462979793548584,
0.3009651005268097,
-0.11247038096189499,
-0.26202401518821716,
0.3020328879356384,
0.22711731493473053,
-0.6315799355506897,
0.6673704981803894,
0.30403366684913635,
0.3551608622074127,
-0.12002748250961304,
0.8419545888900757,
0.45707669854164124,
0.36584627628326416,
-0.3899526000022888,
-0.311804860830307,
-0.6849464774131775,
0.4120180308818817,
-0.18575969338417053,
-0.4411080479621887,
-0.1212412640452385,
0.42441827058792114,
0.15238045156002045,
-0.5289104580879211,
0.5953437685966492,
-1.0774447917938232,
-0.5762479305267334,
0.02057216875255108,
-0.603416919708252,
0.721335768699646,
-0.021581273525953293,
0.20607611536979675,
-0.9491446018218994,
-0.39746612310409546,
-0.18770170211791992,
-0.31879958510398865,
0.21613825857639313,
-0.10083450376987457,
0.10878459364175797,
0.2576623260974884,
0.9530033469200134,
-0.10194617509841919,
0.09541155397891998,
-0.23420371115207672,
-0.3760039210319519,
0.17211972177028656,
-0.34340664744377136,
0.3819141983985901,
0.05026109516620636,
0.4351901113986969,
-0.19738605618476868,
0.5528305172920227,
-0.2674436867237091,
-0.5548091530799866,
-0.4609858989715576,
-0.816914975643158,
0.3838157057762146,
0.8540274500846863,
-0.27636459469795227,
0.027103878557682037,
-0.5362251996994019,
-0.5609455704689026,
0.3781309723854065,
-0.06959608197212219,
0.6838672161102295,
-0.5216550827026367,
0.029863115400075912,
0.09314441680908203,
-0.6009055972099304,
0.02763752080500126,
-0.0808606743812561,
-0.04079849272966385,
0.18926078081130981,
0.013471155427396297,
0.9830561280250549,
-0.6638078689575195,
-0.4302997589111328,
-0.08953774720430374,
0.8642728328704834,
0.5829044580459595,
0.40496930480003357,
0.623781681060791,
-0.5569339394569397,
-0.008441421203315258,
-0.3532857298851013,
-0.418111115694046,
-0.06886684149503708,
-0.31962427496910095,
0.06600672751665115,
-0.36747556924819946,
0.8375347852706909,
-0.03669218719005585,
1.0506632328033447,
0.3580248951911926,
0.40307536721229553,
0.04610305652022362,
0.6549482941627502,
-0.17132407426834106,
0.3354721665382385,
0.06472998857498169,
-0.33567869663238525,
0.6684312224388123,
-0.9859403371810913,
0.2841275930404663,
0.3774779438972473,
0.10258720815181732,
-0.2717597782611847,
-0.29205620288848877,
0.05549244582653046,
-0.7477800846099854,
0.5752657651901245,
0.4012324810028076,
-0.7275338768959045,
0.4450361728668213,
0.02989264205098152,
0.7957852482795715,
-0.5386097431182861,
0.11898796260356903,
0.6516927480697632,
0.14280632138252258,
0.7996232509613037,
-1.0886892080307007,
0.644446611404419,
-0.5324437022209167,
0.6693436503410339,
0.5056825280189514,
-0.23865436017513275,
-0.39486706256866455,
-0.3878391683101654,
0.03279389068484306,
-0.2854790985584259,
0.1290939450263977,
0.9713843464851379,
-0.3556728959083557,
-0.21869337558746338,
-0.46785131096839905,
-0.46190041303634644,
0.46865224838256836,
-0.36001986265182495,
-0.11825137585401535,
0.30878955125808716,
0.0560663603246212,
0.10868518054485321,
0.6388266086578369,
-0.05901165306568146,
-0.6656663417816162,
-0.0071225157007575035,
-0.31303536891937256,
0.4755695164203644,
0.14380905032157898,
-0.25338971614837646,
-0.5111128091812134,
-0.6175018548965454,
0.052351824939250946,
0.6866135597229004,
0.4405960738658905,
-0.3197750449180603,
-0.21520330011844635,
-0.002539317822083831,
-0.4656360447406769,
0.24749907851219177,
-0.2127484679222107,
0.036868490278720856,
1.0973330736160278,
1.1739778518676758,
0.40767136216163635,
0.03964225947856903,
-0.23746512830257416,
0.2097608596086502,
-0.4719547629356384,
0.5484114289283752,
0.08898487687110901,
-0.2176540046930313,
-0.38949477672576904,
0.0941803976893425,
-0.9022510647773743,
-0.4303096830844879,
0.02911132387816906,
-0.1956280916929245,
0.7089821696281433,
-0.16191338002681732,
-0.9779757261276245,
-0.7085386514663696,
-0.06516522914171219,
-0.653132975101471,
0.7433478236198425,
0.25052303075790405,
-0.22032836079597473,
0.07140456885099411,
-0.16537830233573914,
0.45958152413368225,
-0.22277362644672394,
0.0045737712644040585,
-0.29269248247146606,
0.012761655263602734,
0.5330843925476074,
0.6672751307487488,
0.6255874037742615,
-0.6962666511535645,
0.35694873332977295,
-0.3495277166366577,
0.5044454336166382,
-0.6569519639015198,
-0.3917674124240875,
-0.15224017202854156,
-0.41432714462280273,
-0.1907554566860199,
-0.3476712107658386,
-0.1267652064561844,
-0.13193058967590332,
-0.11856722831726074,
-0.29719480872154236,
-0.448463499546051,
-0.3817608654499054,
-0.3387441039085388,
0.4282997250556946,
0.0999944657087326,
-0.2642943561077118,
0.16503018140792847,
0.526734471321106,
-0.14690080285072327,
0.041857242584228516,
-0.4163091778755188,
-0.4879261553287506,
-0.05730133503675461,
0.053323522210121155,
0.3924708068370819,
-0.548710823059082,
-0.6997446417808533,
-0.07459216564893723,
-0.367263525724411,
0.16181960701942444,
0.5808896422386169,
-0.038508664816617966,
0.11184342950582504,
-0.4665301740169525,
-0.3182755708694458,
0.2477748692035675,
-0.1189335361123085,
-0.2821754813194275,
-0.6604152321815491,
-0.11673933267593384,
-1.0260480642318726,
0.6361173987388611,
-0.23598480224609375,
0.33162033557891846,
0.3261733651161194,
-0.06770586222410202,
0.14766161143779755,
0.25978711247444153,
0.36029714345932007,
-0.25611504912376404,
0.29931601881980896,
0.2737506031990051,
0.4150025248527527,
0.9694263339042664,
-0.5379396080970764,
0.11449351906776428,
-0.4480181336402893,
1.240574598312378,
-0.9007765054702759,
-0.34885844588279724,
-0.016573255881667137,
0.07269620895385742,
0.9235324859619141,
-0.8441048860549927,
0.5449870228767395,
0.46206408739089966,
-0.38251256942749023,
0.8832689523696899,
0.4907296299934387,
-0.5363882780075073,
0.00039501121500506997,
-0.5245904922485352,
-0.9940775632858276,
0.33394870162010193,
0.39320483803749084,
-0.08656662702560425,
-0.7441496849060059,
-0.7391034364700317,
-0.32659703493118286,
0.041115980595350266,
-0.40439364314079285,
0.2987561523914337,
0.09398321062326431,
-0.374942421913147,
-0.12122964859008789,
0.02872321382164955,
-0.33930256962776184,
-0.07848155498504639,
-0.05139503255486488,
-0.023409869521856308,
0.21293942630290985,
0.32954490184783936,
-0.767877995967865,
-0.8038055300712585,
-0.09562328457832336,
0.42187830805778503,
0.220491424202919,
-0.6553588509559631,
0.8873922824859619,
-0.665438711643219,
-0.8775038123130798,
-0.5665394067764282,
-0.45290228724479675,
0.12041319161653519,
0.15339991450309753,
0.3037664592266083,
0.5718400478363037,
0.3915466070175171,
-0.08551086485385895,
0.16994677484035492,
-0.3438206911087036,
-0.11883101612329483,
0.2702890932559967,
-0.7042297720909119,
-0.19433800876140594,
0.2557445764541626,
0.10908106714487076,
-0.6590129733085632,
-0.36874091625213623,
-0.9559088349342346,
0.30848777294158936,
-0.3229001760482788,
-0.6525213718414307,
-0.02581816352903843,
-0.5333438515663147,
-0.01963767595589161,
0.6158133745193481,
0.8350399136543274,
0.1823110580444336,
-0.07333388179540634,
-0.11976209282875061,
-0.16001616418361664,
-0.44114020466804504,
0.3458625376224518,
1.2118326425552368,
-0.229255810379982,
-1.0921363830566406,
-0.4252888858318329,
-0.24678656458854675,
-0.48073625564575195,
-0.07985061407089233,
0.9062609672546387,
-0.04126546531915665,
0.6332375407218933,
0.2262345552444458,
0.050546564161777496,
0.8397719264030457,
0.38506418466567993,
-0.019912362098693848,
-0.4186140298843384,
-0.565106987953186,
-0.62883460521698,
0.1365870237350464,
-0.4100695550441742,
0.04543724283576012,
0.939850389957428,
-0.11073716729879379,
0.18775157630443573,
-0.18822918832302094,
-0.7564781904220581,
-0.050075896084308624,
-0.7193917632102966,
0.24850037693977356,
-1.23993980884552,
-0.1574648916721344,
-0.3028983771800995,
-0.32410672307014465,
0.5090723633766174,
0.4520356357097626,
0.5704284906387329,
0.3603265881538391,
-0.57281893491745,
-0.4009670317173004,
-0.3288593590259552,
-0.06410171836614609,
-0.3454904854297638,
-1.0065116882324219,
-0.23171362280845642,
0.00818747840821743,
-0.314052015542984,
-0.20470722019672394,
0.3118896484375,
0.09772743284702301,
-0.11393117904663086,
0.16375823318958282,
-0.029485424980521202,
0.7122135758399963,
-1.1361044645309448,
-1.2017902135849,
0.5299635529518127,
-0.1782653033733368,
-0.1809813529253006,
0.14542043209075928,
0.31164368987083435,
0.7272258400917053,
0.4239659011363983,
-0.023139283061027527,
-0.6074556708335876,
-0.08501465618610382,
-1.5491175651550293,
-0.4183301031589508,
0.39658379554748535,
-0.36599162220954895,
0.0017708494560793042,
-0.8069682717323303,
-0.36413902044296265,
0.2596561908721924,
-0.9260926246643066,
0.3245944678783417,
-0.3632543385028839,
0.4893713593482971,
-0.42256420850753784,
0.3077344000339508,
0.4778239130973816,
0.016758078709244728,
-0.5050143599510193,
0.490731418132782,
-0.4297487437725067,
0.12626448273658752,
0.14685651659965515,
0.3150692284107208,
-0.12413285672664642,
0.5075734853744507,
0.5978437662124634,
-0.35268887877464294,
-0.41742414236068726,
0.25131306052207947,
-0.1858954131603241,
-0.020089473575353622,
0.1075604036450386,
-0.5973331332206726,
0.10166016966104507,
-0.23247194290161133,
-0.7660484910011292,
0.3059350848197937,
0.5887514352798462,
-0.7802861332893372,
-0.04095867648720741,
-0.3677228093147278,
-0.2945792078971863,
0.048323821276426315,
-0.7734629511833191,
-0.5088697671890259,
-0.19135329127311707,
0.10540652275085449,
-0.40093889832496643,
0.3968345522880554,
-0.2798592448234558,
0.3768829107284546,
-0.15482057631015778,
-0.05541591718792915,
0.20700804889202118,
-0.4764825105667114,
-0.6227713227272034,
-0.1534576416015625,
-1.0189664363861084,
-0.09564302861690521,
-0.2373477667570114,
0.8643755316734314,
-0.20560508966445923,
-0.8216777443885803,
-0.6242454051971436,
0.2432003915309906,
0.739974319934845,
0.3326973021030426,
-0.21233175694942474,
-0.22681118547916412,
-0.6895790100097656,
-0.10590047389268875,
-0.9201356768608093,
-0.4452146291732788,
-0.352576345205307,
0.6934922337532043,
-0.21549919247627258,
-0.8558392524719238,
0.6328743696212769,
-0.0009299351368099451,
-0.08876623213291168,
0.05768574774265289,
-0.06671884655952454,
0.7931928038597107,
0.7855530381202698,
-0.2218361347913742,
0.7369804382324219,
0.04909063130617142,
-0.3315475881099701,
0.44205546379089355,
-0.5281215906143188,
-0.09015663713216782,
0.5805641412734985,
0.03434028476476669,
0.6528258323669434,
0.5538771748542786,
0.29005739092826843,
0.19168245792388916,
0.3268110156059265,
0.2844439744949341,
-0.27729862928390503,
0.35872501134872437,
0.7016943097114563,
0.2681483030319214,
0.07833454757928848,
-0.02465163543820381,
-0.35583096742630005,
-0.2889917194843292,
0.17885245382785797,
-0.08369776606559753,
-0.35506051778793335,
0.16579970717430115,
0.0838746726512909,
-0.03536378592252731,
-0.84958416223526,
-0.6171228885650635,
-0.16973531246185303,
0.5402439832687378,
0.7478463053703308,
0.46838289499282837,
0.21493564546108246,
1.1292808055877686,
0.42521852254867554,
-0.0740058571100235,
0.13488280773162842,
0.8149595856666565,
-0.3440510928630829,
1.1400316953659058,
0.9166439771652222,
0.4639856517314911,
0.3840179741382599,
0.5793709754943848,
0.4907070994377136,
-0.18676435947418213,
-0.1812175214290619,
0.2433406561613083,
-0.8167449831962585,
-0.035650141537189484,
-0.5396735668182373,
0.08565451949834824,
-0.28089454770088196,
-0.7197955250740051,
0.6147060990333557,
-1.0120123624801636,
0.025308001786470413,
0.5945619940757751,
-0.2815879285335541,
0.4665306806564331,
0.7528666853904724,
0.10293573886156082,
-0.2820785641670227,
0.5281815528869629,
-0.12091881781816483,
0.05406197905540466,
1.1867306232452393,
1.3729360103607178,
0.36455708742141724,
-0.19737061858177185,
0.351023405790329,
-1.0355145931243896,
0.4392477869987488,
0.5378293395042419,
-0.5658910870552063,
0.8857965469360352,
-0.30408740043640137,
-0.2424687296152115,
0.7846372723579407,
0.34499019384384155,
0.18493720889091492,
-0.454220175743103,
0.23838777840137482,
0.1151847317814827,
0.15962828695774078,
-0.5150905847549438,
1.4493666887283325,
0.7843549251556396,
-0.8231772184371948,
-0.22092919051647186,
0.03812986984848976,
-0.7067534327507019,
-0.037900518625974655,
-1.0219727754592896,
0.5623592734336853,
-0.20483435690402985,
-0.522323489189148,
-0.19417785108089447,
-0.5230405926704407,
-0.28393077850341797,
-0.6615289449691772,
0.12239401787519455,
-0.5418345332145691,
0.18406857550144196,
0.4679900109767914,
-0.1154906377196312,
0.7818149924278259,
-0.6316903829574585,
0.21797925233840942,
0.6054442524909973,
0.9630210995674133,
-0.19439665973186493,
-0.17401833832263947,
0.565534770488739,
0.5929097533226013,
-0.6163908243179321,
0.6609495282173157,
0.769233226776123,
-0.21994304656982422,
0.5667554140090942,
-0.48121803998947144,
0.27739086747169495,
-0.046134017407894135,
0.07716116309165955,
0.5625286102294922,
0.1692957878112793,
-0.0815606489777565,
-0.4681394398212433,
-0.43687036633491516,
-0.14135654270648956,
-0.8301791548728943,
-0.17945055663585663,
-0.40445321798324585,
0.28694528341293335,
-0.4538111686706543,
0.044937990605831146,
0.3042667806148529,
-0.9043110013008118,
4.313538551330566,
0.8324264883995056,
-0.018077095970511436,
0.3642338216304779,
0.624884307384491,
1.2834588289260864,
-0.3275296092033386,
-0.5440423488616943,
0.40714794397354126,
-0.5566398501396179,
-0.7245948314666748,
-0.007513509131968021,
0.02775563672184944,
0.14376415312290192,
0.22181247174739838,
0.6133117079734802,
-0.4396349787712097,
0.168678879737854,
-0.13578777015209198,
-0.9623361229896545,
-0.7823578715324402,
0.29745036363601685,
0.6141470074653625,
-0.04218659922480583,
0.2730658948421478,
0.5226129293441772,
0.011792629957199097,
-0.8296828269958496,
-0.38835668563842773,
-0.6479012370109558,
-1.0245834589004517,
-0.7035483717918396,
0.2967107892036438,
0.4026455581188202,
-0.9086253046989441,
0.2382594645023346,
0.39274415373802185,
-0.10539259761571884,
0.200283482670784,
-0.2818354070186615,
0.21308580040931702,
-0.3464413285255432,
0.6835668087005615,
-0.2486141473054886,
-0.5066875219345093,
0.863470733165741,
-0.1893453747034073,
0.8241404294967651,
-0.2131059467792511,
-0.33923855423927307,
0.5149781703948975,
0.5411819219589233,
0.6518661975860596,
-0.1650797575712204,
-0.735560417175293,
0.27177220582962036,
-0.5209864974021912,
-0.19779418408870697,
0.3057270646095276,
0.19326740503311157,
0.25551679730415344,
-0.193227156996727,
-0.2976112365722656,
0.39213526248931885,
0.05258176475763321,
0.5924860239028931,
0.37126800417900085,
0.08883265405893326,
-0.3886350691318512,
0.41812270879745483,
0.2188493311405182,
-0.4964083135128021,
-0.2659493386745453,
0.39787057042121887,
0.38326770067214966,
0.09108100086450577,
-0.6677439212799072,
0.45865872502326965,
-0.036539483815431595,
0.11183790117502213,
0.3520304262638092,
-0.5047227144241333,
0.12842094898223877,
-0.12112411111593246,
0.14058835804462433,
0.7017627954483032,
-0.32011744379997253,
0.29421424865722656,
-0.3020595610141754,
0.3266660273075104,
0.28815731406211853,
0.6396823525428772,
0.5046126246452332,
0.32861649990081787,
-0.40043795108795166
] |
Bose Condensation and $Z_N$ Symmetry Breaking in the Mixed Model of Induced QCD
|
The mixed model of the large $ N $ induced QCD, with $ N_f \ll N $ flavors of heavy fermions in fundamental representation, is solved in the local limit. The $ Z_N$ symmetry is broken spontaneously in the large $ N $ limit, evading the Elitzur "no-go" theorem. As a result of this symmetry breaking, there is the Bose condensate of the eigenvalues of the scalar field, proportional to $ \frac{N_f}{N} $. This condensate leads to the mass unit, which goes to zero as fractional power of $ \frac{N_f}{N} $, thus defining the new kind of the local limit of this lattice theory. There is a strong coupling region below this mass scale, which revives the hopes of induction of realistic QCD.
|
A.A. Migdal
|
hep-lat hep-th
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209026
|
hep-lat/9209027
|
[
-0.2025958001613617,
-0.2799960672855377,
-0.12253926694393158,
0.5521118640899658,
0.3660786747932434,
0.38989323377609253,
0.1594170778989792,
0.14118307828903198,
-0.5600862503051758,
1.4956470727920532,
0.5840370059013367,
0.11357244849205017,
0.4603308439254761,
-1.3383046388626099,
-0.18213137984275818,
0.3785197138786316,
-0.03680367022752762,
-0.36168476939201355,
-1.0500476360321045,
0.6426018476486206,
0.5880759358406067,
0.1963391751050949,
-0.6272827982902527,
-1.0507738590240479,
-0.5017862915992737,
1.0407862663269043,
0.2622678875923157,
0.2608012557029724,
1.2906556129455566,
0.7693266272544861,
0.656627893447876,
-0.4493862986564636,
-0.8568611741065979,
-0.46051275730133057,
-0.6801703572273254,
-0.6025997400283813,
-0.3615171015262604,
-0.5478127002716064,
0.5904983878135681,
-0.20502491295337677,
0.6609835624694824,
-0.4356176257133484,
-0.21690918505191803,
-0.12633444368839264,
-0.06822783499956131,
0.2036525011062622,
-0.2974109947681427,
-0.3793025612831116,
0.15756674110889435,
-1.2515430450439453,
0.35162553191185,
0.17318513989448547,
0.8797253370285034,
-0.9284641742706299,
0.2510420083999634,
-0.4452204704284668,
-0.2081575244665146,
0.482150137424469,
-0.43196046352386475,
-0.3898945152759552,
0.16591936349868774,
0.3449054956436157,
0.41482725739479065,
-0.8296828866004944,
0.38372766971588135,
0.6432449817657471,
0.2108723372220993,
0.9489356279373169,
-0.1644376516342163,
-0.05613197758793831,
-0.6492617726325989,
0.01763835921883583,
-0.8481535315513611,
-0.2607974410057068,
-0.8723598122596741,
0.2807714641094208,
-0.12220507860183716,
-0.6013830900192261,
-1.2926223278045654,
-0.648737370967865,
-0.45241227746009827,
-0.11925029009580612,
-0.35652944445610046,
0.655463457107544,
-0.341941773891449,
-0.33638322353363037,
-0.31315067410469055,
-0.38494089245796204,
-0.05639851838350296,
0.5294788479804993,
0.5770776867866516,
1.0392637252807617,
0.04430007189512253,
-0.2353927195072174,
0.7908987402915955,
0.7572518587112427,
-0.22312934696674347,
0.719425618648529,
0.3650578260421753,
0.41418325901031494,
0.08452940732240677,
1.0486524105072021,
-0.486807644367218,
0.5520955324172974,
-0.4769006669521332,
0.1873079091310501,
-0.4478255808353424,
0.34073084592819214,
-0.3929084539413452,
-0.4881758987903595,
0.5934523344039917,
-0.315339058637619,
0.6941123604774475,
0.4197499454021454,
0.30633872747421265,
0.4884694516658783,
-0.46718961000442505,
0.0821985974907875,
-1.1030696630477905,
-0.35384657979011536,
0.36827248334884644,
-0.34177687764167786,
0.7306371927261353,
0.5914940237998962,
-0.5445802807807922,
-0.42238470911979675,
0.47525554895401,
0.3708752691745758,
-0.41380828619003296,
0.463250994682312,
0.37708941102027893,
0.47941771149635315,
-0.5274279713630676,
0.27699825167655945,
-0.5552504062652588,
0.22023555636405945,
-0.9522173404693604,
0.22815541923046112,
0.7234624028205872,
-0.5384219884872437,
0.3590226471424103,
-0.4087861478328705,
0.2804657816886902,
1.0370140075683594,
-0.07595916837453842,
0.4972549080848694,
0.19155018031597137,
-0.3033909499645233,
0.049288056790828705,
0.28027862310409546,
-0.44008368253707886,
-0.22330360114574432,
-0.3844369649887085,
-0.4271974265575409,
0.2509481608867645,
0.42508062720298767,
-0.7271119356155396,
0.5650824308395386,
-0.11351986974477768,
-0.4650890827178955,
0.3583557605743408,
0.37896791100502014,
-0.28341037034988403,
0.5289580225944519,
-0.6253911852836609,
0.0028492140118032694,
-0.7967090606689453,
-0.6599615812301636,
-0.10022260993719101,
-0.6207844614982605,
0.20762881636619568,
0.3639845848083496,
-0.25061994791030884,
0.457199364900589,
0.9834792017936707,
0.4109085500240326,
0.5609840154647827,
-0.6978768110275269,
-0.02977844513952732,
0.47812390327453613,
-0.16819964349269867,
-0.6902631521224976,
0.5562303066253662,
0.5361283421516418,
-0.4470168352127075,
0.020873215049505234,
-0.42738544940948486,
-0.22624525427818298,
0.3874196410179138,
-0.1347452998161316,
-0.304848313331604,
0.48935091495513916,
-0.1510443091392517,
0.13279969990253448,
-0.8524631261825562,
0.7429535984992981,
-1.3584318161010742,
0.3406202793121338,
-0.1794278621673584,
-0.71418696641922,
-0.23865433037281036,
0.303609699010849,
-0.8620608448982239,
0.26766014099121094,
-1.074607014656067,
-0.2485293596982956,
0.9216678142547607,
0.11341255903244019,
-0.36688706278800964,
-0.6125078797340393,
0.3498040735721588,
-0.12374123185873032,
0.36581483483314514,
-0.5190168023109436,
0.5373212099075317,
0.6001238822937012,
-0.42158228158950806,
-0.21836794912815094,
0.26682791113853455,
0.022914646193385124,
0.5007522702217102,
0.20890869200229645,
-0.37065061926841736,
1.049587368965149,
-0.2746368944644928,
-0.7441295981407166,
-0.20067842304706573,
0.5390055775642395,
0.1525026261806488,
-0.03621186688542366,
-0.250795841217041,
0.22187891602516174,
-0.17457154393196106,
0.4470226764678955,
0.2912985682487488,
0.051101502031087875,
0.37337154150009155,
0.7979477047920227,
0.5008788108825684,
0.5994926691055298,
-0.049260854721069336,
0.06582262367010117,
0.7518972158432007,
-0.09575493633747101,
-0.40349534153938293,
0.19326849281787872,
-0.9201218485832214,
0.0998801440000534,
-0.8689220547676086,
0.8227573037147522,
-0.16639837622642517,
0.2659075856208801,
-0.2271919697523117,
0.09409213066101074,
-1.1862821578979492,
-0.20336192846298218,
-0.3117944300174713,
0.07370731234550476,
0.1175369918346405,
-0.48697468638420105,
-0.23714721202850342,
0.37919047474861145,
-0.2040998935699463,
-0.9447627067565918,
0.004164554178714752,
1.0775846242904663,
-0.184674933552742,
0.18266235291957855,
0.3623409867286682,
-0.2583724856376648,
-1.0952939987182617,
0.06577615439891815,
-1.0043702125549316,
0.5121403336524963,
-0.8271166086196899,
0.29663175344467163,
0.5030264258384705,
-0.24853946268558502,
0.5245586037635803,
-0.19236011803150177,
-0.4968411326408386,
0.11784730851650238,
-0.4805185794830322,
0.017179222777485847,
0.7086906433105469,
-0.04349113255739212,
-0.8491098880767822,
-0.03220069035887718,
-0.6700170636177063,
-0.40498676896095276,
-0.7073392868041992,
-0.46809011697769165,
0.9812461137771606,
-0.13646642863750458,
0.02197190187871456,
-0.13521194458007812,
0.07758352905511856,
-0.28416353464126587,
-0.07306269556283951,
-0.5590484142303467,
0.4685801565647125,
-0.014474752359092236,
-0.35137975215911865,
0.47483131289482117,
-1.312657117843628,
0.7748100161552429,
-0.10410010069608688,
-0.12882696092128754,
0.7105371952056885,
0.2798196077346802,
-0.6429429054260254,
0.8790223598480225,
0.2093922197818756,
0.08264463394880295,
-0.28404152393341064,
0.8711206316947937,
0.5966218113899231,
0.011272165924310684,
0.1334693282842636,
-0.2565561830997467,
-0.20895718038082123,
-0.08800581097602844,
0.059234801679849625,
-0.6449152231216431,
0.002565926406532526,
0.6717947721481323,
0.24524782598018646,
-0.7730897665023804,
0.0021627768874168396,
-0.9018145799636841,
-0.11343985795974731,
0.020487075671553612,
-0.1461244374513626,
0.35481297969818115,
-0.3690834045410156,
-0.16308259963989258,
-0.8501352071762085,
0.07635419070720673,
0.6015728116035461,
0.25922101736068726,
0.5724272131919861,
-0.5145276784896851,
0.5225215554237366,
0.7052543759346008,
0.3542974591255188,
-0.44185301661491394,
-0.012173316441476345,
-0.3976113200187683,
-0.8562359809875488,
0.39921486377716064,
-0.9391202926635742,
0.1790783703327179,
0.07134874165058136,
0.11871012300252914,
0.5787597894668579,
0.6652650237083435,
-0.11275661736726761,
-0.6640440225601196,
-0.3034180998802185,
-0.2291896492242813,
0.5210393667221069,
0.33258140087127686,
0.4261206090450287,
-0.3246901333332062,
-0.9413539171218872,
-0.5401576161384583,
-0.12114118784666061,
-0.18590570986270905,
0.7619366645812988,
-0.9052106738090515,
0.35504233837127686,
0.16592663526535034,
-0.1681915819644928,
0.3506574332714081,
-0.2944456934928894,
0.5273574590682983,
0.1876325011253357,
-0.05983112379908562,
0.6642501354217529,
-0.4231429100036621,
-0.56068354845047,
0.08870857208967209,
0.466745525598526,
0.8026756644248962,
0.7865020632743835,
0.34964045882225037,
-0.2657434642314911,
0.722902238368988,
-0.07959366589784622,
-0.30419549345970154,
-0.32813242077827454,
-0.45838287472724915,
-0.10105510801076889,
-0.41504621505737305,
0.29708853363990784,
-0.18517735600471497,
0.4395100176334381,
0.1399899423122406,
0.3418765068054199,
0.4510800242424011,
0.840158224105835,
0.4562150239944458,
0.7063762545585632,
0.6094696521759033,
-0.14521649479866028,
0.27070552110671997,
-0.9289492964744568,
0.5998464822769165,
0.4165964722633362,
0.470921128988266,
-0.28967830538749695,
-0.7068811655044556,
-0.1093311458826065,
-0.32613420486450195,
0.7652437686920166,
-0.02554437704384327,
-0.8290717601776123,
0.43333157896995544,
0.5390906929969788,
0.3336995840072632,
-0.1423397809267044,
0.027453213930130005,
1.1950181722640991,
0.5543895363807678,
0.28580617904663086,
-0.4270123839378357,
-0.3761565387248993,
-0.7058987617492676,
0.8045793175697327,
0.1748945266008377,
-0.8090561628341675,
-1.3770503997802734,
-0.9753589034080505,
0.4046691954135895,
-0.3449525237083435,
-0.11787405610084534,
0.46743932366371155,
0.15297254920005798,
0.4805432856082916,
-0.5730454921722412,
-0.1470787227153778,
0.3642956614494324,
-0.3476594388484955,
-0.11615658551454544,
0.22289949655532837,
0.42126038670539856,
-0.08400367200374603,
0.7522590756416321,
-0.07087884843349457,
-0.42608729004859924,
-0.37820976972579956,
0.0914832353591919,
0.2967939078807831,
0.3055056929588318,
-0.5358355045318604,
-0.19491317868232727,
-0.5499100685119629,
0.02960200048983097,
0.42196062207221985,
-0.17769941687583923,
-0.45303359627723694,
0.3040248453617096,
-0.05670063942670822,
0.3443996012210846,
-0.061326123774051666,
0.40266677737236023,
0.24060042202472687,
1.386519432067871,
0.6817700862884521,
0.4086450934410095,
0.5591846108436584,
-0.23473720252513885,
0.29717952013015747,
0.05742998421192169,
0.4860561192035675,
-0.3820171058177948,
-0.18860629200935364,
-0.38364773988723755,
0.04118496552109718,
-0.5892415642738342,
-1.0751159191131592,
0.5705640316009521,
-0.2528419494628906,
0.5209747552871704,
0.01707644760608673,
-0.8006725311279297,
0.10425399243831635,
-0.809490978717804,
-1.1041629314422607,
0.8532834649085999,
-0.15475179255008698,
-0.46931326389312744,
0.7970904111862183,
0.0008437321521341801,
0.281782865524292,
-0.6662693023681641,
-0.29424503445625305,
-0.6999377608299255,
0.16842733323574066,
0.526823878288269,
0.3543076515197754,
0.2842290699481964,
-0.45996415615081787,
-0.02260730043053627,
-0.500350296497345,
0.38528499007225037,
-0.47181156277656555,
0.577653169631958,
-0.4480987787246704,
-0.31866464018821716,
0.3314352035522461,
-0.10012473165988922,
-0.25943735241889954,
-0.354716956615448,
0.21096254885196686,
0.0176167581230402,
-0.01856340281665325,
0.023032953962683678,
-0.1882951557636261,
0.7796761393547058,
-0.17777763307094574,
-0.6354435086250305,
0.17554228007793427,
1.3229023218154907,
-0.07930377870798111,
0.10396381467580795,
0.42453181743621826,
-0.4239695370197296,
-0.10361818224191666,
-0.012225396931171417,
1.3345972299575806,
-0.8394510746002197,
-0.22525538504123688,
-0.04528231918811798,
-0.16155895590782166,
0.3639938235282898,
1.0265558958053589,
-0.3224785327911377,
0.34394264221191406,
-0.5437716841697693,
-0.01619090884923935,
0.6500557661056519,
0.21436014771461487,
0.2001168578863144,
-0.42268452048301697,
-0.3700543940067291,
-0.8288378715515137,
0.7999299168586731,
-0.4500022828578949,
0.5110177397727966,
0.2749797999858856,
0.15196608006954193,
-0.034668926149606705,
0.7328602075576782,
0.307595819234848,
-0.06625805050134659,
-0.055859632790088654,
0.41641664505004883,
0.22917334735393524,
0.39779841899871826,
-0.6711289882659912,
0.4527123272418976,
-0.7709629535675049,
1.0192712545394897,
-0.29622992873191833,
-0.09348873794078827,
0.2788015604019165,
0.3514479696750641,
0.833638608455658,
-0.7884069681167603,
0.3265009820461273,
0.43503129482269287,
-0.1635942906141281,
0.6036640405654907,
-0.3050130307674408,
-0.858982503414154,
-0.46240684390068054,
-0.6800984144210815,
-0.9829462766647339,
0.4321421980857849,
0.039491452276706696,
-0.3031264841556549,
-0.42590323090553284,
-1.005960464477539,
0.19427913427352905,
0.13078893721103668,
0.23133036494255066,
0.9046679735183716,
0.12261172384023666,
0.29914119839668274,
0.2438971847295761,
-0.07343827188014984,
-0.6199200749397278,
0.11630173027515411,
-0.07319004833698273,
-0.32984301447868347,
0.1527649462223053,
-0.174193874001503,
-0.4827579855918884,
-0.8740243315696716,
0.04146772250533104,
-0.1533559262752533,
-0.34201881289482117,
-0.7644081711769104,
0.6086121797561646,
0.18323779106140137,
-0.2663426697254181,
-0.32975736260414124,
-0.08215401321649551,
0.1650509089231491,
0.25716349482536316,
0.5698816180229187,
0.6570903658866882,
-0.1993652731180191,
0.29815348982810974,
1.0106916427612305,
-0.8028131723403931,
-0.6383355259895325,
0.6043704152107239,
-0.6057460904121399,
-0.3003464639186859,
0.4286576509475708,
0.05111045762896538,
-0.21162791550159454,
-0.09520652145147324,
-0.7905893921852112,
-0.2955740690231323,
0.18114137649536133,
0.14321111142635345,
-0.1772920787334442,
-0.12244933098554611,
-0.362374484539032,
0.4909517467021942,
0.8231515884399414,
0.18995384871959686,
0.44911202788352966,
0.5617797374725342,
-0.7130222916603088,
-0.1284501999616623,
-0.32766756415367126,
1.1681288480758667,
0.04211902990937233,
-0.8981094360351562,
-0.4207901954650879,
0.21342147886753082,
-0.425244003534317,
-0.1650978922843933,
0.8658958673477173,
-0.6787416934967041,
0.16456389427185059,
-0.2506314814090729,
0.4180954396724701,
0.6478028893470764,
0.5811852216720581,
-0.33420082926750183,
0.038706663995981216,
0.09493614733219147,
-0.8633556365966797,
-0.13748541474342346,
-0.5849882364273071,
0.1208648756146431,
0.3108254075050354,
-0.14494602382183075,
0.218043714761734,
0.24625007808208466,
-0.5235313177108765,
-0.661703884601593,
-0.8558761477470398,
-0.09986480325460434,
-1.001434087753296,
-0.4000352621078491,
-0.9116409420967102,
0.10203611850738525,
-0.29175594449043274,
0.41750821471214294,
-0.24544577300548553,
0.06308664381504059,
-0.2976037263870239,
0.32503095269203186,
0.22531519830226898,
0.7499365210533142,
-0.053123828023672104,
-0.7160459756851196,
-0.5045371651649475,
-0.4940461814403534,
-0.8056908845901489,
-0.18720145523548126,
0.024176429957151413,
-0.6761665344238281,
0.011893470771610737,
-0.08093380928039551,
0.13064350187778473,
0.3178907036781311,
-0.42283567786216736,
-0.6794923543930054,
0.34353014826774597,
0.21685653924942017,
-0.80462646484375,
0.41665101051330566,
0.0962226539850235,
0.3045823872089386,
0.4887537360191345,
0.6932136416435242,
-0.1519961804151535,
0.2486216127872467,
-0.9617356061935425,
0.17813241481781006,
0.08685370534658432,
0.11623840034008026,
0.1622745394706726,
-0.3707718551158905,
0.1107538565993309,
0.07002752274274826,
-0.6785814762115479,
0.5684635639190674,
-0.5909708142280579,
-0.569492757320404,
-0.43258360028266907,
0.07775824517011642,
0.6158517599105835,
0.33092981576919556,
-0.4141395092010498,
0.6939898729324341,
-0.3167397379875183,
0.32866719365119934,
0.19617608189582825,
0.17667937278747559,
-0.28597211837768555,
-0.20860037207603455,
0.278971791267395,
-0.43650731444358826,
-0.45804640650749207,
0.24759367108345032,
-0.3685019314289093,
0.6261916160583496,
0.016925165429711342,
-0.20611216127872467,
-0.17349793016910553,
-0.012507245875895023,
-0.9488120675086975,
0.28816118836402893,
0.07904032617807388,
-0.3780232071876526,
0.31506937742233276,
-0.5332558751106262,
-0.7781670689582825,
0.07931719720363617,
-0.4945265054702759,
-0.49367251992225647,
-0.3045978546142578,
0.015412230044603348,
-0.36754080653190613,
0.3647823631763458,
-0.3761703670024872,
0.14866161346435547,
0.14792481064796448,
0.15939243137836456,
-0.027167269960045815,
-0.6664138436317444,
0.3169495165348053,
0.23647569119930267,
-0.8968461751937866,
-0.14443430304527283,
-0.6519685983657837,
0.8990851640701294,
-0.24756230413913727,
-0.09789492934942245,
0.1527242362499237,
0.290109783411026,
0.2610337734222412,
0.021479200571775436,
-0.5745479464530945,
-0.24357883632183075,
0.11356077343225479,
-0.16889230906963348,
-0.13174986839294434,
-0.6690603494644165,
-1.3478479385375977,
0.23661646246910095,
-0.09356768429279327,
-0.7845315337181091,
0.48089414834976196,
0.6116661429405212,
-0.2319810390472412,
-0.17799490690231323,
-0.30032795667648315,
0.876959502696991,
-0.08595462143421173,
-0.07031721621751785,
0.6402281522750854,
0.5549041628837585,
-0.04799167439341545,
-0.019141757860779762,
-0.08606909215450287,
-0.058071378618478775,
-0.43353337049484253,
0.6160632967948914,
0.7270002365112305,
0.5334731340408325,
0.11942276358604431,
0.2743505537509918,
0.3725922405719757,
0.3254992961883545,
0.45451757311820984,
-0.3249500095844269,
0.19027158617973328,
0.6666046977043152,
0.021093042567372322,
-0.1144692599773407,
-0.06395627558231354,
-0.2756516635417938,
0.05474387854337692,
-0.4524894654750824,
-0.603431761264801,
-0.05288693681359291,
0.13805840909481049,
0.06445672363042831,
-1.1073979139328003,
0.16197071969509125,
-0.2674773335456848,
-0.010310744866728783,
0.4797358512878418,
-0.2987106144428253,
-0.376799613237381,
0.3887990415096283,
0.5638784170150757,
-0.14330817759037018,
-0.002365597290918231,
0.3670009970664978,
-0.40530797839164734,
1.055867075920105,
0.7864497900009155,
0.31172817945480347,
0.9025381207466125,
0.6186074614524841,
0.2355823665857315,
-1.0259885787963867,
0.40150412917137146,
0.6416513919830322,
-0.5298579335212708,
0.5633746981620789,
0.4587603211402893,
-0.3629964292049408,
-0.28591448068618774,
-0.20478029549121857,
0.17476291954517365,
-0.7600604295730591,
-0.20031294226646423,
0.4577632248401642,
-0.1226208433508873,
-0.24237199127674103,
0.8771260380744934,
-0.32532864809036255,
0.4613732397556305,
0.5429507493972778,
0.20362518727779388,
-0.0520508736371994,
0.645021378993988,
1.4915857315063477,
0.06458092480897903,
0.21767356991767883,
-0.013819114305078983,
-0.8918912410736084,
0.22654251754283905,
0.5438023209571838,
-0.7184967398643494,
0.2768062949180603,
-0.4758663475513458,
-0.11954271793365479,
-0.06418893486261368,
0.04124454781413078,
-0.06392744928598404,
-0.18488799035549164,
0.3756530284881592,
0.25830504298210144,
-0.41454237699508667,
-0.4071236252784729,
1.576568841934204,
0.702828049659729,
-0.9439703822135925,
-0.7777937054634094,
-0.005503300577402115,
-0.4497692883014679,
-0.3151940107345581,
-0.8825095295906067,
0.36876386404037476,
-0.5170747637748718,
-0.6765170097351074,
-0.156162291765213,
-0.3434229791164398,
-0.3586064577102661,
-0.6861921548843384,
0.6975205540657043,
-0.9865214824676514,
0.7180806994438171,
0.5686891674995422,
0.09760009497404099,
0.2884451150894165,
-0.6556058526039124,
-0.19147910177707672,
-0.07681583613157272,
0.935685932636261,
0.09330614656209946,
0.12749753892421722,
0.4738992154598236,
0.5594788789749146,
-0.7605504393577576,
0.11116843670606613,
0.7495327591896057,
-0.6607605218887329,
0.7570263743400574,
-0.3048121929168701,
0.09693092107772827,
0.5182237029075623,
0.0734468400478363,
0.3881213366985321,
-0.3227856159210205,
0.12053166329860687,
-0.591401994228363,
-0.41094276309013367,
-0.6760404109954834,
-0.4054199457168579,
0.2125096619129181,
-0.5077513456344604,
0.03281104564666748,
-0.047249168157577515,
0.008736096322536469,
0.3979775607585907,
-0.8373798727989197,
4.223237991333008,
0.5806797742843628,
0.5417717695236206,
0.025597644969820976,
0.5350155234336853,
1.3035153150558472,
-0.19726049900054932,
0.06429405510425568,
0.16416361927986145,
-0.7791915535926819,
-0.5377269387245178,
0.22209805250167847,
-0.2374495267868042,
-0.24778664112091064,
-0.223943829536438,
0.9436802864074707,
-0.1859109103679657,
-0.03403124958276749,
-0.33927321434020996,
-1.0218316316604614,
-0.40461236238479614,
-0.25145795941352844,
0.3277488052845001,
-0.24461883306503296,
0.6229717135429382,
-0.054986923933029175,
0.2029116302728653,
-1.1840654611587524,
-0.7797272205352783,
-0.7765625715255737,
-0.5119084715843201,
-0.49009937047958374,
0.033828891813755035,
0.1558627337217331,
-1.0887374877929688,
-0.007536234799772501,
0.21892492473125458,
-0.29528310894966125,
0.00044242985313758254,
-0.2902476191520691,
-0.3676595985889435,
-0.2636335790157318,
0.2509697377681732,
-0.6860625743865967,
0.014640776440501213,
0.7835068702697754,
-0.07160623371601105,
0.9898496270179749,
0.7300778031349182,
-0.34126198291778564,
0.6603384613990784,
0.23761411011219025,
0.7215780019760132,
-0.477810800075531,
-0.6289823651313782,
0.2147996425628662,
-0.3001372814178467,
-0.21822991967201233,
0.40553799271583557,
0.28615301847457886,
0.20714177191257477,
-0.11314182728528976,
-0.09779758006334305,
-0.04653867706656456,
0.30133289098739624,
0.6488863229751587,
0.12490236014127731,
0.18820714950561523,
-0.2385098934173584,
0.04172521457076073,
0.09975379705429077,
-0.8606951236724854,
-0.6193758249282837,
0.29729828238487244,
-0.06404314190149307,
0.45273497700691223,
0.21323144435882568,
0.8486090898513794,
0.5412858128547668,
0.3184175491333008,
-0.6030170917510986,
0.18172237277030945,
-0.30623671412467957,
-0.03987864404916763,
0.2516297996044159,
0.8670737743377686,
-0.45629560947418213,
-0.4287715554237366,
-0.4899914860725403,
0.41498854756355286,
0.1366182565689087,
1.3270550966262817,
0.09513192623853683,
0.07121986895799637,
-0.9399065971374512
] |
Chern-Simons term in the 4-dimensional SU(2) Higgs Model
|
Using Seiberg's definition for the geometric charge in SU(2) lattice gauge theory, we have managed to apply it also to the Chern-Simons term. We checked the periodic structure and determined the Chern-Simons density on small lattices $L^4$ and $L^3 \times 2,\, 4$ with $L=4,\, 6,\mbox{ and }8$ near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature.
|
F. Karsch, M. L. Laursen, T. Neuhaus and B. Plache
|
hep-lat
|
September
| 1,992 |
https://arxiv.org/abs/hep-lat/9209027
|
hep-lat/9210001
|
[
0.44759753346443176,
-0.020190561190247536,
0.01742211915552616,
-0.09402589499950409,
0.4604852497577667,
-0.17642366886138916,
-0.18938371539115906,
-0.09644631296396255,
-0.6554436087608337,
1.517307162284851,
1.0449292659759521,
0.02791578136384487,
0.05731624364852905,
-0.71775221824646,
-0.21558013558387756,
0.40345001220703125,
-0.481929749250412,
-0.9231752157211304,
-0.7098485827445984,
-0.0439768023788929,
0.11335206031799316,
0.06934753805398941,
-1.4779726266860962,
-0.6289740800857544,
-0.39618614315986633,
1.1267606019973755,
0.5555883646011353,
0.13570748269557953,
1.430424690246582,
0.9590662121772766,
1.1468617916107178,
-0.12126650661230087,
0.14625664055347443,
-0.40971359610557556,
-0.32955119013786316,
-0.4519009590148926,
0.562017560005188,
-0.23234713077545166,
0.6069353222846985,
-0.31643906235694885,
0.8497465252876282,
-0.1749999225139618,
0.2721588909626007,
-0.6022469997406006,
-0.8095672130584717,
-0.4645581841468811,
0.01733110472559929,
-0.03151737526059151,
0.545602023601532,
-1.3841382265090942,
0.11085456609725952,
0.05542580783367157,
0.3341425061225891,
-0.9138389825820923,
-0.8360191583633423,
-0.5589165091514587,
0.7663848400115967,
0.06753648817539215,
-1.0522923469543457,
-0.01711239106953144,
1.0307302474975586,
0.5475441217422485,
0.3013467490673065,
-1.472252607345581,
0.7209054231643677,
0.6953936219215393,
-0.06172609329223633,
-0.25319018959999084,
-0.0768333226442337,
-1.0001144409179688,
-0.6041088700294495,
-0.7848228216171265,
-0.32284262776374817,
0.06049785763025284,
0.11944830417633057,
0.7461380958557129,
-0.46972280740737915,
-0.43094682693481445,
-1.1396989822387695,
-0.27880463004112244,
-0.1251988261938095,
0.030497973784804344,
-0.7202625274658203,
0.5085852146148682,
-0.008847260847687721,
0.1879863291978836,
0.4223646819591522,
0.7421807050704956,
0.44568872451782227,
0.18630509078502655,
0.056858208030462265,
0.48603105545043945,
0.40608087182044983,
-0.42388397455215454,
0.44911396503448486,
1.2086124420166016,
-0.079747773706913,
1.0133440494537354,
0.382209450006485,
0.1972985565662384,
-0.07725635915994644,
1.7662715911865234,
-0.549817681312561,
0.873826265335083,
-0.34691131114959717,
0.31415870785713196,
0.28394055366516113,
0.07068032026290894,
-0.26677146553993225,
-0.6447891592979431,
0.1800106167793274,
-0.11615663766860962,
0.4440001845359802,
0.4883434772491455,
-0.08864286541938782,
0.6954335570335388,
-0.45388704538345337,
-0.041628628969192505,
-0.8985912203788757,
-0.1979447454214096,
0.08060865104198456,
0.1554759442806244,
0.7696738243103027,
0.19632212817668915,
0.2653346061706543,
-0.9544039964675903,
0.22437933087348938,
0.7312366366386414,
-0.7038442492485046,
-0.23350021243095398,
0.20081748068332672,
-0.17432139813899994,
-0.2751443386077881,
0.20716333389282227,
-0.4687238335609436,
-0.19949032366275787,
-0.19070890545845032,
0.25556766986846924,
-0.4776630103588104,
-0.6967588663101196,
0.5201785564422607,
-0.4659934639930725,
-0.11806449294090271,
1.1335054636001587,
-0.2300359308719635,
0.49647411704063416,
0.12146464735269547,
-0.037514496594667435,
-0.3731832802295685,
0.21825365722179413,
-0.48905596137046814,
-0.45997169613838196,
-0.44172900915145874,
0.6890038847923279,
0.22101524472236633,
0.19299127161502838,
-1.0716153383255005,
0.6593393683433533,
-1.0367730855941772,
-0.8986866474151611,
0.4615151882171631,
-0.015036402270197868,
0.12273705005645752,
1.3605432510375977,
-0.5951917171478271,
0.41124510765075684,
-0.8446471095085144,
0.08327082544565201,
-0.16130420565605164,
-0.2295774519443512,
0.2834155261516571,
-0.38357892632484436,
-0.14427554607391357,
0.36213046312332153,
0.7916164994239807,
0.28474000096321106,
0.29195740818977356,
-0.5853033065795898,
0.5337216854095459,
0.5410786271095276,
-0.26827818155288696,
-0.8469776511192322,
1.4924112558364868,
0.9633049964904785,
-0.6581754684448242,
-0.343847393989563,
-0.45881223678588867,
-0.47863325476646423,
-0.003450651653110981,
0.284766286611557,
-0.682138979434967,
0.8799697160720825,
-0.8211675882339478,
0.5731828808784485,
-0.4759148955345154,
0.0003278111689724028,
-0.5838112831115723,
0.39911121129989624,
-0.7298638820648193,
-0.7561900615692139,
-0.035966575145721436,
0.09471332281827927,
-0.1390514075756073,
0.15518711507320404,
-1.2336984872817993,
0.3237968683242798,
0.06701190769672394,
0.05390545353293419,
-0.46848466992378235,
-0.23796658217906952,
0.4210461974143982,
-0.3328191041946411,
0.5395328998565674,
-0.42527395486831665,
0.08841884136199951,
0.23209455609321594,
0.08651525527238846,
0.36629951000213623,
0.6355752944946289,
-0.03468766808509827,
1.1568539142608643,
0.7252886891365051,
-0.34109580516815186,
0.8435428142547607,
-0.4651435911655426,
0.18135784566402435,
-0.12436491250991821,
1.171341896057129,
0.1860811710357666,
0.6337185502052307,
0.7759788632392883,
0.5074337124824524,
0.3692876398563385,
0.09290903806686401,
0.7796727418899536,
0.680252730846405,
0.6146239042282104,
0.9754409193992615,
-0.16135120391845703,
0.0523420050740242,
0.20152747631072998,
0.16187438368797302,
0.5291150808334351,
-0.04264917969703674,
-0.026833904907107353,
0.7794457077980042,
0.20729835331439972,
0.9785459637641907,
-0.5824910402297974,
0.5588803887367249,
-0.6894939541816711,
0.7728732228279114,
-0.1063644140958786,
-0.4347180724143982,
-0.7761776447296143,
0.21254953742027283,
-0.0033230276312679052,
0.8492059111595154,
0.2834198474884033,
-0.76628577709198,
-0.01608552783727646,
0.5232014060020447,
0.44709065556526184,
-0.7093275785446167,
-0.7157279253005981,
0.6399929523468018,
-0.1534898579120636,
0.34336909651756287,
0.23212681710720062,
-0.40044304728507996,
-1.5624178647994995,
-0.2688870131969452,
-0.7361752986907959,
0.0643056109547615,
0.16101425886154175,
-0.09743176400661469,
0.4838773012161255,
-0.4493805468082428,
0.5175933837890625,
-0.048277582973241806,
-0.0426550917327404,
-0.01597231812775135,
-0.022235414013266563,
0.13119788467884064,
0.29742899537086487,
-0.28199294209480286,
-0.7082629799842834,
-0.04418616369366646,
-0.41766592860221863,
0.23918205499649048,
-0.7018014788627625,
-0.09813408553600311,
0.6111018061637878,
-0.15163643658161163,
0.4431726932525635,
-0.19359390437602997,
-0.6080430746078491,
-0.3218928873538971,
0.12451682239770889,
-0.6293416023254395,
0.06339091807603836,
0.29796379804611206,
0.8139731287956238,
0.21941931545734406,
-0.6101201772689819,
1.0028481483459473,
0.5382411479949951,
-0.09912776947021484,
0.5087474584579468,
-0.16475382447242737,
-0.29707756638526917,
-0.6613758206367493,
0.31371739506721497,
-0.080952949821949,
-0.18548138439655304,
1.1106494665145874,
1.0059361457824707,
-0.0946207195520401,
0.4438328444957733,
-0.34651100635528564,
-0.3514416515827179,
-0.32231488823890686,
0.15998244285583496,
-0.5250222086906433,
0.3292410969734192,
1.1315388679504395,
0.3339954614639282,
-1.302496075630188,
0.6935234665870667,
-0.7844664454460144,
-0.32099899649620056,
-0.27841538190841675,
-0.9544004201889038,
0.3575096130371094,
0.08972888439893723,
-0.012858680449426174,
-0.3165503740310669,
-0.5400822162628174,
-0.0008684638305567205,
0.397574782371521,
0.5997889041900635,
-0.3249559998512268,
0.01098819449543953,
0.36685633659362793,
0.6457192897796631,
0.1455293744802475,
0.25139179825782776,
-0.21228834986686707,
-0.06780356168746948,
0.481163889169693,
-0.147219717502594,
0.0777256041765213,
0.18714328110218048,
0.1724686175584793,
0.1658787876367569,
-0.17150060832500458,
0.19023087620735168,
-0.6943022012710571,
-0.7992782592773438,
-0.2520274817943573,
-0.1919146329164505,
-0.14748243987560272,
-0.33574196696281433,
0.02457251027226448,
-0.679168164730072,
-0.47563475370407104,
0.05676586553454399,
-0.2521238327026367,
0.898613691329956,
-0.9038628339767456,
0.35201284289360046,
0.351022869348526,
-0.017050698399543762,
0.08115679025650024,
-0.12295658886432648,
0.2256263792514801,
-0.07432134449481964,
0.2897053360939026,
0.05915409326553345,
-0.15477339923381805,
-1.036105990409851,
0.2195153683423996,
0.7810573577880859,
0.6113482117652893,
0.8621460795402527,
-0.0034476593136787415,
0.06228245794773102,
-0.037017855793237686,
0.04843548685312271,
-0.39499661326408386,
-0.30691438913345337,
-0.6771403551101685,
-0.5435900092124939,
-0.5591104030609131,
-0.4104216992855072,
0.006577781867235899,
0.5026283264160156,
0.9376862049102783,
0.9667269587516785,
0.21169038116931915,
0.43142810463905334,
0.32108667492866516,
0.1191190630197525,
0.9632079005241394,
-0.13967129588127136,
-0.1809595227241516,
-1.2270399332046509,
0.7528440952301025,
0.1849765032529831,
0.0010579789523035288,
0.06865020841360092,
-0.7807896137237549,
0.6435607075691223,
-0.48531439900398254,
0.9785267114639282,
0.4946168065071106,
-0.8496435284614563,
0.47818848490715027,
-0.41375797986984253,
0.3588307499885559,
-0.5481734275817871,
-0.40797409415245056,
0.7725863456726074,
0.7914628982543945,
-0.25339508056640625,
-0.6758804321289062,
-0.6908740997314453,
-0.7212968468666077,
0.6051174998283386,
0.41641974449157715,
-1.154228925704956,
-1.1558574438095093,
-0.25934815406799316,
-0.5860899686813354,
-0.48535028100013733,
0.32934945821762085,
1.1562026739120483,
-0.5295239686965942,
0.16216890513896942,
-0.15923404693603516,
-0.4487003982067108,
0.06346462666988373,
0.009556703269481659,
-1.0365676879882812,
0.47699376940727234,
0.11010776460170746,
-0.5646716356277466,
0.7775992751121521,
-0.16940155625343323,
-0.5028755068778992,
-0.36132776737213135,
-0.36263591051101685,
0.19979719817638397,
-0.41161492466926575,
-0.4993469715118408,
-0.36052432656288147,
0.01610873080790043,
-0.46797865629196167,
0.727962076663971,
-0.3153877258300781,
-0.026018505915999413,
-0.030152345076203346,
-0.007532445248216391,
-0.5730148553848267,
0.178518146276474,
0.05398013815283775,
-0.08195815235376358,
0.3725835680961609,
0.43076106905937195,
0.20193354785442352,
0.5072598457336426,
0.5967715978622437,
0.039520908147096634,
0.5415051579475403,
0.4379171133041382,
-0.5243639945983887,
0.2008194923400879,
-0.48227062821388245,
-0.09476399421691895,
-0.6466454863548279,
-0.8272677063941956,
0.40122681856155396,
-0.4566519856452942,
0.41580384969711304,
-0.41175952553749084,
-0.2893669903278351,
-0.7457162737846375,
-0.33758440613746643,
-0.6819639205932617,
0.37158456444740295,
-0.5916178822517395,
-0.006943614222109318,
0.6733507513999939,
-0.6964309811592102,
-0.31244713068008423,
0.2327236384153366,
0.029599111527204514,
0.286171555519104,
-0.18842735886573792,
0.9597867131233215,
-0.27479124069213867,
0.5790373086929321,
-0.986451268196106,
0.14212346076965332,
-0.22256982326507568,
-0.2615249752998352,
-0.825354278087616,
-0.4832286834716797,
-0.09433799237012863,
0.3807750940322876,
-0.24780899286270142,
-0.7861253619194031,
-0.0030278002377599478,
0.27314212918281555,
0.35557013750076294,
-0.07725361734628677,
-0.17792776226997375,
-0.26196789741516113,
-0.03549661487340927,
0.8659180998802185,
-0.09571919590234756,
-0.9456274509429932,
0.021417854353785515,
0.7345958948135376,
0.12119433283805847,
0.5877313017845154,
-0.07165328413248062,
-0.21135447919368744,
0.44690707325935364,
-1.1288543939590454,
-0.04911431670188904,
-1.2864218950271606,
-0.7216287851333618,
-0.09484339505434036,
-0.15038444101810455,
0.07995831221342087,
0.41502758860588074,
0.34464842081069946,
-0.43556150794029236,
-0.057837020605802536,
-0.28736522793769836,
0.33188921213150024,
-0.527967631816864,
0.15244784951210022,
-0.4294552206993103,
-0.2991301119327545,
-0.4213535487651825,
0.6251431107521057,
0.1385672241449356,
0.23231486976146698,
0.3223569393157959,
0.048273149877786636,
-0.4388900399208069,
0.647436261177063,
0.4323151111602783,
-0.4167349636554718,
-0.2797473669052124,
0.5721310377120972,
0.17304426431655884,
-0.15233658254146576,
-0.4105212688446045,
0.43598729372024536,
-0.6571609973907471,
0.6101900339126587,
-0.4368298053741455,
0.2754039168357849,
0.07085789740085602,
-0.133029043674469,
0.9338544011116028,
-0.6540298461914062,
0.25434762239456177,
0.3741389513015747,
-0.16358958184719086,
0.8477674722671509,
-0.058820754289627075,
-0.849012553691864,
-0.2486342489719391,
-0.25161856412887573,
-0.7439568638801575,
0.6602049469947815,
-0.019436059519648552,
-0.5063536763191223,
-1.0833320617675781,
-0.7336658835411072,
0.7851153016090393,
-0.1816157102584839,
-0.006005371455103159,
0.6140487194061279,
0.39752721786499023,
0.10436802357435226,
-0.44278839230537415,
-0.35955023765563965,
-0.7807512283325195,
0.08552853018045425,
0.6071441173553467,
-0.36367854475975037,
-0.4142782390117645,
-0.08308303356170654,
-0.38439518213272095,
-1.118208646774292,
-0.43193531036376953,
0.6912306547164917,
0.05833115801215172,
-0.04905373230576515,
0.4495398700237274,
-0.43484723567962646,
-0.4210664629936218,
-0.5905112028121948,
-0.14236369729042053,
-0.4304776191711426,
-0.22563080489635468,
0.35175275802612305,
0.49598023295402527,
-0.21962624788284302,
-0.3722582757472992,
0.40130484104156494,
-0.7696702480316162,
-0.21528784930706024,
0.6953942775726318,
-0.386596143245697,
-0.18606337904930115,
0.4469834268093109,
-0.28944823145866394,
-1.0754231214523315,
-0.6461701989173889,
-0.7399133443832397,
-0.49760615825653076,
0.5135853886604309,
-0.506015956401825,
0.40713968873023987,
-0.24499860405921936,
0.0800238847732544,
0.4277576208114624,
0.6678398251533508,
-0.22795754671096802,
-0.16848410665988922,
0.5202879309654236,
-0.2813020348548889,
-0.2113122045993805,
0.4239073693752289,
1.0880627632141113,
-0.2951503098011017,
-0.8283501863479614,
-0.21180488169193268,
-0.5277220010757446,
0.30651819705963135,
-0.32167789340019226,
0.13310353457927704,
-0.9719034433364868,
0.3697556257247925,
0.7246570587158203,
0.7038474082946777,
0.17845997214317322,
0.4546866714954376,
0.2544924318790436,
-0.044200994074344635,
-0.7393530011177063,
-0.6736550331115723,
-0.27164122462272644,
0.5201640725135803,
-0.0015892545925453305,
1.2206535339355469,
-0.48143270611763,
0.06147483363747597,
0.0494261160492897,
-0.43508610129356384,
-0.2581568658351898,
-1.4247915744781494,
-0.19345876574516296,
-1.2726484537124634,
-0.897564709186554,
-0.7313393950462341,
-0.7569534778594971,
0.20893289148807526,
0.03483891114592552,
-0.27822259068489075,
0.4163561463356018,
0.12433265894651413,
-0.18073323369026184,
0.12341271340847015,
1.0497961044311523,
-0.6513662934303284,
-0.8526796698570251,
-0.774920642375946,
0.19386088848114014,
-0.07033640146255493,
-1.4238150119781494,
-0.352870911359787,
0.22634315490722656,
-0.11126687377691269,
0.3462750017642975,
-0.2609420716762543,
0.9539281129837036,
-0.568183183670044,
-0.36150822043418884,
0.1644858717918396,
-0.33384570479393005,
-0.6103845834732056,
0.34526336193084717,
-0.5247832536697388,
0.5699536800384521,
-0.196555957198143,
0.4014433026313782,
-0.20662760734558105,
-0.24097999930381775,
-0.5714533925056458,
-0.06272660195827484,
-0.16076306998729706,
0.20535129308700562,
-0.16193222999572754,
-1.1212387084960938,
0.6519203186035156,
-0.08705467730760574,
-1.1038755178451538,
0.42757004499435425,
-0.43501436710357666,
0.23854154348373413,
-0.42746567726135254,
0.08658479899168015,
0.08530567586421967,
0.757514238357544,
-0.1513814479112625,
0.9164465665817261,
-0.2661403715610504,
0.16774605214595795,
-0.3971439599990845,
0.14585377275943756,
-0.09260425716638565,
0.5619850754737854,
-0.1607903242111206,
-0.5900195240974426,
0.29535120725631714,
-0.3544234335422516,
-0.1106920912861824,
-0.19662077724933624,
-0.5054362416267395,
0.1611308455467224,
-0.33082833886146545,
0.05640764161944389,
-0.15888622403144836,
0.7788958549499512,
0.4633886218070984,
-0.42241212725639343,
-0.18714642524719238,
-0.5639939308166504,
-0.6847094893455505,
0.14997194707393646,
-0.6622163653373718,
-0.8611120581626892,
0.08645903319120407,
-0.2996162176132202,
0.12124960869550705,
0.6104360222816467,
-0.07165554165840149,
0.09714622795581818,
0.3147842586040497,
0.8473530411720276,
0.41824355721473694,
0.2505682706832886,
-0.2524263262748718,
0.3840699791908264,
-0.4573243260383606,
-0.7198252081871033,
-0.25582462549209595,
0.7144619822502136,
-0.8620612025260925,
-0.7777870893478394,
-0.422970712184906,
0.08623757213354111,
0.0683932900428772,
-0.35568416118621826,
0.08551499992609024,
-0.3364093601703644,
0.09155816584825516,
-0.42444944381713867,
-0.6249645352363586,
0.20927098393440247,
-0.6616685390472412,
0.33879759907722473,
-0.15573255717754364,
-0.5618278980255127,
0.6463913917541504,
-0.15800701081752777,
0.6649650931358337,
0.36703920364379883,
-0.2613522708415985,
0.6879837512969971,
-0.29660356044769287,
-0.6390530467033386,
0.9754917025566101,
0.33427509665489197,
0.6597254872322083,
0.3062703609466553,
-0.09668813645839691,
0.9185832738876343,
0.5809934139251709,
0.3276159167289734,
0.7257987856864929,
0.31030312180519104,
-0.4033149480819702,
0.04903557151556015,
0.4147756099700928,
0.09938208013772964,
0.16737452149391174,
0.3106781244277954,
0.771970272064209,
0.5923396944999695,
-0.27664557099342346,
0.09304262697696686,
-0.14433406293392181,
0.6886071562767029,
0.49140995740890503,
0.16217531263828278,
-0.002807575510814786,
0.02184586226940155,
0.09304783493280411,
0.7948636412620544,
-0.9013094902038574,
-0.37929725646972656,
-0.7629494071006775,
0.6060248613357544,
0.41630318760871887,
0.0277461688965559,
-0.5444255471229553,
0.15556152164936066,
0.33283674716949463,
0.2683965265750885,
-0.24659883975982666,
1.1435805559158325,
0.6399847865104675,
0.06456982344388962,
0.4169829189777374,
0.8126781582832336,
0.6638314723968506,
0.4133799076080322,
0.12157362699508667,
-1.0833611488342285,
-0.562749445438385,
0.587027907371521,
-1.1115901470184326,
0.27445659041404724,
-0.28767845034599304,
-0.5197616219520569,
-0.33330294489860535,
-0.8082774877548218,
-0.03400862216949463,
-0.17269104719161987,
0.5122779011726379,
0.3367631137371063,
0.4486702084541321,
-0.5457236766815186,
0.6499432921409607,
0.19171373546123505,
0.48370280861854553,
0.9325247406959534,
0.16247940063476562,
-0.018784018233418465,
0.9711787104606628,
0.6743845343589783,
0.6565426588058472,
0.5992010831832886,
-0.42102333903312683,
-0.5375488996505737,
0.7369959354400635,
0.13405866920948029,
0.37485289573669434,
0.8028717637062073,
-0.6933855414390564,
-0.250066876411438,
-0.30760160088539124,
-0.0022049087565392256,
-0.4830130636692047,
-0.23397159576416016,
0.23984618484973907,
0.7861566543579102,
0.19823870062828064,
0.21239103376865387,
1.1672228574752808,
0.396817147731781,
-0.40832576155662537,
-0.394086092710495,
0.5035216212272644,
-0.7759295105934143,
0.41767117381095886,
-1.0368976593017578,
0.315997838973999,
0.2642168402671814,
-0.03557802736759186,
-0.34947773814201355,
-0.6477273106575012,
-0.33135396242141724,
-0.6655522584915161,
0.05126029998064041,
-0.5499448776245117,
0.2390654981136322,
0.4755505919456482,
0.15401120483875275,
0.6997305154800415,
-0.9850901365280151,
-0.15991853177547455,
-0.5522387623786926,
0.8965097665786743,
-0.23958727717399597,
0.07750540226697922,
1.079828143119812,
0.6114073395729065,
-1.192415714263916,
0.2989421486854553,
0.44146186113357544,
-0.778376042842865,
0.7277684211730957,
-0.286210298538208,
0.01784471981227398,
0.14543624222278595,
-0.04273449257016182,
0.12672093510627747,
0.02190553955733776,
0.3868093490600586,
-0.546576738357544,
-0.6984607577323914,
-0.2551441490650177,
-0.5484050512313843,
0.517553448677063,
-1.1670323610305786,
0.482082337141037,
0.48016518354415894,
0.5195447206497192,
0.05070312321186066,
-0.1975468248128891,
3.9621262550354004,
1.0227192640304565,
0.6260781288146973,
0.060462795197963715,
1.2152286767959595,
0.8403221368789673,
0.137665256857872,
-0.22528214752674103,
0.5109426975250244,
-0.37705639004707336,
0.004695451352745295,
0.5638889670372009,
-0.27214473485946655,
0.14675922691822052,
-0.31178349256515503,
0.43471837043762207,
-0.38492918014526367,
-0.39777687191963196,
-0.5773035287857056,
-0.6877759099006653,
-0.4722582995891571,
0.19587211310863495,
0.5209543108940125,
0.08119317144155502,
0.2942185699939728,
0.11704257130622864,
0.6827054023742676,
-0.9234762191772461,
-0.6586437225341797,
-0.32422012090682983,
-0.5278229117393494,
-0.7533391714096069,
-0.5847025513648987,
0.44881096482276917,
-0.9265499711036682,
0.2613849937915802,
0.08932621777057648,
-0.5898597240447998,
0.21086792647838593,
0.19689610600471497,
0.48641830682754517,
0.21562792360782623,
0.03277868032455444,
-0.29533201456069946,
-0.7066993117332458,
0.5720167756080627,
-0.015529906377196312,
0.45039594173431396,
0.5514944195747375,
-0.7969642281532288,
0.42146244645118713,
0.0022852506954222918,
0.7530948519706726,
-0.6908696889877319,
-1.299328327178955,
-0.64286208152771,
-0.028696725144982338,
-0.4920225739479065,
0.4246640205383301,
0.42948952317237854,
0.3006773889064789,
0.14664523303508759,
-0.05331161990761757,
0.4117380976676941,
0.09490519016981125,
0.6023810505867004,
0.40624579787254333,
-0.7330449223518372,
-0.20590655505657196,
-0.0737839937210083,
-0.3070450723171234,
0.17528119683265686,
-0.8726406097412109,
-0.18745076656341553,
-0.26811376214027405,
0.33105283975601196,
0.06672137975692749,
1.0389715433120728,
-0.11502408236265182,
0.40509533882141113,
-0.32886165380477905,
-0.24809254705905914,
0.3395252823829651,
0.297507643699646,
0.05046239122748375,
1.1959166526794434,
0.1983068734407425,
-0.10843992978334427,
-0.05793406069278717,
0.5295693278312683,
-0.223169207572937,
0.8480892181396484,
-0.22279399633407593,
-0.21864834427833557,
-1.1138042211532593
] |
Non-uniform measure in 4d simplicial quantum gravity
|
Four-dimensional euclidean quantum gravity has been studied as a discrete model based on dynamical triangulations by Ambjorn and Jurkiewicz and by Agishtein and Migdal. We discuss a particular implementation of a Monte Carlo simulation of simplicial quantum gravity. As an application we introduce a non-uniform measure and examine its effect on simple aspects of the mathematical geometry. We find that the transition region from the hot to the cold phase is shifted and that the criticality of the transition changes.
|
Bernd Bruegmann
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210001
|
hep-lat/9210002
|
[
0.16249291598796844,
-0.23101326823234558,
-0.05896880850195885,
0.24456700682640076,
0.44980812072753906,
-0.23936782777309418,
0.03836708143353462,
-0.3302513062953949,
-0.7386422157287598,
1.151870846748352,
0.656147837638855,
0.029270300641655922,
0.2399480938911438,
-0.4881102740764618,
0.0067752208560705185,
0.42533910274505615,
-0.47658392786979675,
-0.7589009404182434,
-1.175734043121338,
0.19966141879558563,
0.41285333037376404,
0.2040674239397049,
-1.302364468574524,
-0.4095994234085083,
-0.5732505321502686,
1.034304141998291,
0.2783799469470978,
0.2651726007461548,
1.6340763568878174,
1.3076759576797485,
0.9343848824501038,
-0.4505428969860077,
0.034679148346185684,
-0.4169110059738159,
-0.4120253920555115,
-0.26038843393325806,
0.3459566533565521,
-0.21239249408245087,
0.6570298671722412,
-0.15498295426368713,
0.39784273505210876,
-0.06362231075763702,
0.2345685511827469,
-0.34285423159599304,
-0.7689769268035889,
-0.4152717590332031,
0.1227811723947525,
-0.4906429648399353,
0.4157201945781708,
-1.3717007637023926,
0.13924333453178406,
-0.22602994740009308,
0.9180514812469482,
-0.7451092600822449,
-0.605219304561615,
-0.4744742214679718,
1.0049701929092407,
0.1534387767314911,
-0.7629532814025879,
-0.33988070487976074,
0.7595012187957764,
0.5305248498916626,
0.4748978018760681,
-1.2524278163909912,
0.4843597710132599,
0.8614886403083801,
-0.17630521953105927,
-0.06866958737373352,
0.11929784715175629,
-0.9981503486633301,
-0.74003005027771,
-1.0386126041412354,
-0.22819198668003082,
-0.01609116420149803,
-0.17532671988010406,
0.2739618718624115,
-0.5086542367935181,
-0.2912499010562897,
-0.7690207362174988,
-0.7624474167823792,
0.023720936849713326,
0.16846665740013123,
-1.2138291597366333,
0.191434845328331,
-0.0548836775124073,
0.12893891334533691,
0.13863687217235565,
0.5409414768218994,
0.2874995768070221,
0.1260010153055191,
0.05167613923549652,
0.7390606999397278,
0.15882772207260132,
-0.22180142998695374,
0.606323778629303,
1.1679764986038208,
-0.2414407730102539,
0.8184458613395691,
0.196745827794075,
0.1782769113779068,
-0.07726117968559265,
1.4404518604278564,
-0.5577216148376465,
0.774742066860199,
-0.31223782896995544,
0.36088764667510986,
0.02926604449748993,
-0.2669568955898285,
-0.0340178981423378,
-0.6586925983428955,
0.27259570360183716,
0.3885633051395416,
0.4698515832424164,
0.43880167603492737,
-0.012542962096631527,
0.3337026834487915,
-0.5566883683204651,
-0.6267701983451843,
-0.8748438954353333,
-0.13542914390563965,
0.05728617683053017,
0.03876921162009239,
0.8393151164054871,
0.1815410852432251,
0.21304161846637726,
-0.79984050989151,
0.4721132814884186,
0.45645204186439514,
-0.6102883219718933,
0.1732463836669922,
0.01236226037144661,
-0.4381190538406372,
0.038887668401002884,
0.15479676425457,
-0.43144527077674866,
-0.47421401739120483,
-0.5435614585876465,
-0.0023667053319513798,
-0.2508727014064789,
-0.19028982520103455,
0.5498483777046204,
-0.6116472482681274,
0.08281749486923218,
0.8657092452049255,
0.011778479442000389,
0.4560605585575104,
-0.38932812213897705,
0.5200926065444946,
-0.3702404201030731,
0.006391181610524654,
-0.40890103578567505,
-0.200462207198143,
-0.24918429553508759,
0.5163189172744751,
0.09140197932720184,
0.09413963556289673,
-0.9049859642982483,
0.7486562728881836,
-0.6939274668693542,
-0.5621336698532104,
0.5524579286575317,
-0.2366020679473877,
0.16341319680213928,
1.1333873271942139,
-0.9138219356536865,
0.23576301336288452,
-0.10350757837295532,
-0.07185177505016327,
0.06820815801620483,
0.2943846881389618,
0.3244215250015259,
0.14509175717830658,
-0.530694305896759,
0.4787468910217285,
0.9128451347351074,
0.4303530156612396,
0.1838073581457138,
-0.39662110805511475,
0.5902859568595886,
0.4380365014076233,
0.3269141614437103,
-1.1085429191589355,
1.0247451066970825,
1.1674208641052246,
-0.6298091411590576,
-0.0831659659743309,
0.3566738963127136,
-0.10139044374227524,
0.22080329060554504,
-0.3372531533241272,
-0.6574077010154724,
0.45964398980140686,
-1.0893502235412598,
0.844399094581604,
-0.3586004674434662,
0.18412774801254272,
-0.880770742893219,
0.29931530356407166,
-0.16697978973388672,
-0.3510178029537201,
-0.1530168056488037,
0.3821004033088684,
-0.4059416651725769,
0.07477865368127823,
-1.3709453344345093,
0.11542131006717682,
0.2884966731071472,
0.39711692929267883,
-0.46530425548553467,
0.14619100093841553,
0.5250164270401001,
-0.041614919900894165,
0.44979479908943176,
-0.07427853345870972,
-0.11517252027988434,
0.027058016508817673,
0.29518041014671326,
0.6176449656486511,
0.5562332272529602,
0.0019558146595954895,
0.824822187423706,
0.5400734543800354,
-0.4722887873649597,
0.4917445778846741,
-0.5534286499023438,
0.24895238876342773,
-0.012427126988768578,
1.1288539171218872,
-0.06074923649430275,
0.7171692252159119,
0.667506217956543,
0.7168903350830078,
-0.022598763927817345,
0.39185279607772827,
0.6777451634407043,
0.4444715082645416,
0.6571571230888367,
0.9644755721092224,
0.22918707132339478,
-0.2269039899110794,
0.37132227420806885,
-0.06036946550011635,
0.4116007387638092,
-0.09055128693580627,
-0.39820396900177,
0.5205475687980652,
0.4440337121486664,
0.5961729884147644,
-1.047508955001831,
0.5234556794166565,
-0.7971678376197815,
0.7733448147773743,
0.4174959659576416,
-0.1675090491771698,
-0.8450928926467896,
-0.04786507785320282,
-0.14278317987918854,
0.43877583742141724,
0.21245382726192474,
-0.26155129075050354,
-0.009924188256263733,
0.07134725153446198,
0.49756327271461487,
-0.8548563122749329,
-0.5931614637374878,
0.5632305145263672,
-0.3349800705909729,
0.13975024223327637,
0.08482655137777328,
-0.025100314989686012,
-1.1377534866333008,
-0.06939547508955002,
-0.720599353313446,
0.21404634416103363,
-0.22186648845672607,
0.1520305573940277,
0.2601804733276367,
-0.6736190915107727,
0.576718807220459,
0.05338645353913307,
-0.1298866868019104,
-0.09624789655208588,
-0.24315454065799713,
0.2629963159561157,
0.3294830620288849,
-0.16567844152450562,
-0.8704450726509094,
-0.19087748229503632,
-0.40946754813194275,
-0.029893020167946815,
-0.4470869302749634,
-0.12067866325378418,
0.9794399738311768,
-0.32672473788261414,
0.5505277514457703,
0.17332015931606293,
-0.9098819494247437,
-0.9276409149169922,
0.08520972728729248,
-0.7260457873344421,
-0.02651725523173809,
0.12152772396802902,
0.6312748193740845,
0.43466758728027344,
-0.16341105103492737,
1.0920084714889526,
0.4597073197364807,
0.12260694056749344,
0.6880954504013062,
-0.29514825344085693,
-0.1624664068222046,
0.041099753230810165,
0.423384428024292,
0.6185864210128784,
-0.376056432723999,
0.9999087452888489,
0.953876793384552,
-0.43684881925582886,
0.2145618498325348,
0.15001815557479858,
-0.6338388919830322,
-0.025901375338435173,
0.24878279864788055,
-0.930466890335083,
0.2395171970129013,
0.8476287126541138,
0.12536178529262543,
-1.080865740776062,
0.5895443558692932,
-0.8747602105140686,
-0.5668855309486389,
-0.032103512436151505,
-1.1415557861328125,
0.23711760342121124,
-0.31389179825782776,
0.3335035443305969,
-0.6170623302459717,
-0.42865705490112305,
0.5414739847183228,
0.5510688424110413,
0.384874165058136,
0.0018384073628112674,
0.1279376894235611,
0.00013233025674708188,
0.29492804408073425,
0.41172388195991516,
0.03992633521556854,
-0.3939683735370636,
-0.26463383436203003,
0.509270191192627,
-0.22135835886001587,
0.8212674260139465,
0.11743558943271637,
0.05156600847840309,
0.1748041957616806,
-0.08300282806158066,
0.14275753498077393,
-0.6753254532814026,
-1.0121110677719116,
-0.35376858711242676,
-0.2674611508846283,
-0.11930398643016815,
-0.1099298968911171,
-0.6751421689987183,
-1.1942576169967651,
-0.9152886271476746,
0.023026958107948303,
-0.08187415450811386,
1.0599216222763062,
-0.8738515377044678,
0.1870870292186737,
0.30851197242736816,
-0.09674447774887085,
0.2788067162036896,
-0.6258924603462219,
0.18556082248687744,
-0.15931560099124908,
0.4717729687690735,
0.21920721232891083,
-0.2527146637439728,
-0.9108753800392151,
0.14378932118415833,
0.9610073566436768,
0.4755283296108246,
0.9470371603965759,
0.09904230386018753,
-0.459104984998703,
0.5713525414466858,
0.04716598242521286,
-0.007008117623627186,
-0.05807366967201233,
-0.4186413586139679,
-0.49300894141197205,
-0.6679279804229736,
-0.009654552675783634,
-0.15938034653663635,
0.5560579299926758,
0.7872541546821594,
1.0217103958129883,
0.14145807921886444,
0.24733929336071014,
0.4002366364002228,
0.004057622514665127,
1.0556544065475464,
-0.5599373579025269,
-0.22901472449302673,
-0.9925293326377869,
0.6541783213615417,
0.5942341089248657,
0.06759672611951828,
0.04957910627126694,
-0.5042295455932617,
0.23774220049381256,
-0.28138917684555054,
0.6666476726531982,
0.16812705993652344,
-0.7534885406494141,
0.021329259499907494,
-0.12406449764966965,
0.23592467606067657,
-0.4583733379840851,
-0.3209814429283142,
0.7939122915267944,
0.2685244381427765,
-0.12543298304080963,
-0.5152039527893066,
-0.5897696614265442,
-0.478746622800827,
0.6365031003952026,
0.8577165603637695,
-1.353888988494873,
-0.9819366335868835,
-0.06950321048498154,
-0.46561092138290405,
-0.6754472255706787,
0.19101043045520782,
0.8622429966926575,
-0.10763853043317795,
0.43951740860939026,
-0.2765667140483856,
-0.43129962682724,
0.16246581077575684,
0.018340125679969788,
-0.7987099885940552,
0.057560987770557404,
-0.09089954197406769,
0.03623257577419281,
0.3957703411579132,
0.07068837434053421,
-0.6404011249542236,
-0.03139729052782059,
-0.4935844838619232,
-0.19753612577915192,
-0.05501032993197441,
-0.44074878096580505,
-0.4670620262622833,
0.21878449618816376,
-0.4372680187225342,
0.855040431022644,
-0.20320674777030945,
0.008993699215352535,
-0.03406931087374687,
0.16375623643398285,
-0.19043833017349243,
0.813724160194397,
0.39055442810058594,
0.32524412870407104,
0.644956111907959,
0.7244858145713806,
0.658717691898346,
-0.027163583785295486,
0.33892229199409485,
0.1913229376077652,
0.059614866971969604,
0.322149395942688,
-0.5388290882110596,
-0.02755780890583992,
-0.3903798460960388,
-0.397763192653656,
-0.3617463707923889,
-0.9109083414077759,
0.8599234819412231,
-0.607453465461731,
0.5364806652069092,
-0.6356683373451233,
-0.31835758686065674,
-0.5741780996322632,
-0.6528314352035522,
-0.8029018044471741,
0.4594968557357788,
-0.3014228343963623,
-0.0461006723344326,
1.08939790725708,
-0.649429202079773,
0.09880506247282028,
0.10169641673564911,
-0.30065375566482544,
0.14052553474903107,
-0.2505466043949127,
0.5519042611122131,
-0.1193181648850441,
1.1989833116531372,
-1.358649730682373,
0.04229523241519928,
-0.15058766305446625,
-0.03157442435622215,
-0.5626120567321777,
-0.49868690967559814,
-0.058590423315763474,
0.34057286381721497,
-0.10345262289047241,
-0.9354283809661865,
0.35993021726608276,
0.5212810039520264,
0.383053183555603,
-0.32767927646636963,
-0.16426189243793488,
-0.14061588048934937,
-0.20045527815818787,
0.7266241312026978,
0.16083918511867523,
-0.6272769570350647,
-0.1914384812116623,
0.6818934679031372,
0.37984132766723633,
0.010422722436487675,
-0.31696373224258423,
0.13875450193881989,
0.375802218914032,
-0.8607915639877319,
0.1783352643251419,
-1.1604613065719604,
-0.8268631100654602,
-0.023154031485319138,
-0.3699720501899719,
0.6163739562034607,
0.5169357657432556,
0.29392123222351074,
-0.23352475464344025,
-0.08617410808801651,
-0.16615481674671173,
0.19050215184688568,
-0.4231463372707367,
-0.21451792120933533,
-0.9663005471229553,
-0.395356148481369,
-0.38342657685279846,
0.7195686101913452,
0.01291766669601202,
0.3127140700817108,
0.05115334689617157,
0.24347588419914246,
-0.15480518341064453,
0.7332321405410767,
0.5011231899261475,
-0.18694783747196198,
-0.4734746515750885,
0.6223710775375366,
0.13453350961208344,
0.08215215057134628,
-0.559904932975769,
0.4891236424446106,
-0.8361071944236755,
0.5578816533088684,
-0.5892208814620972,
-0.08692692220211029,
0.10227585583925247,
-0.6071775555610657,
1.1157400608062744,
-0.6103373765945435,
-0.18908929824829102,
-0.008817142806947231,
-0.2637960910797119,
0.5313972234725952,
0.22399376332759857,
-1.1851956844329834,
-0.493660569190979,
-0.3296056389808655,
-0.4094240665435791,
0.3584844172000885,
-0.367351233959198,
-0.5571751594543457,
-0.7739494442939758,
-0.6870410442352295,
0.547179639339447,
-0.047242049127817154,
0.10147275030612946,
0.5302990078926086,
0.4438270330429077,
-0.08836235105991364,
-0.6579651832580566,
-0.41653767228126526,
-0.8589290976524353,
0.19796159863471985,
-0.0750834122300148,
-0.5480327010154724,
-0.1384192705154419,
-0.01444941759109497,
-0.518969714641571,
-1.4062776565551758,
-0.32817360758781433,
0.35488325357437134,
0.10831809788942337,
-0.1961309164762497,
0.6705737113952637,
-0.3719223141670227,
-0.2878051996231079,
-0.7346735000610352,
0.1763155460357666,
-0.47886720299720764,
-0.1254705935716629,
0.1448291391134262,
0.6942376494407654,
-0.3913905620574951,
-0.6095122694969177,
0.9049216508865356,
-0.7259382605552673,
-0.35124728083610535,
0.3090265393257141,
-0.1331472247838974,
-0.4698162078857422,
0.4664495885372162,
0.08026940375566483,
-1.0070064067840576,
-0.3473963737487793,
-1.0337566137313843,
-0.2878170907497406,
0.6595668196678162,
-0.6873811483383179,
0.12730540335178375,
-0.18613502383232117,
0.2913879156112671,
0.6965764164924622,
0.8614540696144104,
-0.10616394877433777,
-0.1837632954120636,
0.45262497663497925,
-0.45232078433036804,
-0.10099070519208908,
0.3158041834831238,
1.1574236154556274,
-0.3251246511936188,
-1.1331995725631714,
-0.021712712943553925,
-0.05127127841114998,
0.3168231248855591,
-0.3256615996360779,
0.5113674402236938,
-0.4426232874393463,
-0.13726721704006195,
0.4261886477470398,
0.7884899377822876,
0.3042645752429962,
0.2778654098510742,
0.14795252680778503,
0.0688115805387497,
-0.8255648612976074,
-0.8866275548934937,
-0.32722702622413635,
0.5116503238677979,
0.015168813057243824,
1.198720097541809,
-0.5845156908035278,
0.3027260899543762,
0.2388051152229309,
-0.1489928960800171,
-0.6252536773681641,
-1.5110641717910767,
-0.2191949337720871,
-1.244611382484436,
-0.8146476149559021,
-1.1411938667297363,
-0.259235680103302,
0.1475566029548645,
-0.07516482472419739,
-0.37547650933265686,
-0.04135863482952118,
0.03742906078696251,
-0.31223559379577637,
-0.009978847578167915,
0.5590174794197083,
-0.8397306799888611,
-0.659591555595398,
-0.8688725233078003,
-0.05791553109884262,
-0.0818258598446846,
-1.2093595266342163,
0.07913641631603241,
-0.02502371184527874,
-0.07011069357395172,
0.17446038126945496,
-0.26002949476242065,
1.1693296432495117,
-0.3642379343509674,
-0.4397350549697876,
0.0987321212887764,
0.39354029297828674,
-0.5132924914360046,
0.48946231603622437,
-0.48526546359062195,
0.2787596583366394,
-0.1276642084121704,
0.681019127368927,
-0.4855394959449768,
0.17386846244335175,
-0.6405954957008362,
-0.46843773126602173,
0.05296872928738594,
-0.23687289655208588,
-0.144699364900589,
-1.1828173398971558,
0.8547117114067078,
-0.5089859366416931,
-0.9439679980278015,
0.018437253311276436,
-0.31209802627563477,
0.06581439077854156,
-0.715748131275177,
-0.0037595948670059443,
0.0007636066293343902,
0.5839985609054565,
-0.5784479975700378,
0.9998016357421875,
-0.02496296539902687,
0.10213592648506165,
-0.252798467874527,
0.3536149859428406,
0.14833380281925201,
0.704919159412384,
-0.4622456133365631,
-0.11985952407121658,
0.11374072730541229,
-0.043489471077919006,
-0.33984994888305664,
0.24894046783447266,
-0.6462664604187012,
-0.35708773136138916,
-0.30903640389442444,
-0.14917421340942383,
-0.08713025599718094,
0.8723632097244263,
0.4647390842437744,
-0.08321228623390198,
0.1690199375152588,
-0.4738072454929352,
-0.5076554417610168,
0.11769765615463257,
-0.7709683179855347,
-0.8336393237113953,
0.28229501843452454,
0.2756999731063843,
0.3247781991958618,
0.4431856572628021,
-0.1690932661294937,
-0.07371289283037186,
0.26146838068962097,
0.9774504899978638,
0.5589104890823364,
-0.0007045178208500147,
-0.10461115837097168,
-0.11629834026098251,
-0.3067721426486969,
-0.6131136417388916,
-0.009821201674640179,
0.5758474469184875,
-0.6323695778846741,
-0.6319626569747925,
-0.5021387934684753,
0.19801484048366547,
-0.16156238317489624,
-0.2638925015926361,
0.4630494713783264,
-0.9467869997024536,
0.24063093960285187,
-0.4707920253276825,
-0.558720588684082,
0.2691631317138672,
-0.7655879259109497,
0.012751917354762554,
-0.028970638290047646,
-0.6636874675750732,
0.4435063898563385,
0.16696324944496155,
0.18582412600517273,
0.4073728024959564,
-0.33633795380592346,
0.8749538660049438,
-0.43534085154533386,
-0.5864120125770569,
1.090775728225708,
0.2840944528579712,
0.7998237013816833,
0.358055055141449,
-0.4129069447517395,
0.8970884680747986,
0.8217661380767822,
0.09454034268856049,
0.9953052997589111,
0.526477575302124,
-0.18875259160995483,
0.2288699895143509,
0.45091450214385986,
0.4895690679550171,
0.2624669075012207,
0.2734393775463104,
1.2470593452453613,
0.4128744304180145,
-0.26327285170555115,
0.39805179834365845,
0.366747111082077,
0.9417699575424194,
0.5889204740524292,
-0.004981103353202343,
-0.1135450229048729,
0.2495279312133789,
0.5503332018852234,
0.6274809241294861,
-0.5066484808921814,
-0.414339154958725,
-0.24965696036815643,
0.15350565314292908,
0.6215149760246277,
-0.12096421420574188,
-0.5659811496734619,
0.47849422693252563,
0.30947551131248474,
0.19253043830394745,
-0.20408396422863007,
0.8039071559906006,
0.5051838755607605,
0.4411979615688324,
0.6550494432449341,
0.35346314311027527,
0.8778358101844788,
0.6889195442199707,
-0.10804916173219681,
-0.7683700323104858,
-0.35289502143859863,
0.6856421828269958,
-1.0765358209609985,
0.34701111912727356,
-0.16919048130512238,
-0.172098770737648,
-0.7932460904121399,
-0.9300957918167114,
-0.21548043191432953,
-0.10464020818471909,
0.24976928532123566,
0.12303284555673599,
0.17513979971408844,
0.01514466479420662,
0.5144939422607422,
0.13357888162136078,
0.5576046109199524,
0.7112341523170471,
0.20583099126815796,
-0.23402974009513855,
0.5055304169654846,
1.0068415403366089,
0.5341855883598328,
0.4683646261692047,
-0.29689252376556396,
-0.5150320529937744,
1.0507564544677734,
0.028903156518936157,
0.5397290587425232,
0.5500996708869934,
-0.6150168180465698,
-0.40990421175956726,
0.04854539781808853,
0.06068756431341171,
-0.07553581148386002,
-0.28212863206863403,
0.19647592306137085,
0.974005401134491,
0.07545510679483414,
-0.09455643594264984,
1.1088188886642456,
0.19117219746112823,
-0.7445867657661438,
-0.6804154515266418,
0.33235809206962585,
-0.7755607962608337,
-0.0010632115881890059,
-0.9804642796516418,
0.3953259289264679,
0.2305612862110138,
-0.12084266543388367,
-0.2733696699142456,
-0.6205008625984192,
-0.7512074112892151,
-0.46448954939842224,
0.16834762692451477,
-0.6816356182098389,
0.1372644305229187,
0.558068573474884,
-0.16210605204105377,
0.6395245790481567,
-0.991814374923706,
-0.05938475951552391,
-0.5679038166999817,
1.1904078722000122,
-0.04481012374162674,
0.5747242569923401,
0.8441554307937622,
0.024041354656219482,
-1.2360666990280151,
0.3820778429508209,
0.5948383212089539,
-0.5999616980552673,
0.6026203036308289,
-0.21470114588737488,
-0.04554838314652443,
0.6555652022361755,
-0.2613375186920166,
0.6929933428764343,
-0.28298139572143555,
0.16830797493457794,
-0.20868702232837677,
-0.16589026153087616,
-0.165705606341362,
-0.544283926486969,
0.9147902131080627,
-0.8866050839424133,
-0.010094703175127506,
-0.04172961041331291,
0.5704907774925232,
0.13892045617103577,
-0.408814400434494,
3.9561922550201416,
0.8277591466903687,
0.43872305750846863,
0.1643112450838089,
1.2116758823394775,
1.2029606103897095,
-0.0971250832080841,
0.3527630567550659,
0.5056894421577454,
-0.9404834508895874,
-0.04559733718633652,
0.585680365562439,
-0.6977486610412598,
-0.13719023764133453,
-0.19746127724647522,
0.5824362635612488,
-0.3818405866622925,
0.001281448407098651,
-0.8093998432159424,
-0.6243202686309814,
-1.0425777435302734,
0.39595353603363037,
0.4100671708583832,
0.18523097038269043,
0.20102666318416595,
-0.05690940096974373,
0.28620338439941406,
-0.8365182876586914,
-0.8441059589385986,
-0.13987891376018524,
-0.40843716263771057,
-1.1137547492980957,
-0.1693362146615982,
0.11340304464101791,
-1.3135478496551514,
0.24032710492610931,
0.4151734411716461,
-1.036088466644287,
0.2603447139263153,
0.3161863088607788,
0.044806916266679764,
0.12159357219934464,
0.48400765657424927,
-0.36607423424720764,
-0.4233161211013794,
0.5721447467803955,
-0.1660318374633789,
0.3873399794101715,
0.1560668647289276,
-0.5587700009346008,
0.8823803663253784,
0.0774945542216301,
0.6855207085609436,
-0.7311801910400391,
-1.397255539894104,
-1.0126560926437378,
-0.42116937041282654,
-0.41313105821609497,
0.5932353734970093,
0.4396607577800751,
-0.011956495232880116,
0.10026174783706665,
-0.19745157659053802,
0.19029411673545837,
0.406117707490921,
0.5127725601196289,
0.2799398601055145,
-0.35305243730545044,
0.0008343050139956176,
-0.2583964467048645,
0.016327954828739166,
0.09964046627283096,
-0.8213817477226257,
0.09385183453559875,
-0.34839165210723877,
0.20995572209358215,
-0.26848679780960083,
1.0208526849746704,
-0.23918721079826355,
0.5199987888336182,
-0.3571242094039917,
-0.3691413700580597,
0.22172310948371887,
0.0003866502083837986,
0.3353953957557678,
0.7523432970046997,
0.28765997290611267,
-0.30500802397727966,
-0.24948248267173767,
0.513272225856781,
-0.18343585729599,
1.1372359991073608,
-0.03465458005666733,
-0.03303906321525574,
-0.8955692648887634
] |
4d Simplicial Quantum Gravity with a Non-Trivial Measure
|
We study 4d simplicial quantum gravity in the dynamical triangulation approach with a non-trivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the (possible) critical theory. We discuss how the lattice theory could be used to fix the quantum measure in a non-ambiguous way.
|
Bernd Bruegmann and E. Marinari
|
hep-lat gr-qc hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210002
|
hep-lat/9210003
|
[
0.48849058151245117,
-0.11090068519115448,
-0.19653041660785675,
0.5913693308830261,
-0.2616826295852661,
0.10671208053827286,
-0.519591748714447,
-0.2470751851797104,
-0.7405143976211548,
1.3920469284057617,
0.5253356099128723,
-0.32215309143066406,
-0.46148449182510376,
-0.641785740852356,
-0.3387574255466461,
0.5049587488174438,
0.386703222990036,
-0.17438846826553345,
-1.197103500366211,
0.6905695796012878,
0.17177265882492065,
-0.28592777252197266,
-1.2818647623062134,
-0.3006637692451477,
-0.14283397793769836,
0.8505514860153198,
0.008385620079934597,
0.16393813490867615,
1.00830078125,
0.1453673243522644,
0.4299151599407196,
-0.5546203851699829,
-0.154697448015213,
-0.09241342544555664,
-0.9701418876647949,
-0.2778903543949127,
-0.07253477722406387,
-0.17481644451618195,
1.0143628120422363,
-0.4456958472728729,
0.8107418417930603,
-0.4651787579059601,
-0.0475328266620636,
-0.5541528463363647,
-0.7348947525024414,
0.2359807938337326,
-0.2575175166130066,
-0.42686688899993896,
-0.010649031028151512,
-1.3112163543701172,
0.02302934043109417,
0.5899761319160461,
0.9532594084739685,
-0.6554688811302185,
-0.43793201446533203,
-0.2964533567428589,
0.15159112215042114,
0.35206860303878784,
-0.811042070388794,
-0.16229917109012604,
0.37720200419425964,
-0.0575881190598011,
0.5946065783500671,
-0.3963002860546112,
-0.08973932266235352,
0.7976444363594055,
-0.1983974128961563,
0.5937355756759644,
0.17206601798534393,
-0.0887252688407898,
-0.07043476402759552,
-0.06457799673080444,
-1.0055758953094482,
0.23472626507282257,
-0.6393609642982483,
0.01454932801425457,
-0.13546647131443024,
-0.5771230459213257,
-0.8541857600212097,
0.28209930658340454,
-0.1890658736228943,
0.06613311171531677,
-0.34926730394363403,
0.024539301171898842,
-0.2579186260700226,
-0.42324382066726685,
-0.2726988196372986,
-0.23191575706005096,
-0.009759369306266308,
0.8696257472038269,
0.48475053906440735,
0.7365264296531677,
-0.5304856896400452,
0.1409815400838852,
0.2785014510154724,
0.23272113502025604,
-0.025575600564479828,
0.34180712699890137,
0.3925692141056061,
0.13027149438858032,
0.10347311198711395,
0.3481304347515106,
-0.8080683350563049,
-0.02059013955295086,
-0.8063206672668457,
0.8900774121284485,
-0.18904747068881989,
-0.34055888652801514,
0.05136127769947052,
-0.7797119617462158,
0.1927594691514969,
-0.03542333468794823,
0.29259157180786133,
0.4964046776294708,
-0.15200044214725494,
0.39579808712005615,
-0.1948574185371399,
0.12672193348407745,
-0.2893388569355011,
-0.5348490476608276,
0.250864714384079,
0.003000942524522543,
0.162202849984169,
0.4309910237789154,
-0.12328653037548065,
-0.30091509222984314,
0.04482826963067055,
0.3425057828426361,
-0.7063291668891907,
-0.01857404038310051,
-0.3953525125980377,
-0.10132510960102081,
-0.6655869483947754,
0.25897136330604553,
-0.42770445346832275,
-0.2853682041168213,
-0.27863919734954834,
0.0583430752158165,
0.13749171793460846,
-0.20854203402996063,
0.7428673505783081,
-0.8199290633201599,
-0.0960763543844223,
1.3361685276031494,
-0.16541609168052673,
0.06601174920797348,
0.06818028539419174,
0.60480135679245,
-0.3123231530189514,
0.42255374789237976,
-0.7405219674110413,
0.3886925280094147,
-0.2823890447616577,
0.29772889614105225,
0.26154422760009766,
0.6599732041358948,
-0.5078108310699463,
0.1675163060426712,
-0.17477594316005707,
-0.6158762574195862,
0.13551831245422363,
0.20536597073078156,
-0.670569121837616,
0.21528829634189606,
-0.5798988342285156,
-0.47320953011512756,
-0.5903254747390747,
-0.4520226716995239,
0.8794416785240173,
-0.6872233152389526,
0.03746739402413368,
0.5472358465194702,
-0.46707460284233093,
1.2512511014938354,
0.1947624534368515,
0.7970539927482605,
0.1778908222913742,
-0.6909719109535217,
-0.02748870477080345,
0.2613847851753235,
-0.231970876455307,
-0.2857755720615387,
0.344655841588974,
0.24837332963943481,
-0.12779338657855988,
-0.3745024502277374,
0.12773960828781128,
-0.19145527482032776,
0.2781509757041931,
0.1619206815958023,
-0.5400802493095398,
0.7272691130638123,
-0.19544093310832977,
0.5713015794754028,
-0.428890585899353,
-0.14626772701740265,
-1.1397924423217773,
0.4036683440208435,
-0.6136309504508972,
-0.34441399574279785,
0.2745662033557892,
-0.28028950095176697,
-0.17493385076522827,
-0.06107329949736595,
-1.4515596628189087,
0.1190449669957161,
1.0988417863845825,
-0.27044743299484253,
-0.5985015034675598,
-0.47272080183029175,
0.4386027753353119,
-0.09537382423877716,
0.6066951155662537,
0.04354280233383179,
0.05406351014971733,
0.19438008964061737,
0.22176991403102875,
0.43625330924987793,
0.8463008999824524,
0.7215169072151184,
-0.04682931303977966,
0.27400240302085876,
-0.1530408263206482,
0.9724074006080627,
-1.066786289215088,
-0.9128115773200989,
0.6327948570251465,
0.40218883752822876,
0.18151266872882843,
-0.16901324689388275,
-0.09163408726453781,
0.6574116349220276,
-0.3504687547683716,
0.36031198501586914,
0.5289038419723511,
-0.042158883064985275,
0.6231199502944946,
0.16027086973190308,
0.3580343425273895,
0.5230077505111694,
-0.3003266453742981,
0.6874662637710571,
0.4449079632759094,
-0.044228505343198776,
-0.2550601661205292,
-0.04238241910934448,
-0.31679651141166687,
0.1687908172607422,
-0.9153926968574524,
0.04327236860990524,
-0.3482816815376282,
0.49326223134994507,
0.06583929806947708,
0.5716670751571655,
-0.8471739888191223,
0.14204034209251404,
-0.0035223180893808603,
0.2988967299461365,
-0.23644910752773285,
0.030301831662654877,
0.2856784462928772,
-0.02971256710588932,
-0.23403404653072357,
-0.29741206765174866,
0.02462226152420044,
1.0510293245315552,
-0.0681016743183136,
0.39076560735702515,
0.6218474507331848,
-0.3157893419265747,
-1.015712022781372,
0.5301584601402283,
-0.8142773509025574,
0.2076781839132309,
-0.6937739253044128,
-0.19667655229568481,
0.6481193900108337,
-0.6500188112258911,
0.8232043385505676,
-0.2631417512893677,
-0.4570761024951935,
0.5259171724319458,
-0.9153450131416321,
0.12345315515995026,
0.253854900598526,
-0.37561067938804626,
-0.7445135712623596,
0.17185135185718536,
-0.7997605800628662,
-0.3336179256439209,
-0.47704216837882996,
0.2070222795009613,
0.8466398119926453,
-0.3848273456096649,
0.49578359723091125,
0.018096288666129112,
-0.29069533944129944,
0.43531134724617004,
0.347766637802124,
-0.739431619644165,
0.24778319895267487,
0.3188331425189972,
0.06618616729974747,
-0.5331723093986511,
-1.3857814073562622,
0.4946271479129791,
0.5750414133071899,
0.0795544683933258,
0.47316890954971313,
0.0030268740374594927,
-0.3464549481868744,
0.2973095774650574,
-0.2731867730617523,
0.5308387279510498,
-0.025649579241871834,
1.220882773399353,
0.45853888988494873,
0.1674627810716629,
-0.04871049523353577,
-0.7063981294631958,
-0.26015400886535645,
0.4645480513572693,
0.06085535138845444,
-0.2686026394367218,
-0.21736937761306763,
0.805974543094635,
-0.2814604341983795,
-0.33447912335395813,
0.5656153559684753,
-0.8982678651809692,
-0.2524532079696655,
0.14705127477645874,
-0.451137900352478,
0.0941246971487999,
-0.4498777985572815,
0.34132516384124756,
-0.8400253057479858,
0.38014712929725647,
-0.010634755715727806,
0.20445838570594788,
0.6898511648178101,
-0.13012464344501495,
0.2774125933647156,
0.49517175555229187,
0.13158996403217316,
-0.3381425738334656,
-0.3468385338783264,
-0.15642403066158295,
-0.2879275977611542,
0.4325687885284424,
-1.152742862701416,
0.15077216923236847,
-0.04802439361810684,
0.5157262086868286,
0.21334119141101837,
0.27615880966186523,
-0.3165675699710846,
-0.18948598206043243,
-0.6753174662590027,
-0.8697814345359802,
-0.18488271534442902,
0.9348093271255493,
-0.036351513117551804,
-0.29114237427711487,
-0.639729917049408,
-0.5355461239814758,
0.3916633427143097,
0.14263437688350677,
0.3603868782520294,
-0.5280754566192627,
-0.25715363025665283,
0.09270184487104416,
-0.31889262795448303,
-0.20960433781147003,
0.33935546875,
0.7262746691703796,
0.011442688293755054,
-0.006160295102745295,
0.93012535572052,
-0.1465640813112259,
-0.2335273176431656,
0.5175189971923828,
0.6896077990531921,
0.7008705735206604,
0.49113571643829346,
0.46932315826416016,
0.04944070056080818,
0.12534195184707642,
-0.20893900096416473,
-0.6189960837364197,
-0.4710565507411957,
0.08368909358978271,
0.5881665349006653,
-0.03936748206615448,
0.5875495672225952,
-0.11981642991304398,
0.37257060408592224,
0.2072252482175827,
0.5114593505859375,
-0.18198640644550323,
0.21824797987937927,
0.07687681913375854,
0.8001723885536194,
0.8139585852622986,
0.3951731026172638,
0.46099498867988586,
-0.9867138862609863,
0.322867751121521,
-0.3606884181499481,
0.5972614884376526,
-0.26264217495918274,
-0.3806232213973999,
-0.11893913149833679,
-0.4664955139160156,
0.21490433812141418,
-0.17270906269550323,
-0.9562452435493469,
0.3008503019809723,
-0.13811084628105164,
0.662756621837616,
0.15151776373386383,
-0.07100509852170944,
0.6173499226570129,
-0.0008792259031906724,
0.56409752368927,
-0.4138597249984741,
0.7067332863807678,
-0.39777517318725586,
0.7099345326423645,
0.2355322241783142,
-1.0925623178482056,
-0.40784791111946106,
-0.8515328764915466,
-0.524224579334259,
-0.5533387660980225,
0.6197469234466553,
1.2736098766326904,
0.15609075129032135,
0.13357321918010712,
-0.5435051918029785,
-0.5145589709281921,
0.3796793818473816,
-0.4129015803337097,
-0.9070570468902588,
0.4691324234008789,
-0.1972220242023468,
-0.23135200142860413,
0.39683955907821655,
-0.2172357738018036,
-0.6565913558006287,
0.28866395354270935,
-0.4983042776584625,
0.04902298003435135,
-0.40490052103996277,
-0.4144513010978699,
-0.372391939163208,
-0.477815717458725,
-0.5551379323005676,
0.25699877738952637,
0.18587398529052734,
-0.13716574013233185,
0.3522140383720398,
-0.05214669927954674,
-0.17686748504638672,
0.35852885246276855,
-0.02355046197772026,
-0.5123384594917297,
0.7220632433891296,
0.8741722702980042,
0.20966342091560364,
0.18739250302314758,
0.23293636739253998,
0.1682666838169098,
0.16023436188697815,
0.3579329550266266,
0.1728070080280304,
0.06989100575447083,
-0.22782503068447113,
0.21201592683792114,
-1.0995272397994995,
-0.5128791928291321,
0.13980679214000702,
-0.17024338245391846,
0.4250345230102539,
0.4502428472042084,
-0.3470127284526825,
-0.13574370741844177,
-0.5767965316772461,
-0.7425283193588257,
0.5341273546218872,
-0.11070810258388519,
-0.4444413185119629,
0.8509867191314697,
-0.1477990597486496,
0.06643525511026382,
-0.33883383870124817,
0.14646098017692566,
-0.2912468910217285,
0.3041894733905792,
0.7271067500114441,
0.5599159598350525,
0.2920019328594208,
-1.1992465257644653,
0.5905265212059021,
-0.45539650321006775,
-0.28187796473503113,
-0.5259625315666199,
-0.1627427488565445,
0.0764172375202179,
-0.05091436579823494,
0.33160173892974854,
-0.18874843418598175,
-0.06432869285345078,
0.24581561982631683,
-0.6668369770050049,
-0.1849185973405838,
0.4518522322177887,
-0.3152582049369812,
0.21921919286251068,
0.6041378974914551,
0.40404561161994934,
-0.22786271572113037,
0.014474298804998398,
0.9625802040100098,
-0.05201200395822525,
0.0496407188475132,
0.13333135843276978,
-0.3203684985637665,
0.41334301233291626,
-0.5074299573898315,
0.5116790533065796,
-0.3762247860431671,
-0.5242031216621399,
0.3190065920352936,
-0.8021231889724731,
0.24235954880714417,
0.18815042078495026,
-0.023921987041831017,
-0.02226993255317211,
-0.8720909953117371,
-0.433214008808136,
0.5155473947525024,
-0.07611539214849472,
0.19435465335845947,
-0.6660612225532532,
0.06666610389947891,
-0.07901386171579361,
0.9021483659744263,
-0.27221864461898804,
0.7215909361839294,
0.2702826261520386,
-0.007885018363595009,
0.517151951789856,
0.46399733424186707,
0.3058094382286072,
-0.35215362906455994,
-0.02905150130391121,
0.2792498767375946,
0.26552721858024597,
0.5152546763420105,
-0.34977880120277405,
0.14402168989181519,
-0.5474629402160645,
1.1390290260314941,
-0.6586784720420837,
-0.013770333491265774,
0.05246168375015259,
-0.14500492811203003,
0.533573567867279,
-0.22450457513332367,
0.43373021483421326,
1.0783517360687256,
-0.03189022094011307,
0.22909311950206757,
0.2860725224018097,
-0.6842408180236816,
-0.13560079038143158,
-0.9367976784706116,
-0.6069328188896179,
0.2487563043832779,
0.17854970693588257,
-0.46702879667282104,
-0.5758589506149292,
-0.8015953302383423,
0.03251061961054802,
-0.19563476741313934,
0.19374340772628784,
0.47910669445991516,
-0.2801746428012848,
0.5544087886810303,
0.08119915425777435,
-0.18940342962741852,
-0.49503836035728455,
0.4916970431804657,
0.04701552912592888,
-0.11848578602075577,
0.14635993540287018,
-0.21291878819465637,
-0.8192329406738281,
-0.5087279081344604,
-0.1465551108121872,
0.43713435530662537,
0.341501921415329,
-0.33787813782691956,
0.7957127094268799,
-0.10603480041027069,
-0.6713414192199707,
-0.3748796582221985,
0.5419839024543762,
0.17488448321819305,
0.3814072012901306,
0.20647820830345154,
0.28583037853240967,
0.5097290277481079,
-0.2414906769990921,
0.5530394315719604,
0.009459552355110645,
-0.6999012231826782,
0.6799793839454651,
-0.8487728238105774,
-0.29378247261047363,
0.46113109588623047,
-0.04446517303586006,
-0.49653464555740356,
-0.13471436500549316,
-1.0321122407913208,
0.4889596402645111,
-0.6782872676849365,
-0.34586843848228455,
-0.20056289434432983,
-0.4532027542591095,
-0.23944653570652008,
0.3600333034992218,
0.7298331260681152,
-0.18013690412044525,
0.13370490074157715,
-0.28050437569618225,
-0.22139526903629303,
-0.1806829571723938,
-0.29519322514533997,
1.2558876276016235,
0.45797908306121826,
-0.7914962768554688,
0.09516090899705887,
-0.03871830925345421,
-0.10682068020105362,
0.18794330954551697,
1.0053799152374268,
-0.7289223074913025,
0.5490358471870422,
-0.013376866467297077,
0.2389959692955017,
0.12044107913970947,
0.8951186537742615,
0.43293654918670654,
0.4237687587738037,
-0.25311481952667236,
-0.7187222242355347,
0.022505128756165504,
-0.49812328815460205,
0.28677189350128174,
0.7112033367156982,
0.3402882218360901,
0.4448641538619995,
-0.46083539724349976,
-0.2858435809612274,
0.19898226857185364,
-0.7907442450523376,
0.161200612783432,
-1.0910910367965698,
-0.2736583650112152,
-0.15404589474201202,
-0.6288776993751526,
-0.021152174100279808,
0.7814836502075195,
-0.18819338083267212,
-0.3946385681629181,
-0.7847872376441956,
0.0028342611622065306,
0.12857450544834137,
0.635726273059845,
-0.4787660837173462,
-0.735804557800293,
-0.17214034497737885,
-0.044293731451034546,
-0.1456911265850067,
-0.3313983082771301,
-0.0828414261341095,
-0.17990320920944214,
-0.4654127061367035,
0.37832188606262207,
-0.10411080718040466,
0.8723267912864685,
-1.2243762016296387,
-0.8036974668502808,
-0.08479859679937363,
-0.3023133873939514,
-1.0579332113265991,
0.3689199388027191,
0.04780448228120804,
1.0186285972595215,
0.4845794439315796,
0.02533598430454731,
-0.6021085381507874,
0.01500575803220272,
-0.5259895920753479,
0.1096208319067955,
0.3653236925601959,
0.195384681224823,
-0.612099289894104,
-0.62828528881073,
-0.2850961685180664,
0.3106246590614319,
-0.764091968536377,
0.46146413683891296,
-0.6950055360794067,
0.062386058270931244,
-0.4637000262737274,
0.12826983630657196,
0.5050697922706604,
0.4697153866291046,
0.27381381392478943,
0.7187818884849548,
-0.08013138175010681,
-0.06720685213804245,
0.41954365372657776,
0.42307931184768677,
-0.11704923957586288,
-0.20292678475379944,
0.0160001702606678,
-0.4267462491989136,
-0.10018257796764374,
0.747910737991333,
-0.06827176362276077,
-0.20307092368602753,
-0.26345181465148926,
-0.43491649627685547,
0.045469753444194794,
-0.5782204866409302,
-0.645768404006958,
0.4525812268257141,
0.15951240062713623,
-0.49258187413215637,
-0.7321963310241699,
-0.3899860084056854,
-0.49617135524749756,
0.7278336882591248,
-0.9397834539413452,
-0.3948569595813751,
-0.17062616348266602,
-0.1913851499557495,
-0.17310334742069244,
0.5297667980194092,
-0.406602144241333,
0.1924647092819214,
0.29088887572288513,
-0.31770867109298706,
-0.22434964776039124,
0.11960111558437347,
-0.3490374684333801,
-0.09797922521829605,
-0.2265985757112503,
-0.37377575039863586,
-0.1322089582681656,
0.5542365908622742,
-1.3924224376678467,
-0.8441896438598633,
-0.21186470985412598,
0.6252462863922119,
0.23600153625011444,
-0.09983488917350769,
-0.36721575260162354,
0.016535459086298943,
-0.23933054506778717,
0.0659198984503746,
-1.1728483438491821,
-0.11274148523807526,
-0.503404974937439,
0.35927054286003113,
-0.03886823356151581,
-0.17985939979553223,
0.3963128328323364,
-0.19133050739765167,
0.18030978739261627,
-0.007957125082612038,
-0.5110029578208923,
0.7905024886131287,
0.4751230478286743,
0.026206359267234802,
0.5991742014884949,
0.0328633077442646,
0.2528655529022217,
0.4714685380458832,
-0.8144768476486206,
0.5776186585426331,
0.5914966464042664,
0.39459502696990967,
0.6348848938941956,
0.428887277841568,
0.14599719643592834,
0.3467428386211395,
0.030567465350031853,
-0.06877826899290085,
-0.3336764872074127,
0.05086468532681465,
0.3169328570365906,
0.21260051429271698,
0.10591774433851242,
-0.45938706398010254,
0.16543909907341003,
-0.31783485412597656,
-0.30286216735839844,
-0.3735809624195099,
-0.49454453587532043,
-0.3484516441822052,
0.1618475317955017,
0.2396356761455536,
-0.17804625630378723,
-0.6058194041252136,
0.050892967730760574,
-0.18432797491550446,
0.6299256682395935,
-0.09710830450057983,
0.018993640318512917,
0.49212712049484253,
0.3010138273239136,
0.5704528093338013,
0.11944800615310669,
0.4022946059703827,
0.24206234514713287,
1.3485636711120605,
0.6415717005729675,
0.616870105266571,
0.14472998678684235,
0.5218023061752319,
0.3118434250354767,
-0.7875632643699646,
0.5837137699127197,
0.7219456434249878,
-0.9414591193199158,
0.2921394407749176,
-0.6650919318199158,
-0.006743604317307472,
-0.5477298498153687,
-0.025165986269712448,
0.5617634057998657,
-0.46019306778907776,
0.03273627534508705,
0.5745998620986938,
-0.5360485315322876,
0.22972315549850464,
0.801080584526062,
0.10628020018339157,
0.06506086885929108,
0.6938877105712891,
-0.1554446965456009,
0.5154783725738525,
0.8060265779495239,
1.528778314590454,
0.2534067928791046,
-0.2544202208518982,
0.45986586809158325,
-0.39972975850105286,
0.4834160804748535,
0.27225998044013977,
-0.5498225092887878,
0.9904572367668152,
-0.8143720626831055,
-0.40976378321647644,
-0.0769093856215477,
0.31096962094306946,
-0.11034035682678223,
-0.5116204619407654,
0.21323011815547943,
0.05637756362557411,
-0.8994667530059814,
-0.9319188594818115,
1.8843343257904053,
0.42290550470352173,
-0.3067246079444885,
-0.784744918346405,
0.3803466856479645,
-0.4616645574569702,
0.04735594242811203,
-0.2275368869304657,
0.10878759622573853,
-0.6742158532142639,
-0.05351899936795235,
0.12803038954734802,
-0.548897922039032,
-1.0863953828811646,
-0.6794518232345581,
0.8494781851768494,
-0.681252121925354,
0.3495514690876007,
0.23616459965705872,
-0.25310343503952026,
0.21831417083740234,
-0.523093044757843,
-0.07477787882089615,
0.2776813209056854,
1.253379464149475,
0.2528257369995117,
-0.03339242562651634,
0.7302880883216858,
0.23293766379356384,
-1.2075400352478027,
0.7298120856285095,
0.6508608460426331,
-1.1394078731536865,
0.49628323316574097,
-0.25540515780448914,
0.6217600703239441,
0.7199382781982422,
0.048151444643735886,
0.5868709683418274,
-0.4756663739681244,
0.41416606307029724,
0.4021218419075012,
0.07461213320493698,
-0.4025719463825226,
-0.9279613494873047,
0.015389014966785908,
-0.31159380078315735,
0.21022340655326843,
0.28116267919540405,
-0.04170402139425278,
0.2604493796825409,
-1.0152729749679565,
4.350625991821289,
0.2891566753387451,
0.5463141202926636,
0.5376339554786682,
0.18945088982582092,
0.48037636280059814,
-0.3699341416358948,
-0.6637510657310486,
0.07624629884958267,
-0.5089703798294067,
-0.5496801137924194,
-0.010500350035727024,
0.09459666907787323,
-0.032457660883665085,
0.08707874268293381,
0.658827543258667,
-0.46984729170799255,
-0.21360811591148376,
0.3573884665966034,
-0.7767993211746216,
-0.5022498369216919,
-0.024616077542304993,
-0.11896027624607086,
0.18567395210266113,
0.20901140570640564,
0.1297149509191513,
-0.01870809495449066,
-0.25536835193634033,
-0.6408406496047974,
-0.463331937789917,
-0.08726516366004944,
-0.6292720437049866,
0.3272708058357239,
-0.528695285320282,
-0.5302149057388306,
0.5408578515052795,
0.10259464383125305,
-0.32179734110832214,
-0.20835167169570923,
0.4125269949436188,
-0.14768479764461517,
-0.3798861503601074,
0.18447914719581604,
-0.5526458024978638,
-0.21298876404762268,
0.5445689558982849,
0.0037114080041646957,
0.7937449812889099,
0.16979250311851501,
-0.8889702558517456,
0.2736697196960449,
0.13669627904891968,
0.7110185623168945,
0.0490226149559021,
-0.8415271639823914,
0.15361055731773376,
-0.7675272226333618,
0.07741730660200119,
0.055540166795253754,
0.41116470098495483,
0.14202705025672913,
-0.6965279579162598,
-0.3408346474170685,
0.20267291367053986,
0.06527043879032135,
0.5676901340484619,
-0.4619712233543396,
0.5471304059028625,
-0.603445827960968,
0.2881840467453003,
-0.49930188059806824,
-0.8036283850669861,
-0.08763313293457031,
0.2941794991493225,
0.15030205249786377,
-0.047700751572847366,
0.05876273289322853,
0.5965561270713806,
0.16338208317756653,
0.16290514171123505,
0.3722946345806122,
-0.1269657015800476,
-0.7872213125228882,
0.015083609148859978,
0.08193748444318771,
0.778194785118103,
-0.6354101300239563,
0.10445880889892578,
-0.0984029546380043,
0.23951713740825653,
-0.054740965366363525,
1.1203759908676147,
0.1500931680202484,
-0.3794301152229309,
-0.7594202756881714
] |
The Running Coupling from SU(3) Gauge Theory
|
We present high precision results on the static quark-antiquark-potential on 32^4 and smaller lattices, using the standard Wilson action at BETA = 6.0, 6.2, 6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (1%) we did not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9 fm up to 3.3 fm. We find violations of asymptotic scaling in the bare coupling up to BETA = 6.8. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safer extrapolation of LAMBDA_Lattice to its continuum value. We are also able to see and to quantify the running of the coupling from the interquark force. From this we extract the ratio \sqrt{SIGMA}/LAMBDA_L. Both methods yield consistent values for the LAMBDA-parameter: LAMBDA_MSbar = 0.558(-0.007+0.017)\sqrt{SIGMA} = 246(-3+7) MeV.
|
G.S. Bali and K. Schilling
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210003
|
hep-lat/9210004
|
[
0.2672109603881836,
-0.33783388137817383,
0.0014139824779704213,
0.20881517231464386,
0.15882554650306702,
-0.4154035151004791,
0.09967312216758728,
-0.3092191219329834,
-0.5772208571434021,
1.5444610118865967,
0.2856787145137787,
-0.11649394035339355,
0.12819890677928925,
-0.6950571537017822,
-0.5384228229522705,
0.7860599160194397,
0.05720064416527748,
-0.9422648549079895,
-0.9484431147575378,
0.28983598947525024,
0.4658241868019104,
-0.20029941201210022,
-0.9751635193824768,
-0.5764394402503967,
-0.3342992663383484,
1.0715680122375488,
0.22616620361804962,
0.4712646007537842,
0.8483597636222839,
0.29802247881889343,
0.1338505744934082,
-0.25779274106025696,
0.009548531845211983,
-0.5764979720115662,
-0.6071577668190002,
0.013360440731048584,
-0.2158365398645401,
-0.21654704213142395,
0.5244495272636414,
-0.4853445589542389,
0.6780728101730347,
-0.45485368371009827,
0.2924917936325073,
-0.286618709564209,
-0.1780366450548172,
0.008563702926039696,
-0.3271764814853668,
0.08288831263780594,
0.22308020293712616,
-1.5602200031280518,
0.1801292896270752,
0.6250330805778503,
0.21555405855178833,
-0.20360703766345978,
-0.6396697759628296,
-0.39977535605430603,
0.6210975050926208,
0.17264938354492188,
-0.5534458756446838,
-0.6963556408882141,
0.7360990643501282,
-0.15454763174057007,
0.6564229130744934,
-0.8815668821334839,
0.06436612457036972,
0.8789336085319519,
-0.1448056995868683,
0.6230550408363342,
0.25386765599250793,
-0.4773646295070648,
-0.41957834362983704,
-0.145049050450325,
-0.3516470491886139,
0.09184800833463669,
-0.8813167214393616,
0.37548744678497314,
-0.04214223846793175,
-0.8712871074676514,
-0.49258512258529663,
-0.40341803431510925,
-0.08425035327672958,
0.19607098400592804,
-0.13536885380744934,
0.6803586483001709,
-0.3405611217021942,
-0.23877885937690735,
0.016371285542845726,
-0.4580148756504059,
0.1313830316066742,
0.6523293256759644,
0.3321278989315033,
0.7980033159255981,
-0.35147592425346375,
0.0628332793712616,
0.10628914088010788,
0.6875627636909485,
0.014996177516877651,
0.6146587133407593,
0.18703515827655792,
0.5600192546844482,
0.034293174743652344,
0.7408159971237183,
-0.7604617476463318,
0.33211594820022583,
-1.0649735927581787,
0.0018650195561349392,
-0.1345137357711792,
0.15321974456310272,
0.14929507672786713,
-0.22338980436325073,
0.3405536115169525,
-0.5620165467262268,
0.31479981541633606,
0.3295777440071106,
0.8012017011642456,
0.937109649181366,
0.057068247348070145,
-0.13438838720321655,
-1.4184815883636475,
-0.6653129458427429,
0.3261202275753021,
0.22318287193775177,
0.3906146287918091,
0.9390007853507996,
0.32494109869003296,
-0.09513342380523682,
0.34012553095817566,
0.6619290113449097,
-0.42604517936706543,
1.0645263195037842,
-0.07450173795223236,
-0.30684709548950195,
-0.16483424603939056,
0.8076844215393066,
-0.7977321147918701,
0.10448099672794342,
0.20455461740493774,
0.8525936603546143,
0.4908731281757355,
0.02985779382288456,
0.8749366402626038,
-0.587076723575592,
-0.247502863407135,
1.0827292203903198,
0.563504159450531,
-0.31115010380744934,
-0.236229807138443,
0.3275660574436188,
0.09421638399362564,
0.39879268407821655,
-0.6646744608879089,
-0.03250136971473694,
0.27853676676750183,
0.3897571861743927,
-0.046380940824747086,
0.9156363606452942,
-0.4316340684890747,
0.1830824613571167,
-0.6784040331840515,
-0.4948509931564331,
0.3221530616283417,
-0.0046926746144890785,
-0.5904974341392517,
0.6110073924064636,
-0.050903722643852234,
0.24024374783039093,
-0.2105216085910797,
-0.3914332091808319,
-0.16996560990810394,
-0.7291905879974365,
-0.21750248968601227,
0.5614395141601562,
-0.2767854928970337,
0.854511559009552,
0.17891451716423035,
0.28140661120414734,
0.8552544713020325,
-0.9028111696243286,
0.12335289269685745,
0.2844533324241638,
-0.17235775291919708,
-0.7119501829147339,
-0.0046817343682050705,
-0.04232608899474144,
-0.4582867920398712,
-0.37885886430740356,
0.24268339574337006,
-0.2366020232439041,
-0.26694077253341675,
0.38348743319511414,
-0.6244385242462158,
0.3219435214996338,
-0.019791750237345695,
0.7885684370994568,
-0.9489474296569824,
-0.07365517318248749,
-0.6769200563430786,
0.21795842051506042,
-0.9722644090652466,
0.12228551506996155,
-0.1916281133890152,
0.567830502986908,
-0.8715693354606628,
-0.041480984538793564,
-2.0645947456359863,
-0.3432522714138031,
0.36790430545806885,
-0.1371229588985443,
-0.7813225984573364,
0.3533448576927185,
0.6684157848358154,
-0.7975661754608154,
0.12021007388830185,
-0.2632856070995331,
-0.17536431550979614,
0.2867116332054138,
0.07608360797166824,
0.26192349195480347,
0.950974702835083,
0.506890594959259,
1.0682507753372192,
-0.08944433927536011,
-0.1023261696100235,
1.1846246719360352,
-0.6064819097518921,
-0.6286106705665588,
-0.2693597376346588,
0.9033776521682739,
0.3787979483604431,
-0.9065942764282227,
0.08811648190021515,
0.39919939637184143,
0.13391394913196564,
0.9359235763549805,
0.6746110916137695,
0.11304409801959991,
0.43404942750930786,
0.5547822117805481,
0.430624395608902,
0.07490375638008118,
0.23893189430236816,
-0.2511110305786133,
0.511030375957489,
0.3353073000907898,
0.5373802781105042,
0.1274954229593277,
-0.7283924221992493,
-0.13087640702724457,
-0.5058364868164062,
0.1954023540019989,
-0.02742011286318302,
0.6427711844444275,
0.04483580216765404,
0.6712251305580139,
-1.4762639999389648,
-0.16598132252693176,
-0.030494920909404755,
0.17075961828231812,
-0.35815858840942383,
-0.43095216155052185,
-0.09179295599460602,
-0.13322682678699493,
-0.2956489622592926,
-0.7062301635742188,
-0.3884062170982361,
0.7657800912857056,
-0.1877569705247879,
0.009985407814383507,
0.9644504189491272,
-0.35194072127342224,
-0.7145482301712036,
0.04465934634208679,
-0.8217920660972595,
-0.041510097682476044,
-0.669719934463501,
0.1530744880437851,
0.5414572954177856,
-1.0147802829742432,
0.32118067145347595,
-0.06458942592144012,
0.23076198995113373,
0.14483200013637543,
-0.8991373181343079,
-0.1595667451620102,
0.5400773286819458,
0.6938864588737488,
-0.7141807079315186,
-0.19642966985702515,
-0.49438923597335815,
0.1303698718547821,
-0.07919035106897354,
-0.33965009450912476,
0.8399903774261475,
-0.39349350333213806,
0.28457704186439514,
0.034612756222486496,
-0.610205352306366,
0.0901046171784401,
-0.3034096360206604,
-0.24334101378917694,
0.2813833951950073,
0.46754488348960876,
-0.17978717386722565,
-0.41703975200653076,
-0.5916959643363953,
0.5399388670921326,
0.10664395987987518,
-0.3473986089229584,
0.10837732255458832,
0.08834412693977356,
-0.30988648533821106,
0.22956101596355438,
0.13361449539661407,
0.025671541690826416,
0.004302085842937231,
0.2755967676639557,
0.41501593589782715,
0.26133137941360474,
-0.24792560935020447,
-0.5027848482131958,
-0.6597398519515991,
0.0031795345712453127,
0.5923711657524109,
0.281107634305954,
-0.18384698033332825,
0.5079911351203918,
0.8347834944725037,
-0.3745133876800537,
0.4029512107372284,
-0.987089991569519,
-0.9065338373184204,
0.10030893981456757,
-0.8308178782463074,
0.2851841151714325,
-0.1532236486673355,
0.36507081985473633,
-1.0730092525482178,
0.09428516775369644,
0.21676227450370789,
0.27085602283477783,
0.9216341972351074,
0.25984135270118713,
0.46623027324676514,
0.2006893754005432,
0.5413466691970825,
-0.19101224839687347,
0.23087956011295319,
-0.18462680280208588,
-0.7824901342391968,
0.5294505953788757,
-0.6062048673629761,
0.02917209267616272,
0.3220829963684082,
0.5334985852241516,
-0.0454915426671505,
0.6089938282966614,
-0.30018308758735657,
-0.5367622375488281,
-0.5301172137260437,
-0.5481514930725098,
0.661726713180542,
1.3784222602844238,
-0.749199628829956,
-0.06215813755989075,
-0.04863344505429268,
-0.19145400822162628,
0.36433589458465576,
-0.04776136577129364,
0.5206975936889648,
-0.6761765480041504,
0.1445799171924591,
0.14590446650981903,
-0.32868778705596924,
0.5383522510528564,
-0.20044372975826263,
-0.5463857650756836,
1.0342355966567993,
1.003901720046997,
1.132920265197754,
-0.4257293939590454,
-0.8223503828048706,
-0.1449700891971588,
1.1489750146865845,
0.6566096544265747,
0.6629093885421753,
0.24413679540157318,
-0.5256047248840332,
0.3320232331752777,
-0.5617340803146362,
-0.49152910709381104,
-0.5566473603248596,
-0.2171631008386612,
0.29616647958755493,
-0.4051743447780609,
-0.04508700221776962,
0.08185043185949326,
0.11108499765396118,
0.7041611075401306,
-0.24992600083351135,
-0.018983615562319756,
0.5925981998443604,
0.439371794462204,
0.48398613929748535,
0.8392121195793152,
0.12658128142356873,
0.06500270962715149,
-0.5051932334899902,
0.19158905744552612,
0.009016729891300201,
0.1434134840965271,
-0.24602703750133514,
-0.20745818316936493,
-0.3163658082485199,
-0.7958874106407166,
1.0270423889160156,
0.27752751111984253,
-0.6043298244476318,
0.1749555468559265,
-0.0026465028058737516,
0.9921570420265198,
-0.6326246857643127,
-0.06457968801259995,
0.6143327355384827,
0.7533648014068604,
0.524304211139679,
-0.8614535331726074,
0.1638810634613037,
-0.4609113037586212,
0.2390868216753006,
0.432697594165802,
-0.2594436705112457,
-1.148672103881836,
-0.6201008558273315,
-0.7196372151374817,
-0.49256765842437744,
0.2154369354248047,
0.9422551393508911,
0.21829010546207428,
0.028382819145917892,
-0.5368380546569824,
-0.3377251923084259,
1.4427123069763184,
-0.42160218954086304,
-0.35179945826530457,
0.21419134736061096,
-0.10930007696151733,
0.07553433626890182,
0.28913983702659607,
-0.6559481024742126,
-0.7001357078552246,
0.29067498445510864,
-0.4452359080314636,
0.058728981763124466,
-0.36921072006225586,
-0.9536847472190857,
-0.5282151699066162,
-0.2880077064037323,
-0.2058282494544983,
0.8424698710441589,
-0.12081418186426163,
-0.2509835660457611,
-0.08734411001205444,
0.41432997584342957,
-0.6334237456321716,
0.04817118123173714,
-0.002020162995904684,
0.595303475856781,
1.37024986743927,
1.005271077156067,
0.0503229945898056,
0.29330259561538696,
0.30109310150146484,
-0.042313192039728165,
-0.028780611231923103,
0.15213891863822937,
-0.2614916265010834,
-0.4514087736606598,
-0.5621445178985596,
0.13805633783340454,
-0.9472268223762512,
-0.3861909806728363,
-0.11912888288497925,
-0.5162172317504883,
0.47622010111808777,
0.3455994427204132,
-0.562099039554596,
-0.5154994130134583,
-0.5158014297485352,
-1.0277526378631592,
0.3266100287437439,
-0.1399710774421692,
-0.40191444754600525,
0.5115273594856262,
-0.306443989276886,
-0.47090399265289307,
-0.04608961194753647,
-0.39481794834136963,
-0.3643428683280945,
0.02994384430348873,
0.40882667899131775,
0.3912201523780823,
0.8143381476402283,
-0.5295165181159973,
1.1075881719589233,
-1.0508242845535278,
0.425981730222702,
-0.6198822259902954,
-0.22324196994304657,
-0.4217377305030823,
-0.3055630326271057,
0.2380746603012085,
-0.24603568017482758,
-0.4877808094024658,
-0.27777376770973206,
-0.38902541995048523,
-0.0591171458363533,
-0.33718618750572205,
-0.33934202790260315,
-0.22867874801158905,
0.3314415514469147,
0.28938719630241394,
-0.8859897255897522,
0.27779072523117065,
0.17342175543308258,
0.7251318097114563,
0.09603572636842728,
-0.017989791929721832,
-0.5748559236526489,
0.5818852186203003,
-0.3125183582305908,
0.387297660112381,
-1.14982271194458,
-0.12363696098327637,
0.012044822797179222,
-0.36864763498306274,
0.39943835139274597,
0.601406991481781,
0.32475510239601135,
0.018201425671577454,
-0.3981233835220337,
-0.19004777073860168,
0.11863245069980621,
-0.5814165472984314,
-0.7833786010742188,
-0.574038028717041,
-0.22052764892578125,
-0.20679855346679688,
0.5495151877403259,
-0.4388108253479004,
0.7810803055763245,
0.5449635982513428,
0.1501062959432602,
0.22004501521587372,
0.019560670480132103,
0.6067222952842712,
0.2742172181606293,
0.5123468637466431,
0.5379859209060669,
-0.3327247202396393,
0.7926770448684692,
-0.3237335979938507,
0.24836388230323792,
-0.70296710729599,
1.3493636846542358,
-1.0100613832473755,
-0.19406132400035858,
-0.37265637516975403,
0.3896993398666382,
0.8770244717597961,
-0.6931303143501282,
0.45995429158210754,
0.45499879121780396,
0.3069455921649933,
0.4781949818134308,
0.6581187844276428,
-0.622072160243988,
-0.12204303592443466,
-0.42359909415245056,
-1.0353810787200928,
0.7654788494110107,
-0.011770298704504967,
-0.4355751574039459,
-0.5208821296691895,
-1.1130213737487793,
-0.3420122563838959,
0.3647089898586273,
0.03358527645468712,
0.5618195533752441,
0.4757748246192932,
0.4632478654384613,
-0.21749387681484222,
0.5281108021736145,
-0.12358720600605011,
-0.16037492454051971,
-0.6805988550186157,
-0.2874445915222168,
-0.45198002457618713,
0.14643704891204834,
-0.4141799211502075,
-0.975693941116333,
-0.29470863938331604,
0.57486492395401,
-0.06797918677330017,
-0.3125612437725067,
1.0675938129425049,
-0.6298213005065918,
-0.8852553367614746,
0.1265879124403,
0.10105209797620773,
-0.28128939867019653,
0.05066164955496788,
1.1658096313476562,
0.32082679867744446,
0.3117760717868805,
0.4031064510345459,
0.6083346605300903,
0.1965046375989914,
-0.3092518448829651,
0.354215532541275,
-0.30095162987709045,
-0.18028639256954193,
0.40525877475738525,
-0.15319310128688812,
-0.9646691679954529,
-0.07449247688055038,
-1.1608057022094727,
-0.0027733398601412773,
-0.0544765442609787,
0.2565056085586548,
-0.10456763207912445,
-0.31678274273872375,
0.0020226542837917805,
0.6439178586006165,
0.9658689498901367,
-0.03869713470339775,
-0.31758764386177063,
-0.2816082239151001,
-0.7395998239517212,
-0.4272693395614624,
-0.2944483160972595,
1.481545329093933,
-0.13400143384933472,
-0.9219244122505188,
0.20630329847335815,
0.048579342663288116,
-0.7095478177070618,
0.15117447078227997,
0.15279455482959747,
0.007874046452343464,
0.6479114294052124,
0.45232054591178894,
-0.28460249304771423,
0.13090400397777557,
0.16965235769748688,
0.2952381670475006,
-0.13992416858673096,
0.10093924403190613,
-1.1811994314193726,
-0.4647130072116852,
-0.4294130504131317,
0.4788350760936737,
0.6946896910667419,
0.148331880569458,
0.6078143119812012,
-0.4680284857749939,
-0.5594689249992371,
-0.20026826858520508,
-0.9832725524902344,
0.15370118618011475,
-0.7936967611312866,
-0.48628270626068115,
-0.31667783856391907,
0.006816547829657793,
-0.20561936497688293,
0.2848556935787201,
-0.28015998005867004,
-0.11531504988670349,
-0.5307114720344543,
-0.4341302514076233,
0.34375908970832825,
0.4320525825023651,
-0.33848273754119873,
-1.3001244068145752,
-0.5473430156707764,
0.32136037945747375,
-0.3048070967197418,
-0.49172425270080566,
0.06688880920410156,
0.8176743984222412,
0.47392547130584717,
0.6299819946289062,
-0.35765746235847473,
0.6530391573905945,
-0.6428734064102173,
-0.7966116070747375,
0.036972902715206146,
-0.029934294521808624,
-0.23884306848049164,
0.5427940487861633,
0.5763330459594727,
1.3276677131652832,
0.2706172466278076,
-0.30996280908584595,
-0.14750349521636963,
0.3053416311740875,
-0.74454265832901,
-0.09368526190519333,
0.248632550239563,
0.085848368704319,
-0.35835835337638855,
-1.306215524673462,
0.06715895235538483,
0.4585740864276886,
-1.3509799242019653,
0.12478332221508026,
0.02702818252146244,
0.11849376559257507,
-0.5882537364959717,
0.6417571306228638,
0.03372083976864815,
0.2288360893726349,
0.23525558412075043,
1.1873743534088135,
-0.3038911819458008,
0.0299066249281168,
0.436195969581604,
0.8175946474075317,
-0.9009691476821899,
0.1361340880393982,
0.40693914890289307,
-0.2549479007720947,
-0.21627803146839142,
0.6806100606918335,
-0.35898059606552124,
0.3533191382884979,
0.010427124798297882,
-0.7411970496177673,
-0.4872277081012726,
-0.8179476261138916,
-0.49333882331848145,
0.17634515464305878,
0.47063902020454407,
-0.3628401756286621,
-0.25557875633239746,
-0.6789971590042114,
-0.6620944738388062,
0.06668511033058167,
-0.9403588771820068,
-0.26570436358451843,
0.20197942852973938,
-1.142229437828064,
-0.03308416157960892,
0.042260926216840744,
0.05118633061647415,
0.6806471347808838,
0.07721031457185745,
0.30181488394737244,
-0.1798027753829956,
-0.03787419945001602,
-0.027996554970741272,
-0.26646679639816284,
-1.0926318168640137,
-0.45431602001190186,
-0.44200995564460754,
0.39005008339881897,
-0.4906770586967468,
-0.6041462421417236,
-0.6006090044975281,
0.5658331513404846,
0.030759155750274658,
0.4119444787502289,
0.18315589427947998,
-0.37228813767433167,
-0.4462316036224365,
-0.09536250680685043,
-0.5875849723815918,
-0.039655908942222595,
-1.0430182218551636,
0.4583291709423065,
-0.23100538551807404,
-0.9535670280456543,
0.5016101002693176,
-0.3473012149333954,
-0.19269795715808868,
-0.10291856527328491,
0.3168014585971832,
0.6947481036186218,
0.2845468819141388,
-0.3461073637008667,
0.9415752291679382,
-0.13993972539901733,
0.3547850251197815,
0.4280524253845215,
-0.8336236476898193,
-0.06958666443824768,
0.14933818578720093,
0.445955365896225,
0.7443141937255859,
0.39775556325912476,
0.6476356387138367,
0.5534617304801941,
0.46826642751693726,
0.5366193056106567,
-0.010328522883355618,
0.5350008606910706,
0.5798352360725403,
0.688692033290863,
0.05770304799079895,
0.15402495861053467,
0.21872270107269287,
0.19569112360477448,
-0.2732670307159424,
-0.2485729157924652,
0.17250919342041016,
0.05373185873031616,
0.3836362659931183,
0.33353087306022644,
-1.0837464332580566,
-0.8158767819404602,
-0.48937639594078064,
-0.21646682918071747,
0.2354804426431656,
0.26189205050468445,
0.3682297170162201,
0.7916638255119324,
0.7091700434684753,
0.21902790665626526,
0.014925051480531693,
0.7202485799789429,
0.22457315027713776,
0.6915273070335388,
0.684783935546875,
0.3914651572704315,
0.38561901450157166,
-0.1113654375076294,
0.2693745493888855,
-0.6356152296066284,
0.236298605799675,
0.03383218124508858,
-1.4345126152038574,
0.4211031198501587,
-0.059037886559963226,
0.4533874988555908,
-1.0564210414886475,
-0.36477184295654297,
0.37102699279785156,
-0.7540926337242126,
0.049368686974048615,
1.1758228540420532,
-0.7303800582885742,
0.4213727116584778,
0.7662095427513123,
0.2230248600244522,
0.12468930333852768,
0.8098596930503845,
0.3447943925857544,
-0.42348039150238037,
1.1483838558197021,
1.2303459644317627,
-0.2038853019475937,
-0.022428732365369797,
0.33401113748550415,
-0.8068857192993164,
0.5687847137451172,
0.7114259600639343,
-0.15913037955760956,
0.7813976407051086,
-0.5989422798156738,
-0.23360185325145721,
0.12396800518035889,
-0.09747622907161713,
-0.1733274906873703,
-0.5032505989074707,
0.33031272888183594,
-0.2413320243358612,
-0.09783211350440979,
-0.2881838381290436,
1.2664108276367188,
0.5611003041267395,
-0.548728346824646,
-0.1691642850637436,
0.13126185536384583,
-0.22833023965358734,
0.020914195105433464,
-0.768932044506073,
0.10334303975105286,
0.06179100275039673,
-0.18049025535583496,
-0.08035560697317123,
-0.7864782810211182,
-0.47830069065093994,
-0.6729717254638672,
-0.053090646862983704,
-0.5368892550468445,
0.43341413140296936,
-0.0336124412715435,
0.30730465054512024,
0.06115188077092171,
-0.7502087950706482,
0.3484339416027069,
0.15870462357997894,
1.2776203155517578,
0.05888950452208519,
-0.05068395659327507,
0.6799861192703247,
0.32470011711120605,
-0.8722013831138611,
0.30415186285972595,
1.3001056909561157,
-0.10227002948522568,
0.5708304643630981,
-0.6280561685562134,
0.3381637930870056,
0.6472026705741882,
-0.25037747621536255,
-0.00028082134667783976,
0.10085459798574448,
0.03422024846076965,
-0.4707760214805603,
-0.29603809118270874,
-0.4637439548969269,
-0.543335497379303,
0.14201025664806366,
-0.9246456623077393,
0.37395063042640686,
-0.08200649172067642,
0.630256175994873,
0.4151685833930969,
-0.47588691115379333,
4.034544944763184,
1.123389482498169,
0.4364558458328247,
-0.08708285540342331,
0.19399552047252655,
0.9642888307571411,
-0.3543780446052551,
-0.5889245867729187,
0.4423447847366333,
-0.543393611907959,
-0.9267542362213135,
0.02154441922903061,
-0.15033268928527832,
-0.21841691434383392,
-0.5980075597763062,
0.8535096645355225,
-0.3761155605316162,
-0.16041506826877594,
-0.42024749517440796,
-1.188384771347046,
-0.48942801356315613,
0.17682860791683197,
0.52120041847229,
-0.24312739074230194,
-0.11518174409866333,
0.7794769406318665,
0.4671432375907898,
0.10025189816951752,
-0.4347377419471741,
-0.704994797706604,
-1.2125808000564575,
-1.1259592771530151,
0.12187239527702332,
0.4355713725090027,
-0.6458889842033386,
0.48437628149986267,
-0.16118881106376648,
-0.7871788740158081,
0.18688717484474182,
0.05144301801919937,
0.13370144367218018,
-0.4587180018424988,
-0.156359001994133,
-0.2566165626049042,
-0.3338091969490051,
0.5243071913719177,
-0.5272071957588196,
0.5665383338928223,
0.07403845340013504,
-0.6757516860961914,
0.8171182870864868,
-0.3536214828491211,
0.6308716535568237,
-0.11988327652215958,
-1.1826173067092896,
0.2590019106864929,
-0.7397494316101074,
-0.18309195339679718,
0.7148241400718689,
-0.36624592542648315,
0.420086145401001,
-0.07636036723852158,
-0.22624585032463074,
-0.12288880348205566,
-0.2445439249277115,
0.7147482633590698,
0.15056896209716797,
-0.10231667757034302,
-0.3910617232322693,
-0.05802452564239502,
-0.0639500841498375,
-0.025059079751372337,
-0.36341211199760437,
0.4719927906990051,
-0.07257451117038727,
0.18047568202018738,
-0.12495466321706772,
0.3050374686717987,
-0.5041343569755554,
0.017125964164733887,
0.0053519392386078835,
-0.36242812871932983,
-0.2070099264383316,
-0.022481024265289307,
0.3081013858318329,
0.9168955683708191,
-0.4109000861644745,
-0.093099445104599,
-0.3484604060649872,
0.5292047262191772,
0.5049675703048706,
0.9511498212814331,
0.07129023224115372,
0.04384201765060425,
-0.8042665123939514
] |
Multicritical Points in a Lattice Yukawa Model with the Wilson-Yukawa Coupling
|
For a lattice regularized chiral-invariant $SU(2)_L\times~SU(2)_R$ fermion-scalar model with a Yukawa coupling $y$ and a Wilson-Yukawa coupling $w$, we investigate the phase structure and in particular show the existence of the multicritical line, in the strong Yukawa and/or Wilson Yukawa coupling region, at which four phases meet. The result is in good agreement with the Monte Carlo simulation. This analytical result is derived from the effective scalar model obtained by integrating out the fermion field where the action is explicitly obtained from the hopping parameter expansion up to next-to-leading order. For estimates on the correlation function of the scalar field we apply the mean-field method.
|
T. Ebihara and K.-I. Kondo
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210004
|
hep-lat/9210005
|
[
-0.13749155402183533,
-0.15183676779270172,
0.15504950284957886,
-0.18901626765727997,
-0.36718297004699707,
-0.7643679976463318,
0.07378409057855606,
-0.42602890729904175,
-0.9553391933441162,
1.5710536241531372,
0.7928592562675476,
-0.188012033700943,
0.3863549530506134,
-0.3777129054069519,
-0.04897373169660568,
0.5276933908462524,
-0.28701773285865784,
-0.8936646580696106,
-1.0783483982086182,
0.8488660454750061,
0.730798602104187,
0.047590047121047974,
-0.3401339054107666,
-0.9490508437156677,
-0.20956048369407654,
0.53020179271698,
-0.1022254228591919,
0.5887971520423889,
0.855841338634491,
0.7937902212142944,
0.3329125642776489,
-0.08421007543802261,
-0.2519606351852417,
-0.13207173347473145,
-0.4646171033382416,
0.1262495070695877,
-0.33588507771492004,
0.016927344724535942,
0.45474135875701904,
-0.15179593861103058,
0.7108107209205627,
-0.7265819907188416,
-0.09022284299135208,
-0.37685197591781616,
-0.3977408707141876,
0.28160667419433594,
-0.22520506381988525,
0.03455926477909088,
-0.02887248434126377,
-1.6154115200042725,
0.3908112347126007,
-0.15058991312980652,
-0.04233560338616371,
-0.37044447660446167,
-0.3512227535247803,
0.029914945363998413,
0.5323365330696106,
-0.6483915448188782,
-0.3503205478191376,
-0.4477740526199341,
0.4016460180282593,
-0.20438224077224731,
0.4856768846511841,
-1.1163502931594849,
0.37217918038368225,
0.6451274752616882,
-0.47497135400772095,
0.5793516635894775,
0.2628447413444519,
-0.2873002290725708,
0.31490063667297363,
-0.5053393840789795,
-0.9633666276931763,
0.21329185366630554,
-0.27418041229248047,
-0.17609558999538422,
0.2271411120891571,
-0.37103989720344543,
-0.9152235388755798,
-0.35705244541168213,
-0.2788706421852112,
-0.04919321462512016,
-0.3210262358188629,
0.01980266533792019,
-0.6501423120498657,
-0.9235689640045166,
0.16407650709152222,
-0.7907029986381531,
0.0019115948816761374,
0.3557440936565399,
0.2570333182811737,
0.7281513214111328,
-0.4216747283935547,
0.18515653908252716,
0.7100676894187927,
0.8077880144119263,
0.17505815625190735,
0.4787119925022125,
0.3599751591682434,
0.1649661511182785,
0.8017649054527283,
0.9623367190361023,
-0.7197055816650391,
0.3117789626121521,
-0.7664878368377686,
0.31154176592826843,
0.23258095979690552,
-0.07818513363599777,
-0.35575276613235474,
-0.7460657954216003,
0.6252208352088928,
-0.20619799196720123,
0.6424353718757629,
0.917682409286499,
0.6909441947937012,
0.5733803510665894,
0.32762303948402405,
0.24174177646636963,
-1.0448613166809082,
-0.15582211315631866,
-0.12784850597381592,
-0.12194643914699554,
0.5929660201072693,
0.8213306665420532,
-0.07550249248743057,
0.15650387108325958,
0.5234036445617676,
0.7367063760757446,
-0.4849493205547333,
0.44884663820266724,
0.014594675041735172,
-0.2211454212665558,
-0.36132872104644775,
0.8832215666770935,
-0.9044412970542908,
-0.033639032393693924,
-0.3479732871055603,
0.5875974893569946,
0.09851253032684326,
-0.22738653421401978,
0.564503014087677,
-0.9023822546005249,
-0.07371962070465088,
0.5226538777351379,
0.05792567506432533,
-0.2666163742542267,
0.3850931227207184,
0.7278006672859192,
-0.3610258996486664,
0.1762990802526474,
-0.29777517914772034,
0.16724374890327454,
-0.10151220113039017,
0.11608380079269409,
0.4764617681503296,
0.5366986393928528,
-0.7112783789634705,
0.08749555796384811,
-0.08515805751085281,
-0.35304486751556396,
0.0490085706114769,
-0.1282505989074707,
-0.6202205419540405,
0.3719733953475952,
-1.0114028453826904,
0.09173467010259628,
-0.31554412841796875,
-0.5965363383293152,
0.6572275161743164,
-0.8432257771492004,
-0.6319755911827087,
0.29795512557029724,
-0.5618515610694885,
1.2083475589752197,
0.867065966129303,
0.35843944549560547,
0.07887513935565948,
-0.42297762632369995,
-0.02480229176580906,
0.4301089644432068,
-0.37539803981781006,
-0.405693918466568,
0.5442484021186829,
0.11337060481309891,
-0.40129250288009644,
-0.25054430961608887,
-0.03979335352778435,
-0.63660728931427,
0.5744913816452026,
0.206764355301857,
0.09447973966598511,
0.2868810296058655,
-0.5688198208808899,
0.9161806702613831,
-0.42251506447792053,
0.08806794881820679,
-1.0656322240829468,
0.585368812084198,
-0.36019301414489746,
-0.5998362302780151,
-0.15912047028541565,
0.29366743564605713,
-0.7496340870857239,
0.5780395865440369,
-1.3358255624771118,
-0.08705686032772064,
1.1799201965332031,
0.5496253371238708,
-0.39736711978912354,
0.4163779616355896,
-0.12741167843341827,
-0.20524966716766357,
0.03299310803413391,
-0.1488509327173233,
0.7699780464172363,
0.5024592876434326,
0.6543880105018616,
0.4580749273300171,
0.5224428772926331,
0.4559289515018463,
0.3902069926261902,
-0.15530824661254883,
0.32750701904296875,
0.37377092242240906,
-0.5690129995346069,
-0.3590377867221832,
0.4789527356624603,
0.37900474667549133,
0.642774224281311,
-0.1779467612504959,
-0.33845075964927673,
0.24965068697929382,
-0.3805406987667084,
0.5983156561851501,
0.4735713303089142,
-0.29119694232940674,
0.16866004467010498,
0.6818127036094666,
0.7830796837806702,
0.4992657005786896,
-0.3245465159416199,
0.49971774220466614,
0.7480515837669373,
-0.034536510705947876,
-0.1475428342819214,
0.4885392189025879,
-0.5109459757804871,
-0.1311812847852707,
-0.8719014525413513,
0.25302085280418396,
0.08960393071174622,
0.3282510042190552,
0.022968346253037453,
0.030080867931246758,
-1.204826831817627,
-0.6284509897232056,
-0.2553723156452179,
0.33759090304374695,
-0.2750934958457947,
0.03330269828438759,
0.007017317693680525,
-0.39163345098495483,
-0.2568279504776001,
-1.1058375835418701,
-0.03517204895615578,
0.8732535243034363,
0.0986393466591835,
0.44794586300849915,
0.026533596217632294,
-0.1089412048459053,
-1.202756643295288,
-0.20543432235717773,
-0.4287833571434021,
-0.420541912317276,
-0.47210729122161865,
-0.2775273323059082,
0.8116809129714966,
-0.6950145959854126,
0.86544269323349,
0.4197006821632385,
-0.7159364223480225,
0.6928719282150269,
-0.28552472591400146,
0.17040686309337616,
0.7794657349586487,
0.11235693097114563,
-1.136372685432434,
0.25243404507637024,
-0.32832252979278564,
0.17541077733039856,
-0.07510107755661011,
0.058772362768650055,
0.9388979077339172,
-0.19883061945438385,
0.47041353583335876,
-0.3211648166179657,
-0.42438191175460815,
-0.0797177255153656,
-0.19608797132968903,
-0.751396119594574,
0.06545034050941467,
0.602867603302002,
-0.3019557297229767,
-0.40261420607566833,
-0.8112247586250305,
0.9224984049797058,
0.5933942794799805,
-0.5083675980567932,
0.15959449112415314,
0.06569454818964005,
-0.6198194622993469,
0.8914072513580322,
0.01124474685639143,
0.190861314535141,
-0.11315246671438217,
0.5326758623123169,
1.156705379486084,
-0.46721702814102173,
0.21492525935173035,
-0.16969598829746246,
-0.684241771697998,
0.41856691241264343,
-0.10113733261823654,
-0.9432794451713562,
-0.12430042773485184,
0.8436886668205261,
0.17054042220115662,
-0.7228249311447144,
0.6818538904190063,
-0.5932777523994446,
-1.2327566146850586,
0.4032612442970276,
-0.24144814908504486,
0.8442324995994568,
-0.053748756647109985,
0.3065691292285919,
-0.41598597168922424,
-0.43577679991722107,
0.5278576016426086,
0.13066518306732178,
0.6722428202629089,
0.20254479348659515,
0.6143774390220642,
-0.3953864872455597,
0.24172548949718475,
-0.5748397707939148,
-0.0005788638954982162,
-0.2660214900970459,
-0.2955225706100464,
0.3292733430862427,
-0.036371007561683655,
0.12377066910266876,
0.08345143496990204,
0.07248035818338394,
-0.06016245856881142,
0.6712255477905273,
-0.5312630534172058,
-0.279398649930954,
-0.12504316866397858,
-0.6229408979415894,
0.49867305159568787,
0.9943618774414062,
-0.5544828176498413,
-0.2015792727470398,
-0.655246376991272,
-0.5231630802154541,
0.12388313561677933,
0.13222737610340118,
0.9741406440734863,
-0.6084995865821838,
0.5832952857017517,
-0.35476115345954895,
-0.38737016916275024,
0.6142193675041199,
0.013543491251766682,
-0.2905719578266144,
0.5637807250022888,
0.1620984971523285,
0.975188136100769,
-0.6372931003570557,
-0.9346107244491577,
0.330655962228775,
0.9671989679336548,
0.7463057041168213,
0.8317555785179138,
0.24081005156040192,
0.09421533346176147,
-0.44071149826049805,
-0.7644767761230469,
-0.20846207439899445,
-0.45809996128082275,
-0.1538061946630478,
0.1607757955789566,
-0.21716538071632385,
-0.3537580966949463,
0.4003799557685852,
0.26137498021125793,
0.3533758521080017,
-0.026999952271580696,
0.0547616183757782,
0.10776761919260025,
0.42063531279563904,
0.8581636548042297,
0.7710816860198975,
-0.33335310220718384,
0.21537776291370392,
-0.8131977319717407,
0.5334733724594116,
-0.04449441656470299,
-0.2696901857852936,
-0.483369916677475,
0.033979304134845734,
-0.2981472313404083,
-1.0277702808380127,
0.28306591510772705,
-0.09213635325431824,
-0.7047582268714905,
0.10780879110097885,
0.11733834445476532,
0.9019430875778198,
0.17586758732795715,
0.23600336909294128,
0.614804208278656,
0.5275073647499084,
0.28183504939079285,
-0.7657538056373596,
0.131801575422287,
-0.053864214569330215,
0.22749170660972595,
0.25698330998420715,
-0.6017104983329773,
-0.5550029277801514,
-1.0044690370559692,
-0.4799920916557312,
-0.43019959330558777,
0.2009376585483551,
1.1070359945297241,
0.2923488914966583,
0.028117448091506958,
-0.39538222551345825,
-0.2148762196302414,
0.9482756853103638,
-0.909439206123352,
-0.38010141253471375,
0.03927812725305557,
0.19318749010562897,
0.035651374608278275,
0.4818672239780426,
-0.11324037611484528,
-0.06184539571404457,
0.11311347037553787,
-0.7283722162246704,
-0.3775053322315216,
-0.32728472352027893,
-0.44824346899986267,
-0.011026929132640362,
-0.6651206016540527,
-0.3616325557231903,
0.7364474534988403,
0.06183986738324165,
0.1546235829591751,
-0.31838276982307434,
0.21470555663108826,
0.163624107837677,
0.2367691546678543,
0.002421701094135642,
-0.24455931782722473,
0.3458947241306305,
0.755329966545105,
0.7352845072746277,
0.503206729888916,
0.4681927561759949,
-0.3124698996543884,
-0.31570670008659363,
0.41748806834220886,
0.5626723766326904,
-0.4275219440460205,
-0.11706601083278656,
-0.3843185007572174,
-0.5894166827201843,
-0.14193826913833618,
-0.2633659839630127,
-0.3329768478870392,
0.8300042748451233,
-0.10086991637945175,
-0.7040947675704956,
-0.6173655390739441,
-0.26982975006103516,
-0.9598056077957153,
0.36356931924819946,
-0.12775002419948578,
0.27677348256111145,
1.2428271770477295,
-0.4087686538696289,
-0.14411203563213348,
0.1083013042807579,
-0.3414435088634491,
-0.37163522839546204,
0.3293447196483612,
1.1023000478744507,
0.1702962964773178,
0.8328463435173035,
-1.055059790611267,
0.11992327123880386,
-0.2624785900115967,
0.36890149116516113,
-0.35813266038894653,
0.01731976307928562,
-0.6093042492866516,
-0.420150488615036,
-0.10374367237091064,
-0.005516174249351025,
-0.07702600210905075,
-0.31583675742149353,
0.3545060157775879,
-0.13713482022285461,
0.3593403398990631,
-0.6445459723472595,
-0.04345628619194031,
0.34046804904937744,
0.3825727701187134,
-0.7424637079238892,
-0.3018909692764282,
0.4267333447933197,
-0.336295485496521,
-0.05607568845152855,
0.022384408861398697,
-0.2480199933052063,
0.20936784148216248,
0.17545458674430847,
0.27185893058776855,
-0.9464181065559387,
-0.5715943574905396,
-0.5550646781921387,
-0.24744945764541626,
0.3616761267185211,
1.0843192338943481,
-0.4771991968154907,
-0.381186306476593,
-0.04602217301726341,
0.08083546906709671,
0.2986341714859009,
-0.07375630736351013,
0.11747687309980392,
-0.19292883574962616,
-0.2917248606681824,
0.1454983800649643,
0.6116507649421692,
-0.1345134973526001,
0.1384323388338089,
0.16861487925052643,
0.29237762093544006,
0.385934442281723,
0.49648144841194153,
0.08251991868019104,
0.10368583351373672,
-0.2705066502094269,
0.17468713223934174,
0.01426677219569683,
0.871484637260437,
-0.4855901300907135,
0.08155995607376099,
-0.8435993194580078,
1.0662615299224854,
-0.44876033067703247,
-0.34017154574394226,
0.4308062493801117,
0.2862567603588104,
0.5675086379051208,
-1.4031825065612793,
0.48713624477386475,
0.1804291307926178,
-0.3121796250343323,
0.6227193474769592,
0.6471524238586426,
-0.6453180909156799,
-0.279275506734848,
-0.6593940258026123,
-0.8748410940170288,
0.5554701089859009,
0.0322459414601326,
0.17798015475273132,
-0.5616188645362854,
-1.0762587785720825,
0.6086552143096924,
0.19900059700012207,
0.620352029800415,
0.6098620295524597,
-0.19068889319896698,
0.348957359790802,
0.022059958428144455,
-0.40718191862106323,
-0.462500661611557,
-0.24105797708034515,
-0.0672362744808197,
0.13396267592906952,
-0.3631293475627899,
0.27425244450569153,
-0.7320427894592285,
-0.7554475665092468,
0.05363451689481735,
0.20386557281017303,
-0.11363191902637482,
-0.45470523834228516,
0.43143850564956665,
-0.7334342002868652,
-0.4599331021308899,
-0.13915838301181793,
-0.07643537223339081,
0.05581483989953995,
0.006823478266596794,
0.18162016570568085,
0.27238601446151733,
0.5660327672958374,
0.09429407119750977,
0.4777360260486603,
-0.6080777049064636,
0.35501882433891296,
0.46239376068115234,
-0.42375898361206055,
-0.24173220992088318,
0.2283889353275299,
-0.03066922351717949,
-0.6890689730644226,
-0.3715568482875824,
-0.8617905378341675,
0.19364404678344727,
-0.7435611486434937,
-0.6770021319389343,
-0.4535778760910034,
-0.23064349591732025,
-0.3377213478088379,
0.4617109000682831,
1.028017282485962,
-0.21207983791828156,
-0.21605482697486877,
0.3624182641506195,
-1.1058504581451416,
-0.7517866492271423,
0.2534625232219696,
0.9820098876953125,
0.29016801714897156,
-1.1856191158294678,
-0.15986961126327515,
-0.2709118723869324,
-0.3790891766548157,
-0.09040506184101105,
0.6987491846084595,
-0.726632833480835,
0.27822527289390564,
0.21111960709095,
0.33283731341362,
0.3290603756904602,
0.6071670651435852,
0.4423049986362457,
-0.23638547956943512,
-0.5549073219299316,
-1.0253159999847412,
-0.5852765440940857,
-0.4281865060329437,
0.07175274193286896,
1.0852166414260864,
0.01280225906521082,
0.1608133614063263,
0.2134544998407364,
-0.5311222076416016,
-0.13434617221355438,
-1.2006369829177856,
-0.3371923863887787,
-0.9587029814720154,
0.15939578413963318,
-0.9880833625793457,
-0.12837666273117065,
0.6013455986976624,
0.24860802292823792,
-0.342605322599411,
0.26905497908592224,
-0.9733007550239563,
-0.11364976316690445,
0.13815872371196747,
0.0936102345585823,
-0.1659531146287918,
-1.104882836341858,
-0.38025662302970886,
-0.34952378273010254,
0.15150177478790283,
-0.11714091151952744,
-0.06681543588638306,
-0.3251551389694214,
-0.1928359419107437,
0.5270094275474548,
-0.5346488952636719,
1.045667052268982,
-0.8196065425872803,
-0.9657629132270813,
0.06549178808927536,
-0.12748152017593384,
-0.9795358180999756,
0.22702398896217346,
0.06720083951950073,
0.4155125319957733,
0.21961402893066406,
0.1561751663684845,
-0.32507818937301636,
0.2899312376976013,
-0.7351312041282654,
0.07066145539283752,
-0.009578973986208439,
0.2479069083929062,
-0.4401877522468567,
-0.9374538064002991,
0.18527042865753174,
0.47360509634017944,
-1.2510663270950317,
0.1729966402053833,
-0.21649906039237976,
0.26210424304008484,
-0.3245711326599121,
0.5214884281158447,
-0.03195803984999657,
0.5664544701576233,
-0.16829267144203186,
1.2572308778762817,
-0.05599258467555046,
-0.4589465260505676,
-0.35316431522369385,
0.6592977643013,
-0.27798813581466675,
-0.10391648858785629,
0.21731887757778168,
-0.6964963674545288,
-0.0746210440993309,
-0.01767706871032715,
0.16136470437049866,
0.08139345049858093,
-0.4093669354915619,
-0.7464272975921631,
-0.4120355248451233,
-0.19517500698566437,
-0.18124711513519287,
0.16034045815467834,
0.20635738968849182,
-0.6925060749053955,
0.06341460347175598,
-0.6983610391616821,
-0.437724769115448,
0.5359604954719543,
-0.7235814332962036,
0.023498743772506714,
0.2712046504020691,
-0.5224448442459106,
0.15498273074626923,
-0.3386905789375305,
0.11424153298139572,
-0.1508234739303589,
-0.5491977334022522,
0.24927043914794922,
-0.3383573889732361,
0.0451185517013073,
-0.15519461035728455,
0.05854536220431328,
-0.7092669010162354,
0.058155130594968796,
-0.9998036623001099,
0.5608181357383728,
-0.6099951863288879,
-0.9423841238021851,
-0.7512028217315674,
0.9272062182426453,
0.1519189476966858,
-0.02492857165634632,
-0.19267188012599945,
-0.27289044857025146,
-0.11560844630002975,
0.3596234917640686,
0.10904175043106079,
-0.04861166328191757,
-0.9231887459754944,
0.3043983578681946,
0.1429758071899414,
-0.7940294146537781,
0.17668627202510834,
0.039420608431100845,
0.14138539135456085,
-0.5437267422676086,
-0.16290642321109772,
1.1985797882080078,
0.6550226807594299,
-0.06372404098510742,
0.7562475800514221,
-0.3160169720649719,
0.5873857736587524,
0.28077420592308044,
-0.35591500997543335,
0.2712583839893341,
0.1900448501110077,
0.4820602536201477,
0.7670537829399109,
0.8635594844818115,
0.6407700777053833,
0.5008538961410522,
-0.36730021238327026,
-0.3191734254360199,
0.22543342411518097,
0.4125515818595886,
0.05914590135216713,
0.5585905909538269,
-0.3947502076625824,
0.08472484350204468,
-0.31217342615127563,
-0.055086731910705566,
0.13639913499355316,
-0.3251754939556122,
0.2795622646808624,
0.21805864572525024,
0.12328659743070602,
0.6255072951316833,
-0.5466539859771729,
-0.4536706507205963,
-0.45720717310905457,
-0.024546071887016296,
0.36683958768844604,
0.39207109808921814,
-0.3321351706981659,
-0.44225025177001953,
0.909580409526825,
-0.036485571414232254,
-0.19460467994213104,
0.5117019414901733,
0.02512599714100361,
0.6551719307899475,
0.7611433863639832,
0.800527811050415,
0.5435919165611267,
0.06398884207010269,
0.24960418045520782,
-0.9230645895004272,
0.32916465401649475,
0.22939321398735046,
-1.1214354038238525,
0.12049656361341476,
-0.32197293639183044,
0.2665604054927826,
-0.22129854559898376,
-0.7572203874588013,
-0.10120739787817001,
-0.43834277987480164,
-0.35736143589019775,
0.6723324656486511,
-0.6015128493309021,
-0.11825153976678848,
0.9173693656921387,
0.10065889358520508,
0.19963374733924866,
0.4226634204387665,
-0.31310704350471497,
0.4134470820426941,
1.0190098285675049,
0.9484032392501831,
-0.01348442304879427,
0.1974533349275589,
0.49607184529304504,
0.15604408085346222,
-0.12410737574100494,
0.4481141269207001,
-0.5779525637626648,
0.7485452890396118,
-0.5234440565109253,
-0.6621862649917603,
0.433541864156723,
-0.03110802173614502,
0.23779216408729553,
-0.11650968343019485,
0.1512909233570099,
0.6274794936180115,
-0.6573328971862793,
-0.676611065864563,
1.1644318103790283,
0.05265233665704727,
-0.6744574308395386,
-0.49456751346588135,
-0.1905258446931839,
-0.027652300894260406,
0.18535453081130981,
-0.9364641308784485,
0.1909032016992569,
-0.41011759638786316,
0.25796276330947876,
-0.4066457450389862,
-0.31877025961875916,
-0.3120219111442566,
-0.716424822807312,
0.7627972364425659,
-0.4345031976699829,
0.6417026519775391,
-0.08900723606348038,
0.04444900527596474,
0.6786910891532898,
-0.5100652575492859,
-0.018210815265774727,
0.8167798519134521,
0.7754913568496704,
-0.348514199256897,
0.20128561556339264,
0.8208032250404358,
0.0005542382132261992,
-0.6514468193054199,
0.475625216960907,
0.9357308149337769,
-0.8097091913223267,
1.242887258529663,
-1.0763696432113647,
-0.03809230774641037,
0.2600788176059723,
-0.24368979036808014,
0.13003548979759216,
0.3160809874534607,
0.09112773835659027,
0.2081221044063568,
0.050618015229701996,
0.019838891923427582,
-0.7289904952049255,
0.4557715654373169,
-0.8732802271842957,
0.3378409445285797,
-0.31715381145477295,
0.6617338061332703,
0.10469991713762283,
-0.7593587636947632,
4.177279949188232,
0.6792483925819397,
0.37955883145332336,
0.5695533752441406,
0.6162681579589844,
1.4958531856536865,
-0.8325449824333191,
-0.13440503180027008,
0.28429949283599854,
-0.7562363743782043,
-0.5995144844055176,
0.03800085559487343,
0.3079034388065338,
0.13959389925003052,
-0.4904061257839203,
0.46241235733032227,
-0.6643757820129395,
0.35793566703796387,
0.14924649894237518,
-0.7062680721282959,
-0.622604489326477,
0.6356220245361328,
0.750969409942627,
0.366870254278183,
0.287801593542099,
0.10088180005550385,
0.5225701928138733,
-0.3677072823047638,
-0.49846285581588745,
-0.10189655423164368,
-0.5750983953475952,
-0.9244036674499512,
0.4101003110408783,
-0.351752370595932,
-0.4633614718914032,
0.37959444522857666,
-0.1011265218257904,
-0.329164981842041,
-0.014717359095811844,
0.16720910370349884,
-0.3057393729686737,
0.11901302635669708,
-0.009147677570581436,
-0.18671366572380066,
-0.5643565058708191,
1.0930132865905762,
0.13583597540855408,
0.6487142443656921,
0.09336018562316895,
-0.6440930962562561,
0.6420252323150635,
0.19897335767745972,
0.5146510004997253,
-0.3515099883079529,
-0.711690366268158,
-0.21654263138771057,
-0.24826140701770782,
0.5351635813713074,
-0.14377157390117645,
-0.21099549531936646,
0.4107036292552948,
-0.21211834251880646,
-0.35590097308158875,
0.31673043966293335,
0.7447050213813782,
0.11821257323026657,
0.5286768674850464,
0.010391619987785816,
-0.9295977354049683,
-0.18453870713710785,
0.20172393321990967,
-0.23237216472625732,
-0.27498680353164673,
0.39168018102645874,
-0.14312297105789185,
0.2860616147518158,
0.15531295537948608,
0.7630125880241394,
0.1158827543258667,
0.027016326785087585,
-0.18989719450473785,
-0.7386093735694885,
-0.024650169536471367,
-0.21623368561267853,
-0.08406803011894226,
0.5242674946784973,
-0.3418501615524292,
-0.08291701972484589,
-0.5243075489997864,
0.3941819369792938,
0.24652577936649323,
1.3089994192123413,
0.7098898887634277,
0.3167014718055725,
-0.9037611484527588
] |
Fermion Doubling and Gauge Invariance on Random Lattices
|
Random-lattice fermions have been shown to be free of the doubling problem if there are no interactions or interactions of a non-gauge nature. On the other hand, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi identities which could revive the free-field suppressed doubler modes in loop diagrams. Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge theory, we show that indeed the doublers are revived for random lattices in the continuum limit. Some implications of the persistent doubling phenomenon on random lattices are also discussed.
|
C J Griffin and T D Kieu
|
hep-lat hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210005
|
hep-lat/9210006
|
[
-0.1013738289475441,
-0.5240316987037659,
-0.028418945148587227,
-0.40313825011253357,
0.18078777194023132,
-0.6214427351951599,
-0.3462613821029663,
0.18131336569786072,
-0.09200891107320786,
1.080823540687561,
0.08386721462011337,
0.4319241940975189,
0.13725222647190094,
-0.27764326333999634,
-0.14338210225105286,
0.5401461720466614,
-0.43544483184814453,
-0.3696509897708893,
-1.3738106489181519,
0.5652647018432617,
0.5831465721130371,
-0.13677401840686798,
-1.8123817443847656,
-1.185909628868103,
-0.19975511729717255,
0.7640285491943359,
0.2381681501865387,
-0.026442643254995346,
1.2048851251602173,
0.43675944209098816,
0.10938846319913864,
-0.9761032462120056,
-0.012226609513163567,
-0.5836074948310852,
-0.24613286554813385,
0.14050762355327606,
-0.5177800059318542,
0.12745198607444763,
0.6641860604286194,
-0.04214701056480408,
0.729094922542572,
-0.6276189088821411,
-0.11239465326070786,
-0.4007224142551422,
-0.9865900278091431,
-0.2579609751701355,
-0.6395890712738037,
0.18510864675045013,
0.0282591562718153,
-1.2241113185882568,
-0.017822498455643654,
0.5831560492515564,
1.1775683164596558,
-0.4395129084587097,
-0.6153574585914612,
-0.04977622255682945,
-0.15593479573726654,
-0.1558132767677307,
-0.7190065383911133,
0.1055968701839447,
0.9080017805099487,
-0.17575004696846008,
0.5627281665802002,
-0.9319348931312561,
0.1364736557006836,
0.21986402571201324,
-0.599254310131073,
0.43489882349967957,
0.22460566461086273,
-0.6313776969909668,
-0.08535393327474594,
-0.4789038598537445,
-1.4025729894638062,
0.39840376377105713,
-0.8778043985366821,
0.2550598382949829,
-0.5270205736160278,
-0.6479703187942505,
-1.451137661933899,
-0.6018672585487366,
0.16158732771873474,
-0.3995821177959442,
-0.24976055324077606,
0.1673629879951477,
-0.6459335088729858,
-0.23056168854236603,
-0.6439388990402222,
-0.2436065822839737,
-0.2935878038406372,
0.3064146935939789,
0.13464124500751495,
1.2811248302459717,
-0.02312697470188141,
-0.16630597412586212,
0.5487345457077026,
0.5033509731292725,
-0.23583684861660004,
0.5617325901985168,
0.8790289759635925,
0.34712013602256775,
-0.02375171147286892,
0.5712339878082275,
-0.6649764180183411,
0.3697167634963989,
-0.1515234112739563,
0.10015249252319336,
-0.4211201071739197,
0.19460591673851013,
-0.2844814658164978,
-0.4564457833766937,
0.5972789525985718,
-0.5520864725112915,
0.27433282136917114,
1.0072460174560547,
0.014888077042996883,
0.7438985109329224,
0.26696667075157166,
0.6338241696357727,
-0.5207495093345642,
-0.5667426586151123,
0.1930539458990097,
0.1713119000196457,
0.20868410170078278,
0.32702723145484924,
0.20805643498897552,
0.3605085015296936,
-0.36125096678733826,
0.48292306065559387,
-0.6592074632644653,
0.523785412311554,
0.5288510322570801,
-0.488128662109375,
-0.22781598567962646,
0.29956263303756714,
-1.0467655658721924,
0.31847596168518066,
-0.6064382195472717,
0.4894719421863556,
-0.43068385124206543,
-0.3256542682647705,
1.2595252990722656,
-0.6444287300109863,
0.2783437669277191,
1.0295515060424805,
0.9135159850120544,
0.23196566104888916,
0.3171023726463318,
0.33097225427627563,
-0.1486208140850067,
0.544918954372406,
-1.0009526014328003,
-0.29281121492385864,
-0.42252424359321594,
0.340285062789917,
-0.7981418967247009,
0.3134305477142334,
0.002623198786750436,
0.8554267287254333,
-0.30764514207839966,
-0.5612000226974487,
0.17447474598884583,
-0.34946179389953613,
0.14801929891109467,
0.7140817046165466,
-0.3521033525466919,
0.12917138636112213,
-0.2529560625553131,
-0.42700639367103577,
0.35896676778793335,
-0.6021695137023926,
-0.19326192140579224,
0.42453035712242126,
-0.13959772884845734,
0.9432678818702698,
0.56088787317276,
0.34725746512413025,
0.6094285249710083,
-1.0234075784683228,
0.4236224889755249,
0.7014684081077576,
0.1500965654850006,
-0.04286467283964157,
0.7595095634460449,
-0.12791581451892853,
0.271721750497818,
-0.6378300786018372,
-0.2327103316783905,
-0.20200711488723755,
0.11147546768188477,
0.6887897849082947,
-0.21044620871543884,
0.126228466629982,
-0.10965516418218613,
0.5830682516098022,
-0.5169750452041626,
0.05379872024059296,
-0.6659951210021973,
-0.03674079850316048,
-0.781214714050293,
-0.015785841271281242,
0.029200656339526176,
-0.09238074719905853,
-0.7449296116828918,
-0.07449106127023697,
-1.502930760383606,
-0.15634043514728546,
0.6225401163101196,
0.31372737884521484,
-0.6108618378639221,
0.11455117166042328,
-0.19507072865962982,
0.013202797621488571,
0.3213772475719452,
-0.7906129360198975,
0.44315195083618164,
0.3164249360561371,
-0.1316264569759369,
0.20556262135505676,
0.24098537862300873,
0.3915039002895355,
1.031004548072815,
1.1949782371520996,
0.07420476526021957,
0.738647997379303,
-0.7366552948951721,
-0.8297089338302612,
0.4286208748817444,
0.8414602875709534,
0.4131271541118622,
0.4411642253398895,
-0.04850885272026062,
0.7570379376411438,
-0.426757276058197,
0.8333379030227661,
0.36790457367897034,
0.08415555953979492,
0.32543832063674927,
0.28862664103507996,
1.0160038471221924,
0.686710774898529,
0.08054166287183762,
-0.0011662784963846207,
0.3352060317993164,
0.19292007386684418,
-0.2961307466030121,
-0.14824022352695465,
-0.9503241181373596,
-0.1735379844903946,
-0.7893286347389221,
0.34124764800071716,
0.04744081571698189,
0.2603389024734497,
-0.329336017370224,
0.5538855195045471,
-0.8068915009498596,
-0.30100229382514954,
0.8453244566917419,
0.2825152575969696,
-0.3073144257068634,
-0.16155898571014404,
0.5703302621841431,
0.06541884690523148,
-0.09296170622110367,
-1.1124629974365234,
0.5338519811630249,
1.040194034576416,
0.6523281335830688,
0.39976194500923157,
0.6800584197044373,
-0.2396318018436432,
-0.9963207244873047,
-0.044070105999708176,
-0.7932544350624084,
-0.126271054148674,
-1.5170122385025024,
-0.16488505899906158,
0.9799126386642456,
-0.9060448408126831,
0.3182874023914337,
0.0028092628344893456,
-0.1722729653120041,
0.6489636898040771,
-1.0434837341308594,
0.3369867503643036,
0.08676441758871078,
-0.2781778573989868,
-0.10713060945272446,
0.10777290910482407,
-0.5767115354537964,
-0.42961588501930237,
-0.7126929759979248,
0.10689663141965866,
1.131615400314331,
-0.6117550730705261,
0.2738547623157501,
-0.8035364747047424,
-0.16222447156906128,
0.1554332673549652,
-0.18011431396007538,
-0.3021918535232544,
-0.3779953420162201,
1.1396663188934326,
0.5246303677558899,
0.1665932685136795,
-1.1335809230804443,
0.6076700091362,
0.44956791400909424,
-0.31383776664733887,
-0.3619370460510254,
-0.13897980749607086,
-0.6724069714546204,
0.7091887593269348,
0.31241440773010254,
0.3491862416267395,
-0.04183228686451912,
0.9787482023239136,
0.821402370929718,
0.21443842351436615,
-0.11479312181472778,
-0.42301660776138306,
-0.7105395793914795,
0.5440562963485718,
0.016182949766516685,
-0.5043445229530334,
-0.4388735890388489,
0.9896215200424194,
0.1721474975347519,
-0.5850660800933838,
-0.003774042008444667,
-1.1235337257385254,
-0.2860160171985626,
-0.0011079470859840512,
-0.17973768711090088,
0.49951595067977905,
-0.18918004631996155,
-0.13192541897296906,
-0.7271823883056641,
0.19017502665519714,
1.417580008506775,
-0.15578797459602356,
0.29132044315338135,
-0.3666626513004303,
0.2866085171699524,
-0.3194987177848816,
0.5350959897041321,
0.493654727935791,
-0.3659908175468445,
-0.7748841643333435,
0.00020404985116329044,
0.4342261552810669,
-0.3320903778076172,
-0.11291981488466263,
-0.18799543380737305,
0.33645322918891907,
0.2077563852071762,
0.552406370639801,
-0.6402566432952881,
-0.1853250414133072,
-0.7948852777481079,
-0.44308555126190186,
1.076980710029602,
1.18282949924469,
-0.17583097517490387,
-0.3409471809864044,
-0.6442538499832153,
-0.42759621143341064,
0.4179771840572357,
0.15596717596054077,
0.6494547724723816,
-0.5149253606796265,
0.21176965534687042,
-0.2067084014415741,
-0.31106966733932495,
0.5528159141540527,
-0.6752129793167114,
0.4890311360359192,
0.5482099652290344,
0.5373599529266357,
0.7718208432197571,
-0.5213646292686462,
-0.4331136643886566,
-0.054706621915102005,
0.5099326968193054,
0.33729287981987,
0.532239556312561,
0.012791075743734837,
-0.031669992953538895,
0.016749238595366478,
-0.048218727111816406,
-0.4513498544692993,
-0.08285170048475266,
-0.00977387186139822,
0.10800966620445251,
0.013943408615887165,
0.6482519507408142,
-0.13108468055725098,
0.8654327392578125,
0.18779443204402924,
0.603489100933075,
0.03173243626952171,
0.7678388953208923,
0.9111326336860657,
0.7217447757720947,
0.3254584074020386,
0.17651301622390747,
0.6892564296722412,
-0.5042484402656555,
-0.16024719178676605,
0.5965202450752258,
0.7076286673545837,
-0.41528698801994324,
-0.4690539836883545,
0.15277151763439178,
-0.45553430914878845,
0.010650823824107647,
0.6019040942192078,
-1.1923567056655884,
0.5476160049438477,
-0.04032302647829056,
0.5897601842880249,
-0.7892938256263733,
0.12256382405757904,
0.7493427991867065,
0.7096692323684692,
0.41598275303840637,
-0.30111071467399597,
0.0979115217924118,
-0.25711721181869507,
0.07704010605812073,
0.39975646138191223,
-1.0650825500488281,
-0.37252235412597656,
-1.499725103378296,
0.25885456800460815,
-0.7397536635398865,
0.738756537437439,
0.5740405917167664,
0.5345956683158875,
0.3037009835243225,
-0.07483735680580139,
-0.7121687531471252,
0.40243449807167053,
-0.4304347038269043,
-0.01447518914937973,
0.27353107929229736,
-0.010255821980535984,
-0.1529887467622757,
0.8601792454719543,
0.22685064375400543,
-0.401773601770401,
0.47294872999191284,
-0.4934996962547302,
0.407920241355896,
0.07737458497285843,
-0.25997844338417053,
-0.7172148823738098,
-0.07800725847482681,
-0.5036643147468567,
-0.18687814474105835,
0.09189847111701965,
-0.05893024429678917,
-0.7622865438461304,
0.19146592915058136,
-0.1161903515458107,
0.13125167787075043,
0.2533159554004669,
-0.5827589631080627,
0.8986082673072815,
0.8451999425888062,
0.41419628262519836,
0.22750359773635864,
0.17464573681354523,
0.8265914916992188,
-0.1890626847743988,
0.2290826290845871,
0.05356699973344803,
-0.27959370613098145,
-0.24921737611293793,
-0.334105908870697,
-0.5842451453208923,
-0.5736320614814758,
-0.010936315171420574,
-0.2077106535434723,
0.5889548659324646,
0.13414333760738373,
-0.5494398474693298,
-0.6752651929855347,
-0.14397187530994415,
-0.5815579295158386,
0.350294828414917,
0.0170787014067173,
-0.12632302939891815,
0.5868873596191406,
-0.0192722100764513,
0.010896996594965458,
-0.8497620820999146,
-0.5499593019485474,
-0.3892696499824524,
0.5420404076576233,
0.85774827003479,
0.5191757678985596,
0.3599841892719269,
-0.748851478099823,
-0.15590354800224304,
-0.4848158657550812,
0.16473838686943054,
-0.5167589783668518,
-0.5139546990394592,
-0.25160592794418335,
-0.2588081657886505,
0.3474580645561218,
-0.03391382470726967,
-0.2477940022945404,
0.27391713857650757,
-0.2506338953971863,
-0.3693605661392212,
0.05186821520328522,
0.02609638310968876,
-0.4823110103607178,
0.7248208522796631,
0.4348016083240509,
-0.08096357434988022,
-0.05841854587197304,
0.3747729957103729,
-0.38343748450279236,
0.3361750543117523,
0.004508608020842075,
-0.5294344425201416,
-0.04954195022583008,
-0.2461414486169815,
0.5540683269500732,
-1.0099496841430664,
-0.746347963809967,
-0.22874470055103302,
-1.140112280845642,
0.6296166181564331,
0.4847065806388855,
0.03893391042947769,
-0.25355854630470276,
-0.8019713759422302,
-0.2261592596769333,
0.17862717807292938,
-0.217720165848732,
0.33956190943717957,
-0.8070611953735352,
-0.2787539064884186,
-0.4158824384212494,
-0.31772077083587646,
-0.5305814146995544,
0.43298372626304626,
0.15476094186306,
-0.16825158894062042,
0.47073179483413696,
0.5042492747306824,
-0.35213926434516907,
-0.2652108371257782,
-0.2860649526119232,
-0.032302793115377426,
0.00701682036742568,
0.1746288686990738,
-0.3238374590873718,
0.6707105040550232,
-0.8782221078872681,
1.01996910572052,
-0.4250219464302063,
-0.5911893844604492,
0.24268576502799988,
-0.14782944321632385,
1.0566211938858032,
-0.8519931435585022,
-0.10422465950250626,
0.1779957264661789,
-0.1730843484401703,
0.23134198784828186,
-0.3490528464317322,
-0.6423916816711426,
-0.09535031020641327,
-0.4505689740180969,
-0.7791308164596558,
-0.06788697093725204,
-0.11257266998291016,
-0.01035117357969284,
-0.4073907732963562,
-0.942319393157959,
0.14165465533733368,
0.08191141486167908,
0.4023607671260834,
0.2950500547885895,
-0.20130759477615356,
0.07747167348861694,
-0.2740730941295624,
-0.21760232746601105,
-0.30029425024986267,
0.37291279435157776,
-0.6512429118156433,
-0.046293098479509354,
0.2510480284690857,
0.7697728872299194,
-1.1606547832489014,
-0.28679776191711426,
-0.03238485008478165,
0.4132949113845825,
0.09306604415178299,
-0.24779777228832245,
0.9849018454551697,
-0.14894120395183563,
-0.1625531166791916,
-0.2550492584705353,
0.5385466814041138,
-0.25564703345298767,
0.6912922859191895,
0.13104470074176788,
0.5631695985794067,
0.5509136915206909,
0.1975984424352646,
0.7831317186355591,
-0.2326868325471878,
-0.549648106098175,
0.17929501831531525,
-0.8519222736358643,
0.07208574563264847,
-0.3293219804763794,
0.32576048374176025,
-0.854819655418396,
0.024832556024193764,
-0.3219490051269531,
0.4290614426136017,
-0.7422342300415039,
-0.4583981931209564,
-0.43514811992645264,
-0.35788217186927795,
-0.1157437413930893,
0.39957207441329956,
0.6589840054512024,
0.16629306972026825,
0.3246350586414337,
-0.3495643138885498,
-0.6183698773384094,
-0.31693270802497864,
-0.5462334156036377,
1.402994990348816,
0.46386629343032837,
-0.9619858264923096,
0.1623401641845703,
0.0472748838365078,
-0.06155843287706375,
-0.08185137063264847,
0.4208078384399414,
0.19268275797367096,
-0.23979508876800537,
0.5236088633537292,
0.0590808130800724,
0.7008768320083618,
0.8254342675209045,
-0.21984827518463135,
0.0031082641799002886,
0.1257847547531128,
-0.8859424591064453,
-0.020882511511445045,
-0.7392670512199402,
0.4801875054836273,
0.6794471144676208,
0.2304275780916214,
0.36183252930641174,
0.31911927461624146,
-0.5458394885063171,
-0.2628685534000397,
-1.090950846672058,
0.0840955525636673,
-1.2676531076431274,
-0.3077947795391083,
-0.608066737651825,
-0.07933755218982697,
0.6663900017738342,
1.2324126958847046,
-0.26349082589149475,
0.07364212721586227,
-0.44901615381240845,
-0.3553019165992737,
-0.2433391958475113,
0.3574182391166687,
-0.352691650390625,
-0.7934450507164001,
-0.2266073226928711,
0.09689123928546906,
-0.19960123300552368,
-0.4328407943248749,
-0.4226329028606415,
-0.058259498327970505,
0.15827664732933044,
-0.15824395418167114,
-0.07652520388364792,
1.101080060005188,
-1.1177664995193481,
-1.1558341979980469,
0.5015422105789185,
-0.4825705587863922,
-0.9260867238044739,
0.4897077977657318,
-0.01202593557536602,
0.8682230114936829,
0.6544904112815857,
0.5163017511367798,
-0.70064777135849,
0.5481862425804138,
-0.9154438376426697,
-0.2020559310913086,
0.0931386947631836,
0.41218724846839905,
0.21863846480846405,
-0.44898200035095215,
-0.026931503787636757,
0.1728297919034958,
-0.7765517234802246,
0.3505875766277313,
-0.10770153254270554,
0.7544054985046387,
-0.7262723445892334,
0.1363592892885208,
0.01182633638381958,
0.2993217706680298,
-0.11607072502374649,
1.0101594924926758,
-0.22257326543331146,
-0.6918498277664185,
-0.17620305716991425,
-0.1277991682291031,
-0.04875528812408447,
0.4195583462715149,
0.42117422819137573,
-0.33574947714805603,
-0.9115532040596008,
0.5829229354858398,
-0.23373551666736603,
0.38819944858551025,
-0.3968222439289093,
-0.6391189694404602,
-0.2334439903497696,
-0.6696870923042297,
-0.32120949029922485,
0.43536242842674255,
0.2796591818332672,
-0.561846911907196,
0.012768605723977089,
-0.5253925323486328,
-0.4159111976623535,
0.3194792568683624,
-0.9064183831214905,
-0.4883333444595337,
0.07961209863424301,
-0.6384771466255188,
0.03514363244175911,
0.7096796631813049,
-0.2823469340801239,
-0.061097774654626846,
0.05417522415518761,
0.9398660659790039,
-0.6877442598342896,
-0.49041658639907837,
-0.4007853865623474,
0.4955124855041504,
-1.0832488536834717,
-0.2507762014865875,
-0.6052521467208862,
0.5249293446540833,
-0.49681663513183594,
-0.7426095604896545,
0.18362456560134888,
0.21002905070781708,
-0.1450645625591278,
0.3521754741668701,
-0.1109398677945137,
-0.6043583154678345,
-0.1227656826376915,
0.11344357579946518,
-0.8499863743782043,
0.04690024256706238,
-0.609494686126709,
0.31332406401634216,
-0.2118019163608551,
-0.11679751425981522,
0.15819811820983887,
0.8633893132209778,
0.05569063872098923,
0.2304370254278183,
0.07059038430452347,
0.936899721622467,
0.16805525124073029,
-0.4329192638397217,
0.2679964005947113,
0.27964797616004944,
0.18663378059864044,
0.27734076976776123,
-0.9814221858978271,
0.11792320013046265,
0.439611554145813,
0.2868172526359558,
0.6034497022628784,
0.27231481671333313,
0.4392431378364563,
0.24540191888809204,
0.6025227904319763,
0.31692996621131897,
-0.12534235417842865,
0.49155837297439575,
0.8517769575119019,
-0.2717926502227783,
-0.026534810662269592,
0.5092722773551941,
0.160920187830925,
0.4304335117340088,
-0.20140033960342407,
-0.05566135048866272,
-0.38602572679519653,
-0.1082804724574089,
-0.27775096893310547,
0.2285613864660263,
0.3015327453613281,
-0.34884217381477356,
-0.16339151561260223,
-0.011938332580029964,
0.5521655082702637,
-0.07259120047092438,
-0.25015997886657715,
0.5140161514282227,
0.7722005248069763,
-0.1084493100643158,
-0.2539428770542145,
0.4979860782623291,
-0.157124325633049,
1.2148480415344238,
0.5059409141540527,
0.9084192514419556,
0.6462284326553345,
1.1424206495285034,
-0.07777228206396103,
-0.4484868347644806,
-0.1220732033252716,
0.7209082841873169,
-0.7877217531204224,
0.23632961511611938,
-0.5314565896987915,
0.37118807435035706,
0.052121810615062714,
-0.7564490437507629,
0.4962729215621948,
0.15681472420692444,
0.08503583818674088,
0.16042311489582062,
-0.22767116129398346,
-0.4602713882923126,
1.2266687154769897,
0.08747420459985733,
0.40066638588905334,
0.7130120396614075,
-0.20474930107593536,
0.3321033716201782,
0.9914553165435791,
1.3951553106307983,
-0.45176172256469727,
0.2640538811683655,
0.20472446084022522,
-0.2829625606536865,
0.057374294847249985,
0.5362036824226379,
-0.4677378535270691,
-0.26046013832092285,
-0.8823938369750977,
-0.17136117815971375,
0.8276623487472534,
0.08583270013332367,
-0.038318030536174774,
-0.31846052408218384,
0.6044076681137085,
0.09284605085849762,
-0.15996666252613068,
-0.3232227861881256,
1.600992202758789,
0.22486695647239685,
-0.5230323076248169,
-0.22559453547000885,
0.37730520963668823,
-0.6727370023727417,
-0.06600351631641388,
-1.1562587022781372,
0.5795310735702515,
-0.27266725897789,
-0.5112061500549316,
-0.38388538360595703,
-0.4020548462867737,
-0.28139522671699524,
-0.9977011680603027,
-0.07524167746305466,
-0.4054670035839081,
-0.019121766090393066,
0.9192274808883667,
-0.06270729750394821,
0.5308853983879089,
-0.9039156436920166,
-0.025672292336821556,
-0.3386979401111603,
1.0031641721725464,
0.008301856927573681,
0.2616513967514038,
1.0715652704238892,
0.7091039419174194,
-0.3534829020500183,
0.17305105924606323,
1.3818508386611938,
-0.8672695755958557,
0.7957053780555725,
-0.34604284167289734,
0.8353005051612854,
0.2113174945116043,
-0.2940373122692108,
0.40019485354423523,
0.24193882942199707,
-0.24038785696029663,
0.15881042182445526,
-0.1171138808131218,
-0.4569679796695709,
-0.4065702259540558,
0.3359677493572235,
-0.8140978217124939,
0.13100086152553558,
-0.5175046920776367,
-0.094569131731987,
-0.03243489935994148,
-0.7085351347923279,
4.030216693878174,
0.5086555480957031,
0.65042644739151,
0.4945221245288849,
0.5008835792541504,
0.7223250865936279,
-0.654708981513977,
-0.09451249986886978,
0.05509836971759796,
-1.0597867965698242,
-0.7122533917427063,
0.0023912396281957626,
-0.4914446771144867,
0.24894629418849945,
-0.11115708947181702,
0.9575130939483643,
-0.3587736189365387,
-0.050491154193878174,
-0.22885756194591522,
-1.2667019367218018,
-1.2469080686569214,
0.06169944629073143,
0.4347477853298187,
-0.3290179371833801,
-0.1077144667506218,
-0.018351320177316666,
-0.28797483444213867,
-0.6470677852630615,
-0.3860846161842346,
-0.3370426595211029,
-0.4240950345993042,
-1.1195642948150635,
0.1871737539768219,
0.22407275438308716,
-0.7763515114784241,
0.0004883870133198798,
0.003379636211320758,
0.09089454263448715,
-0.5497045516967773,
0.20088626444339752,
-0.21220862865447998,
-0.7631524801254272,
0.1391972303390503,
-0.6525768041610718,
-0.07126182317733765,
1.2486993074417114,
-0.591298520565033,
0.9365914463996887,
0.2664228677749634,
-0.8902567028999329,
0.3773871958255768,
-0.1617390662431717,
0.4429965615272522,
-0.4799399971961975,
-0.5552771091461182,
0.2798909544944763,
-0.22354920208454132,
0.16333003342151642,
0.32338666915893555,
0.4150996506214142,
-0.046425823122262955,
-0.27942991256713867,
0.19659370183944702,
0.13620877265930176,
-0.17798452079296112,
0.29108381271362305,
-0.06891069561243057,
0.5156474709510803,
-0.42602938413619995,
0.5068424344062805,
-0.3391144573688507,
-0.6384275555610657,
-0.19238761067390442,
0.004755128175020218,
0.0758623257279396,
0.18302372097969055,
-0.400359570980072,
0.19461442530155182,
0.21642562747001648,
-0.27614346146583557,
0.31529656052589417,
-0.46955740451812744,
-0.17295995354652405,
-0.6375208497047424,
-0.07822374254465103,
0.26984167098999023,
-0.21076571941375732,
0.4945831894874573,
-0.06232688948512077,
0.5039055943489075,
0.663645327091217,
1.2590683698654175,
0.5836876630783081,
0.2023526281118393,
-0.5075938701629639
] |
Basis States for Hamiltonian QCD with Dynamical Quarks
|
We discuss the construction of basis states for Hamiltonian QCD on the lattice, in particular states with dynamical quark pairs. We calculate the matrix elements of the operators in the QCD Hamiltonian between these states. Along with the ``harmonic oscillator'' states introduced in previous pure SU(3) work, these states form a working basis for calculations in full QCD.
|
Timothy E. Vaughan
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210006
|
hep-lat/9210007
|
[
0.5839031934738159,
-0.5705583095550537,
-0.10428543388843536,
0.5588753819465637,
-0.35561230778694153,
-0.3397045433521271,
-0.14855247735977173,
-0.5173173546791077,
-0.9249919056892395,
1.5998148918151855,
0.46713322401046753,
0.1634259968996048,
-0.019997689872980118,
-0.990132212638855,
-0.36886438727378845,
0.46292930841445923,
0.2510264813899994,
-0.20995458960533142,
-1.7307957410812378,
0.8056747317314148,
0.05942485108971596,
-0.0013911642599850893,
-1.3930357694625854,
0.15578801929950714,
-0.3222934901714325,
0.8526264429092407,
0.2776291072368622,
0.7433272004127502,
0.8769213557243347,
0.16539369523525238,
0.2566118836402893,
-0.10084991157054901,
-0.5873773694038391,
-0.26558372378349304,
-0.36806005239486694,
-0.3600284159183502,
0.0323680117726326,
-0.47073957324028015,
0.9885854125022888,
-0.05905469134449959,
0.8868847489356995,
-0.4183539152145386,
0.002229915466159582,
-0.8387575745582581,
-0.8601267337799072,
0.4099317789077759,
-0.027361642569303513,
0.20165777206420898,
0.22170676290988922,
-1.4596967697143555,
0.24449990689754486,
0.08289987593889236,
0.9607266187667847,
-0.8903167843818665,
-0.41648784279823303,
-0.10845369845628738,
0.04650280624628067,
0.12953774631023407,
-0.8566185832023621,
-0.5255179405212402,
0.2421504110097885,
-0.39843469858169556,
0.45159628987312317,
-0.27673399448394775,
-0.4266730546951294,
0.8890742659568787,
-0.2517564296722412,
0.7374208569526672,
-0.07809843868017197,
-0.6001219153404236,
-0.04387499392032623,
-0.12139341235160828,
-1.0164790153503418,
0.08573997765779495,
-0.9041569828987122,
0.11275684833526611,
-0.059501852840185165,
-0.30095237493515015,
-0.523231029510498,
-0.034625809639692307,
0.18086181581020355,
0.23356622457504272,
-0.2460046410560608,
0.24886110424995422,
-0.4384247362613678,
-0.4414273202419281,
-0.05674232915043831,
-0.4391856789588928,
0.11294665187597275,
0.5621159672737122,
-0.4313560128211975,
0.5484354496002197,
-1.0522503852844238,
-0.22711463272571564,
0.4639204144477844,
0.4649794101715088,
0.038038257509469986,
0.2439674586057663,
0.010332618840038776,
0.12349485605955124,
-0.16094458103179932,
0.9233962893486023,
-0.8676772713661194,
0.14377032220363617,
-0.7056081891059875,
0.5912787914276123,
-0.12109903246164322,
0.4634720981121063,
-0.40809786319732666,
-0.9483668208122253,
-0.09435122460126877,
-0.41493892669677734,
0.7734149098396301,
0.682426393032074,
0.25472110509872437,
0.6084718108177185,
-0.5156965851783752,
0.16778942942619324,
-0.5741932988166809,
-0.22659912705421448,
0.39872288703918457,
-0.3151836097240448,
0.3084406852722168,
0.877140998840332,
-0.3015625476837158,
-0.1642499417066574,
0.15299542248249054,
0.09873826056718826,
-0.2713300585746765,
0.3710188865661621,
0.4325418770313263,
-0.46539077162742615,
-0.5233411192893982,
0.36239778995513916,
-0.42433133721351624,
0.5587403774261475,
0.07885348051786423,
0.08988992124795914,
0.2308310568332672,
0.04371774569153786,
0.7867885231971741,
-0.13527555763721466,
-0.014718715101480484,
1.3084807395935059,
0.6708205938339233,
-0.13199424743652344,
0.7086124420166016,
0.5712952613830566,
-0.43113258481025696,
1.0095138549804688,
-0.4631202518939972,
0.11783435195684433,
0.23133882880210876,
0.31960082054138184,
0.09687274694442749,
0.3207953870296478,
-0.815260112285614,
0.26637327671051025,
-0.5650392174720764,
-0.49125829339027405,
0.02199424058198929,
0.054631926119327545,
-0.30635160207748413,
0.222708061337471,
0.22142264246940613,
0.18086041510105133,
-0.5490161180496216,
-0.49783551692962646,
0.8154914379119873,
-0.47925636172294617,
-0.4864581227302551,
0.7982375621795654,
0.04985669255256653,
1.4176690578460693,
0.747235119342804,
0.6676777005195618,
0.41809260845184326,
-0.3031611144542694,
-0.08347967267036438,
0.6775270700454712,
-0.3575091063976288,
-0.37552762031555176,
0.2015591859817505,
0.04772045090794563,
-0.5541427731513977,
0.3097238540649414,
-0.21617461740970612,
-0.47152650356292725,
0.08952188491821289,
0.36774224042892456,
-0.5252724885940552,
0.5444068312644958,
-0.28877514600753784,
0.2974230647087097,
-0.43133094906806946,
0.06459944695234299,
-1.1849545240402222,
0.4306025803089142,
-0.6223489046096802,
-0.34678781032562256,
0.2309103161096573,
0.19566282629966736,
-0.9498631358146667,
0.242001473903656,
-1.0888638496398926,
-0.08408556878566742,
0.940858006477356,
0.10694421827793121,
-0.07228849828243256,
-0.22036582231521606,
0.5967658758163452,
-0.356581449508667,
0.05809018760919571,
0.07316941767930984,
0.5081031322479248,
-0.3797421157360077,
-0.29011279344558716,
0.46789807081222534,
0.5098809003829956,
0.49250802397727966,
0.2877149283885956,
0.27283841371536255,
-0.055569443851709366,
0.9472565054893494,
-0.6363429427146912,
-0.6719437837600708,
0.2252899408340454,
0.4740481972694397,
0.284810334444046,
-0.1318369060754776,
0.3259216845035553,
0.7038169503211975,
0.38052505254745483,
0.26415684819221497,
0.4888745844364166,
0.08151642233133316,
0.7792884111404419,
0.30559197068214417,
0.5633775591850281,
-0.034665461629629135,
-0.2745434641838074,
-0.09564226865768433,
0.21381694078445435,
0.07798143476247787,
-0.6895025372505188,
0.12444678694009781,
-0.6225048899650574,
0.026222437620162964,
-0.909119725227356,
-0.001265998580493033,
-0.41704636812210083,
0.7399123311042786,
0.047246403992176056,
0.5767868757247925,
-1.6493943929672241,
0.0130008514970541,
-0.5630857348442078,
-0.020592212677001953,
-0.25251802802085876,
-0.28412890434265137,
0.33432191610336304,
-0.019666574895381927,
-0.3221285045146942,
-0.6724085807800293,
-0.35322707891464233,
0.719346821308136,
-0.05665166303515434,
0.06772304326295853,
1.1583340167999268,
-0.17401668429374695,
-0.9655317068099976,
0.08858706057071686,
-0.9153217673301697,
0.17378118634223938,
-0.3855028748512268,
0.42760199308395386,
0.6078364253044128,
-0.6194457411766052,
0.5413789749145508,
0.4002855122089386,
-0.08142010867595673,
0.5100336074829102,
-0.7573383450508118,
0.0067221312783658504,
-0.2048986703157425,
-0.18968084454536438,
-0.7774131298065186,
0.5239433646202087,
-0.8356872200965881,
-0.522914707660675,
0.007685077376663685,
0.3153420090675354,
0.43933629989624023,
-0.35421445965766907,
0.26287642121315,
0.10332523286342621,
-0.2263171672821045,
0.24830663204193115,
0.11366880685091019,
-0.6571844220161438,
0.19918841123580933,
0.3148491680622101,
-0.5980545878410339,
-0.557659924030304,
-1.169919490814209,
0.7016502618789673,
0.5497947335243225,
-0.4010568857192993,
0.17933937907218933,
-0.03597085177898407,
-0.30094102025032043,
0.20387394726276398,
0.3504686653614044,
0.011625571176409721,
-0.15587808191776276,
1.0150787830352783,
0.7494147419929504,
0.17683231830596924,
-0.037578973919153214,
-0.2904614210128784,
-0.29027360677719116,
0.2853733003139496,
0.436724990606308,
-0.4864312708377838,
0.12661151587963104,
0.7204994559288025,
-0.45102575421333313,
-0.43106263875961304,
0.9455115795135498,
-1.2358646392822266,
-0.5032474398612976,
0.11598845571279526,
-0.4183635115623474,
-0.34546157717704773,
0.12779800593852997,
0.011168223805725574,
-1.0735174417495728,
-0.5350565910339355,
-0.5206332206726074,
0.1535799652338028,
0.318780779838562,
-0.2744506299495697,
0.23195047676563263,
0.21607862412929535,
0.5065914988517761,
-0.6874296069145203,
0.26475489139556885,
-0.31160295009613037,
-0.521346390247345,
-0.17810586094856262,
-0.46994656324386597,
-0.13662733137607574,
-0.07985691726207733,
0.13935714960098267,
-0.07715505361557007,
0.3366662263870239,
-0.6952912211418152,
-0.2683994174003601,
-1.0456173419952393,
-0.4705255925655365,
-0.2587703466415405,
0.7733715176582336,
0.3239721655845642,
-0.28323113918304443,
-0.5512022376060486,
-0.2868973910808563,
0.25343799591064453,
0.07914668321609497,
0.5975729823112488,
-0.7054386734962463,
0.43397510051727295,
-0.1486431062221527,
-0.24315805733203888,
0.017983870580792427,
-0.18983565270900726,
0.5011163353919983,
0.7229462265968323,
-0.3103705644607544,
0.762518584728241,
-0.3154453635215759,
-0.8046170473098755,
0.22271667420864105,
0.7622737884521484,
0.7128396034240723,
1.183773159980774,
0.04583760350942612,
0.25796258449554443,
0.07886300981044769,
-0.23867063224315643,
-0.2765846848487854,
-0.6230319142341614,
-0.5582929849624634,
0.2720014154911041,
0.045691028237342834,
0.11515740305185318,
0.2695389986038208,
0.029431505128741264,
0.5727094411849976,
0.19312943518161774,
0.14057670533657074,
0.35894474387168884,
0.012475347146391869,
0.64291912317276,
0.3716300129890442,
0.07615078240633011,
0.05549757927656174,
-0.3701402246952057,
-0.1874832957983017,
0.36001765727996826,
0.14390605688095093,
-0.09222567081451416,
-0.7690317034721375,
-0.4161292314529419,
-0.31212151050567627,
0.41646718978881836,
-0.040871161967515945,
-1.0242658853530884,
-0.021733352914452553,
0.35199105739593506,
0.09111432731151581,
-0.19773830473423004,
0.15379929542541504,
0.5694183707237244,
0.13744601607322693,
0.2424299418926239,
-1.1148860454559326,
0.4593013525009155,
-0.2261098027229309,
0.4050810635089874,
0.32694172859191895,
-0.5197661519050598,
-0.4064967632293701,
-0.6739052534103394,
0.22659184038639069,
-0.15363000333309174,
0.32393577694892883,
0.8220584988594055,
0.26770851016044617,
0.04454731568694115,
-1.1483466625213623,
-0.028467806056141853,
0.9190078377723694,
-0.18612851202487946,
-0.03854251652956009,
0.21594984829425812,
0.06681245565414429,
-0.4712578356266022,
0.8380246758460999,
-0.8281376361846924,
-0.21255463361740112,
-0.21300169825553894,
-0.8655429482460022,
-0.07997004687786102,
-0.5104532837867737,
-0.18443506956100464,
0.47644442319869995,
-0.5139097571372986,
-0.23913313448429108,
0.41714078187942505,
0.15036530792713165,
-0.35427048802375793,
0.3623041808605194,
0.286165714263916,
-0.12078574299812317,
0.269461452960968,
-0.36219558119773865,
0.4489729106426239,
0.41877591609954834,
0.7560789585113525,
0.9934535622596741,
0.46575939655303955,
0.0013914386508986354,
-0.029823625460267067,
0.12380639463663101,
0.014433288015425205,
-0.5902504324913025,
-0.524590253829956,
-0.5715843439102173,
-0.4613707661628723,
-1.0121766328811646,
-0.5499512553215027,
0.3772898316383362,
0.1115889698266983,
0.3661775588989258,
0.5020878911018372,
-0.396236389875412,
-0.5907176733016968,
-0.9139650464057922,
-0.5956922173500061,
0.5844109058380127,
-0.4025660753250122,
-0.31987905502319336,
0.7336837649345398,
-0.4744914770126343,
-0.29095780849456787,
-0.21706552803516388,
0.01829323172569275,
-0.42379724979400635,
0.26683205366134644,
0.3771333396434784,
0.23726779222488403,
0.6553541421890259,
-0.508343517780304,
0.8538523316383362,
-0.1728660613298416,
-0.15813800692558289,
-0.48971009254455566,
-0.8006716370582581,
-0.6157063245773315,
-0.3819864094257355,
0.9674040079116821,
-0.18837057054042816,
-0.08464935421943665,
0.13324014842510223,
-0.13122984766960144,
0.42580798268318176,
-0.24117305874824524,
-0.7552715539932251,
0.07528264820575714,
0.35330837965011597,
0.052346404641866684,
-0.06028411164879799,
0.03644415736198425,
0.8092079758644104,
0.7708930969238281,
0.32978737354278564,
0.07458124309778214,
-0.1911531686782837,
0.23448650538921356,
-0.267557293176651,
0.36831676959991455,
-0.5960608124732971,
-0.08189156651496887,
0.1633237600326538,
0.06130095571279526,
0.24895386397838593,
0.17482590675354004,
0.009396291337907314,
-0.7836883664131165,
-0.9978077411651611,
-0.4772178828716278,
0.7324079871177673,
-0.09837748855352402,
-0.31957677006721497,
-0.4899424612522125,
-0.5452207326889038,
-0.21881084144115448,
1.289648175239563,
-0.3310481011867523,
0.7242921590805054,
0.013877248391509056,
-0.44256892800331116,
0.07659482955932617,
0.30478447675704956,
0.2604537010192871,
-0.12871284782886505,
0.06814884394407272,
0.4696663022041321,
0.18584737181663513,
0.6063278317451477,
-0.4488469958305359,
0.17740698158740997,
-0.9794244170188904,
1.0723600387573242,
-0.5614572167396545,
0.11479934304952621,
0.020819105207920074,
0.4791366457939148,
0.8076809048652649,
-0.8749620914459229,
0.6533118486404419,
0.7661757469177246,
0.06729493290185928,
0.41020384430885315,
0.22059044241905212,
-0.053941089659929276,
-0.2461964190006256,
-0.9399885535240173,
-0.3168017864227295,
0.3730494976043701,
0.19395774602890015,
-0.05572494864463806,
-0.8485375046730042,
-0.5321025848388672,
0.36808326840400696,
-0.20524774491786957,
0.5039259195327759,
0.5039307475090027,
0.14331325888633728,
0.02197529375553131,
0.415500283241272,
-0.21442705392837524,
-0.5886899828910828,
-0.13493399322032928,
-0.18158429861068726,
0.2346450686454773,
0.03247036784887314,
0.36844074726104736,
-0.527426540851593,
-0.4068845212459564,
-0.3489971160888672,
0.40017232298851013,
0.25579753518104553,
-0.7736459374427795,
1.134910225868225,
0.2088288813829422,
-0.6539834141731262,
-0.32169005274772644,
-0.13109619915485382,
0.0620499812066555,
0.05597122758626938,
0.6013411283493042,
0.27922484278678894,
-0.05789976567029953,
0.17520098388195038,
0.43790876865386963,
-0.39871537685394287,
-0.8060940504074097,
0.7381047606468201,
-0.9097859263420105,
0.05288907513022423,
0.4557464122772217,
-0.14453312754631042,
-0.6234296560287476,
-0.49263057112693787,
-1.4641581773757935,
-0.196150541305542,
-0.5347017645835876,
-0.4062776565551758,
0.006340491585433483,
-0.39813026785850525,
-0.2257622629404068,
0.21633127331733704,
0.6184954047203064,
0.11329995840787888,
0.7355250716209412,
-0.16795682907104492,
-0.13061527907848358,
0.41001078486442566,
0.17686043679714203,
1.1083561182022095,
0.42936983704566956,
-0.546843945980072,
0.245416060090065,
0.13903263211250305,
-0.2996765375137329,
0.2033536732196808,
0.8165057897567749,
-0.3739650547504425,
-0.015335028991103172,
-0.2960081398487091,
-0.3239026963710785,
0.1539418250322342,
0.8634719252586365,
0.1539977341890335,
-0.25424233078956604,
-0.47221851348876953,
-0.5395951867103577,
0.391029417514801,
-0.7863869667053223,
0.5200786590576172,
1.0879266262054443,
0.48871085047721863,
0.23462866246700287,
-0.22285087406635284,
-0.1768159121274948,
-0.32657524943351746,
-1.152686357498169,
-0.20565618574619293,
-1.5321701765060425,
-0.386766642332077,
-0.26407623291015625,
-0.2901534140110016,
0.1745365709066391,
0.2711385488510132,
-0.3011206090450287,
-0.3678261339664459,
-0.9581307172775269,
0.5337346196174622,
0.2046440988779068,
0.8215208053588867,
-0.3438352346420288,
-0.5975690484046936,
-0.23288820683956146,
0.4409400522708893,
-0.11723491549491882,
-0.1619609296321869,
-0.40480837225914,
-0.5811214447021484,
0.2573544979095459,
0.6656032204627991,
-0.4665537178516388,
0.676062285900116,
-0.7894852757453918,
-0.47137564420700073,
-0.06646846979856491,
-0.27193683385849,
-0.9683642983436584,
0.7843151688575745,
0.37811240553855896,
0.9967226982116699,
0.6638360619544983,
-0.26577502489089966,
-0.5989068746566772,
0.5429379343986511,
-0.6061320304870605,
0.30333471298217773,
0.07695478945970535,
0.5666331648826599,
-0.31257036328315735,
-0.531309962272644,
-0.32763785123825073,
0.41856181621551514,
-0.7713567018508911,
0.544826090335846,
-0.8467774987220764,
0.4416656196117401,
-0.5162245035171509,
0.1900295466184616,
0.7851295471191406,
-0.1573694944381714,
-0.38945305347442627,
0.921441376209259,
-0.33282971382141113,
-0.08305487781763077,
-0.25669705867767334,
0.2764092981815338,
-0.5044540166854858,
-0.10324829816818237,
0.1586582511663437,
-0.3118787407875061,
-0.1331084668636322,
0.5539455413818359,
-0.3740774095058441,
0.3995836675167084,
-0.06208646669983864,
-0.8012821078300476,
-0.262660950422287,
0.10853803902864456,
-0.6262202858924866,
0.42916205525398254,
0.6303315162658691,
-0.2980157732963562,
-0.37209248542785645,
-0.6130518913269043,
-0.6904616355895996,
0.2623513340950012,
-0.32383888959884644,
-0.07027736306190491,
-0.08661222457885742,
0.35528212785720825,
-0.02668088860809803,
0.6688264608383179,
-0.3127489984035492,
0.1766795665025711,
-0.038824860006570816,
0.5198125839233398,
-0.23407913744449615,
0.05900206416845322,
-0.518494188785553,
0.3247741460800171,
-0.7248102426528931,
0.01630263403058052,
-0.653142511844635,
0.2731074094772339,
-1.0579673051834106,
-0.7718673944473267,
-0.1845775991678238,
0.6316620707511902,
0.16294941306114197,
-0.04939591512084007,
0.20733100175857544,
0.019417088478803635,
-0.3082602918148041,
0.18083764612674713,
-0.43207767605781555,
-0.010608499869704247,
-0.14658892154693604,
0.534064769744873,
0.08500280231237411,
-0.7351974248886108,
0.33566465973854065,
-0.14560171961784363,
0.22762040793895721,
-0.593442976474762,
-0.011781839653849602,
0.9691886305809021,
0.24116244912147522,
0.28380411863327026,
0.0781332477927208,
0.1443425863981247,
-0.04976659640669823,
0.36530184745788574,
-0.7309020757675171,
0.209172785282135,
0.08922436088323593,
0.18355439603328705,
0.6732708215713501,
-0.14311787486076355,
0.5615590810775757,
0.4476950168609619,
-0.01865110546350479,
0.035761184990406036,
-0.11649017035961151,
0.008869776502251625,
0.5940085649490356,
0.6171441674232483,
0.2640092372894287,
-0.08512619137763977,
0.33556652069091797,
-0.5063067674636841,
0.29564934968948364,
-0.36948710680007935,
-0.6590913534164429,
-0.6630389094352722,
-0.02849208563566208,
-0.17165139317512512,
-0.6012341976165771,
-0.5807263255119324,
0.39225074648857117,
-0.23538082838058472,
0.3060570955276489,
0.2963022291660309,
-0.2929456830024719,
0.3792349100112915,
0.6430702805519104,
0.05812116339802742,
0.24251775443553925,
0.5592880249023438,
-0.16256217658519745,
1.2000398635864258,
0.7893147468566895,
0.17084088921546936,
0.36253491044044495,
0.5943588018417358,
0.2174982726573944,
-0.8544560074806213,
0.162088081240654,
0.4993414580821991,
-0.9383366107940674,
0.791693389415741,
-0.34425821900367737,
-0.1130707785487175,
-0.43393784761428833,
-0.2990158200263977,
0.425963819026947,
-0.5751837491989136,
0.26995980739593506,
0.7991808652877808,
-0.587040901184082,
0.4468876123428345,
0.8954960107803345,
0.07270245999097824,
0.4105452001094818,
0.5158133506774902,
-0.27288952469825745,
0.3505898118019104,
1.1472612619400024,
1.1426409482955933,
-0.048789650201797485,
0.20243923366069794,
0.24859242141246796,
-0.16918295621871948,
0.5395708084106445,
0.4257640242576599,
-0.18275104463100433,
0.22549866139888763,
-1.0133916139602661,
-0.5046501159667969,
-0.3328086733818054,
0.3121365010738373,
-0.04257956147193909,
-0.41193529963493347,
0.06174446642398834,
-0.34234321117401123,
-0.9787946939468384,
-0.5115528702735901,
1.4298385381698608,
0.08311005681753159,
-0.4035145342350006,
-0.34653568267822266,
0.016242891550064087,
-0.5456342101097107,
0.038011111319065094,
-0.5130061507225037,
-0.005351739004254341,
-0.5492630004882812,
-0.13889451324939728,
0.21861979365348816,
-0.7986177802085876,
-1.0332123041152954,
-0.937848687171936,
-0.08524847775697708,
-0.7427162528038025,
0.8388029336929321,
0.19287963211536407,
0.8149445652961731,
-0.21572832763195038,
-0.6787179112434387,
-0.4044378995895386,
-0.12892283499240875,
0.4286762773990631,
-0.09056252241134644,
-0.14606943726539612,
0.7099179029464722,
-0.24596258997917175,
-0.7428614497184753,
0.39022329449653625,
0.9132636189460754,
-0.4413284659385681,
0.5105791091918945,
-0.4260145127773285,
0.30022990703582764,
0.6050596237182617,
0.10210191458463669,
0.04187416285276413,
-0.37182316184043884,
0.6314787268638611,
0.615583598613739,
-0.5275753736495972,
-0.22861269116401672,
-0.6447619795799255,
-0.05430066958069801,
-0.19579119980335236,
0.413286417722702,
0.20238204300403595,
0.26176711916923523,
0.2130848914384842,
-0.7924762964248657,
4.275136947631836,
0.5705883502960205,
0.4472943842411041,
0.20322424173355103,
0.2526358664035797,
0.6063626408576965,
-0.07286596298217773,
-0.811732828617096,
-0.1279505044221878,
-0.44145312905311584,
-0.17356298863887787,
0.43810486793518066,
0.5258665084838867,
0.08019128441810608,
0.21514616906642914,
0.7517417073249817,
0.06208563223481178,
-0.3076625168323517,
-0.07578209042549133,
-0.3599306643009186,
-0.1918802112340927,
-0.03866792470216751,
0.5962944626808167,
0.2922378480434418,
0.27099311351776123,
0.0990777537226677,
-0.05598931387066841,
-0.6168873906135559,
-0.8481476306915283,
-0.7407525181770325,
-0.4795306921005249,
-0.8028218746185303,
0.5628769993782043,
-0.3581681251525879,
-0.5252220034599304,
0.3065582513809204,
0.2506132125854492,
-0.520704984664917,
0.16047810018062592,
0.4004899561405182,
0.0804060623049736,
-0.40822380781173706,
0.43775972723960876,
-0.3488196134567261,
-0.17359915375709534,
0.928036093711853,
0.2336723357439041,
0.9703301787376404,
0.7291625738143921,
-0.7064118385314941,
0.23390786349773407,
0.10785260051488876,
0.44538062810897827,
-0.6862854361534119,
-0.7355489134788513,
0.08459951728582382,
-0.9260158538818359,
0.22908146679401398,
0.05811772868037224,
0.11159215122461319,
0.14164461195468903,
-0.4884243607521057,
-0.1455075740814209,
0.2259458303451538,
-0.03590372949838638,
0.3792685270309448,
0.01767902635037899,
0.608596682548523,
-0.0887252688407898,
-0.36840346455574036,
0.029240291565656662,
-0.7009814381599426,
-0.5699377655982971,
0.21077178418636322,
0.3172776699066162,
0.1757785677909851,
0.10896682739257812,
0.5492445826530457,
0.6694716811180115,
0.42393481731414795,
0.1581108272075653,
-0.14819441735744476,
-0.4999483823776245,
0.16463084518909454,
-0.10534332692623138,
0.8273976445198059,
-0.43433573842048645,
-0.2556539475917816,
-0.223131462931633,
0.49540087580680847,
0.339044451713562,
1.1759262084960938,
-0.48248186707496643,
0.0658569484949112,
-0.5955418944358826
] |
The infrared limit of QCD effective string
|
Some model-independent properties of the effective string of gauge field systems in the confining phase , for very large quark separations, are described in terms of two-dimensional conformal field theories. The constraints induced by the gauge theory at the boundaries of the effective string induce a Coulomb- like term in the interquark potential which is universal, but different from the one proposed by L\"uscher. Some universal relations among the string tension, the thickness of the colour flux tube, the location of the deconfining temperature and a lower bound of the glueball spectrum are discussed. (Lectures given at the XXXII Cracow School of Theoretical Physics, Zakopane, Poland 2-12 June 1992)
|
F.Gliozzi
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210007
|
hep-lat/9210008
|
[
0.06996652483940125,
-0.24018771946430206,
0.3049847185611725,
0.11197429150342941,
0.3358036279678345,
-0.07062280178070068,
0.03349746763706207,
-0.2489006072282791,
-0.21891701221466064,
0.9424819946289062,
0.9236177206039429,
0.4730808436870575,
0.37357622385025024,
-0.6692413091659546,
-0.36245328187942505,
0.5943037271499634,
-0.2158331722021103,
-0.13998572528362274,
-1.5927727222442627,
0.8574392795562744,
0.36184850335121155,
-0.1970842033624649,
-1.0774365663528442,
-0.47016918659210205,
-0.29678165912628174,
0.9205232858657837,
0.44390955567359924,
0.6614195704460144,
1.0124664306640625,
0.7234840989112854,
0.51028972864151,
-0.42928025126457214,
-0.16070656478405,
0.11576608568429947,
-0.3420994281768799,
-0.09943056851625443,
-0.6748999357223511,
0.21099267899990082,
0.39244627952575684,
-0.6668562293052673,
0.6092396378517151,
-0.4980475902557373,
0.2535311281681061,
-0.5662720799446106,
-0.2548566162586212,
0.23610833287239075,
0.03274138271808624,
-0.06227592006325722,
0.08262713998556137,
-1.1719948053359985,
-0.3139144778251648,
0.3683655858039856,
0.19182954728603363,
-0.789253294467926,
-0.7230252027511597,
0.1090569719672203,
0.2543174624443054,
0.12694299221038818,
-0.7153942584991455,
-0.2658332884311676,
0.4614070653915405,
0.11240220069885254,
0.02675945870578289,
-0.6277123689651489,
-0.18504241108894348,
0.7194209098815918,
-0.10510987043380737,
0.595270037651062,
0.2737281918525696,
-0.5804247260093689,
-0.7045745253562927,
-0.14224162697792053,
-0.574793815612793,
0.0057145883329212666,
-0.9567497372627258,
0.6805314421653748,
-0.4960598945617676,
-0.38759079575538635,
-0.8329730033874512,
-0.6930502653121948,
0.4844963252544403,
0.4805406630039215,
-0.676994800567627,
0.15005835890769958,
-0.24670255184173584,
-0.5294535160064697,
0.39822420477867126,
-0.20572349429130554,
0.2300543636083603,
0.045911721885204315,
0.41269004344940186,
0.8390887379646301,
-0.02409840002655983,
-0.5084985494613647,
0.5812802314758301,
0.7551448345184326,
-0.2729170620441437,
0.9198310971260071,
0.7138764262199402,
0.11803001165390015,
0.0064544775523245335,
0.38674864172935486,
-0.37221434712409973,
0.07397548854351044,
-0.8279839754104614,
-0.04449249431490898,
-0.5835574865341187,
0.32299160957336426,
-0.3813210725784302,
-0.9481956362724304,
0.2439097762107849,
-0.3408959209918976,
0.7437613010406494,
1.0699282884597778,
0.7560911178588867,
0.5315066576004028,
-0.2578369677066803,
0.311301589012146,
-0.23314300179481506,
-0.7708736658096313,
-0.053809959441423416,
0.40686601400375366,
0.4167065918445587,
0.41961222887039185,
-0.16734929382801056,
-0.0075828745029866695,
0.3180561661720276,
0.2992541193962097,
-0.6260842680931091,
0.7476537823677063,
0.24011963605880737,
-0.20835351943969727,
0.3531436026096344,
0.3637514114379883,
-0.44278591871261597,
-0.2626320719718933,
0.0916992574930191,
0.35531049966812134,
0.05620470270514488,
-0.39517757296562195,
0.9495198130607605,
-0.6428429484367371,
0.1682012528181076,
1.262563705444336,
0.21276076138019562,
0.3496684432029724,
0.5208157896995544,
0.15414294600486755,
-0.15241478383541107,
0.45501869916915894,
-0.4901466965675354,
0.12471097707748413,
0.3831131160259247,
0.7961990833282471,
-0.27477529644966125,
0.16297371685504913,
-1.103206992149353,
0.3563026785850525,
-0.1620650440454483,
-0.2841324210166931,
0.37132498621940613,
0.38525858521461487,
0.1786426603794098,
0.791497528553009,
-0.5062730312347412,
0.16730216145515442,
-0.6216013431549072,
-0.9726295471191406,
0.5411146283149719,
-0.21175335347652435,
-0.3412266671657562,
0.6550281047821045,
-0.47214949131011963,
1.3650472164154053,
0.9328433275222778,
0.2366112768650055,
0.014781726524233818,
0.11802346259355545,
-0.10692333430051804,
0.3133760690689087,
0.08251846581697464,
-0.5542399883270264,
0.6712968349456787,
0.2714565098285675,
-0.5069141983985901,
0.0777125135064125,
0.15211442112922668,
-0.4621522128582001,
0.33310145139694214,
0.5855902433395386,
-0.30523601174354553,
0.3384188115596771,
-0.2905280292034149,
-0.19765892624855042,
-0.7113322615623474,
0.3750514090061188,
-1.208177924156189,
0.39520615339279175,
-0.556747317314148,
-0.07610471546649933,
0.010877043940126896,
-0.05904832482337952,
-1.5985897779464722,
-0.23575438559055328,
-1.2393393516540527,
-0.091598741710186,
0.34294456243515015,
0.7992607951164246,
-0.48925140500068665,
-0.17951224744319916,
0.144712895154953,
-0.29212313890457153,
0.016794851049780846,
-0.38022753596305847,
0.8538663387298584,
-0.11816521733999252,
-0.07869639992713928,
0.26475077867507935,
0.47191697359085083,
-0.18106915056705475,
0.41117438673973083,
0.23405855894088745,
-0.3478859066963196,
1.0502737760543823,
-0.5072540044784546,
-1.21372652053833,
0.5878099203109741,
0.4836125373840332,
0.23559638857841492,
-0.015006260015070438,
-0.10307089239358902,
1.126499056816101,
0.05267724767327309,
0.6395329236984253,
0.5931048393249512,
0.16136108338832855,
0.5106834173202515,
0.6828935146331787,
0.5535843372344971,
0.07426445931196213,
-0.0013404407072812319,
0.25526511669158936,
0.2855748236179352,
0.34958383440971375,
-1.126432180404663,
0.1512022167444229,
-0.28718456625938416,
0.6563021540641785,
-0.6186730861663818,
0.9618215560913086,
-0.10273975133895874,
0.4112456142902374,
-0.3660205006599426,
0.20465019345283508,
-1.4066665172576904,
-0.002033049473538995,
-0.6540287733078003,
-0.09200461208820343,
-0.0659862533211708,
-0.29823076725006104,
0.6373469829559326,
-0.03905891254544258,
-0.07698534429073334,
-0.7089183330535889,
0.3563789427280426,
0.8358298540115356,
-0.26429450511932373,
0.6067033410072327,
0.5804727077484131,
-0.1973998248577118,
-1.2588993310928345,
-0.40528541803359985,
-0.8339568376541138,
0.31564202904701233,
-0.5820664167404175,
0.005970494356006384,
1.3219883441925049,
-0.9781184196472168,
0.6439796090126038,
-0.04335004463791847,
-0.058403924107551575,
0.9087886214256287,
-0.5307396054267883,
-0.01797119528055191,
0.6754476428031921,
0.14592453837394714,
-0.7557860016822815,
-0.12941932678222656,
-0.22581727802753448,
-0.6178165078163147,
-0.6923303604125977,
0.13353517651557922,
0.5068593621253967,
0.07429822534322739,
0.538825511932373,
0.0712745264172554,
0.07515718787908554,
0.23833253979682922,
-0.3901861906051636,
-0.7311152219772339,
0.023090491071343422,
0.4194914400577545,
-0.17209918797016144,
-0.16704240441322327,
-0.5452283620834351,
0.7101322412490845,
-0.3971569538116455,
-0.5945271253585815,
0.020367227494716644,
-0.07016598433256149,
-0.5424850583076477,
0.7282094955444336,
0.3613262474536896,
0.14373759925365448,
-0.17641456425189972,
0.9951990842819214,
0.14680473506450653,
-0.36831313371658325,
-0.14374178647994995,
-0.5507350564002991,
-0.45085716247558594,
0.16608837246894836,
0.5139119625091553,
-0.36564910411834717,
0.1050640419125557,
1.1250063180923462,
0.6191155314445496,
-1.0791081190109253,
0.39963269233703613,
-1.1769180297851562,
-0.444795697927475,
0.23260022699832916,
-0.3150899112224579,
0.40935471653938293,
0.09580361098051071,
0.37518569827079773,
-0.6146758794784546,
-0.022388169541954994,
0.6231682896614075,
0.11942120641469955,
0.49385327100753784,
-0.49106648564338684,
0.054140642285346985,
0.45432642102241516,
0.4832330048084259,
-0.17492765188217163,
0.20413795113563538,
-0.2779436409473419,
-0.5510628819465637,
-0.16178365051746368,
-0.8400851488113403,
0.2845723628997803,
-0.18511962890625,
-0.12324431538581848,
0.42813578248023987,
0.2059372365474701,
-0.6374481916427612,
-0.9960447549819946,
-0.9262324571609497,
-0.4216667115688324,
-0.2175777554512024,
1.1501353979110718,
0.3292647898197174,
-0.6541009545326233,
-0.8434896469116211,
-0.3676598072052002,
-0.07928168773651123,
0.12043970823287964,
0.6093382239341736,
-0.4190150797367096,
0.5480992197990417,
0.12049967795610428,
-0.4397841691970825,
0.5104456543922424,
-0.08693692088127136,
0.47314345836639404,
0.63947594165802,
-0.07410258799791336,
0.5313611626625061,
-0.16395749151706696,
-0.9271212220191956,
-0.30121269822120667,
0.766463041305542,
0.8087677955627441,
0.6489604711532593,
-0.31769993901252747,
0.020186947658658028,
-0.701979398727417,
-0.5036682486534119,
-0.4921993315219879,
-0.6016361117362976,
-0.006678062025457621,
-0.15316608548164368,
-0.15425312519073486,
0.2227477729320526,
0.18025995790958405,
0.7966158390045166,
0.6353349685668945,
0.6570574641227722,
-0.013714327476918697,
0.06858423352241516,
0.22139161825180054,
0.6706093549728394,
0.6905457377433777,
0.0043919445015490055,
0.32976463437080383,
-0.6272623538970947,
0.3632640242576599,
0.11441699415445328,
0.34547218680381775,
0.02110462449491024,
-0.24797651171684265,
-0.302350789308548,
-0.5658267140388489,
0.9013389945030212,
0.26935645937919617,
-0.9996975660324097,
0.6810868978500366,
0.2503666579723358,
0.38205811381340027,
-0.453656941652298,
0.114242322742939,
0.5410714745521545,
0.7752642035484314,
-0.024572711437940598,
-0.3323459029197693,
0.12310049682855606,
-0.22645573318004608,
0.3068642318248749,
0.7308014035224915,
-0.5399436950683594,
-0.7898368835449219,
-0.42912527918815613,
0.023452041670680046,
-0.4151635766029358,
0.15311716496944427,
0.8114767074584961,
0.3673705756664276,
0.0197236817330122,
-0.3990967869758606,
0.049126509577035904,
1.351743221282959,
-0.18349020183086395,
-0.10097428411245346,
0.06311595439910889,
0.12979689240455627,
-0.2668675482273102,
0.5103902816772461,
-0.2639254033565521,
-0.554493248462677,
-0.004292258992791176,
-0.7377732396125793,
0.4210706949234009,
0.07197746634483337,
-0.5810207724571228,
-0.7265613675117493,
-0.0621023029088974,
0.4154936969280243,
0.2036285251379013,
0.04247383400797844,
-0.15604828298091888,
-0.22054871916770935,
-0.09102688729763031,
0.018715443089604378,
0.09044449031352997,
-0.0001984092523343861,
-0.13425807654857635,
1.3136101961135864,
0.6967783570289612,
0.2925558090209961,
-0.010078741237521172,
0.2190975546836853,
0.29707130789756775,
-0.2347337007522583,
0.20426423847675323,
-0.4495750069618225,
-0.46475207805633545,
-0.421111524105072,
-0.24198821187019348,
-0.5981694459915161,
-0.8139578104019165,
0.29512378573417664,
-0.30884429812431335,
0.7687292098999023,
0.6146242022514343,
-0.21372853219509125,
-0.5159051418304443,
-0.4653454124927521,
-0.7683820724487305,
0.4194018840789795,
-0.36824581027030945,
-0.37019920349121094,
0.12281500548124313,
-0.5057100057601929,
0.24895229935646057,
-0.4715251326560974,
-0.36523720622062683,
-0.04796716570854187,
0.19435971975326538,
0.8859980702400208,
0.1671307384967804,
0.5642796754837036,
-0.5564513802528381,
0.014597582630813122,
-0.501716673374176,
0.4254924952983856,
-0.5743489265441895,
-0.5826002955436707,
-0.4442192614078522,
-0.18389150500297546,
0.19273267686367035,
-0.5015307068824768,
-0.1513219028711319,
0.037734899669885635,
0.005684433970600367,
-0.235845685005188,
0.05345045402646065,
-0.6735401749610901,
0.02025001496076584,
0.3898768126964569,
0.15384529531002045,
-1.0180820226669312,
-0.030370093882083893,
0.4339248836040497,
0.44619107246398926,
0.7278541922569275,
-0.3454984426498413,
-0.04185650497674942,
0.37291523814201355,
-0.29649850726127625,
0.49411919713020325,
-0.9488174319267273,
-0.6684631109237671,
-0.15784236788749695,
-0.34855687618255615,
0.17179150879383087,
0.20283761620521545,
-0.36917147040367126,
-0.21691709756851196,
-0.5818590521812439,
-0.6349313855171204,
0.04734133556485176,
-0.38668981194496155,
0.3443472981452942,
-0.6449301242828369,
-0.7378150224685669,
-0.08112642914056778,
0.8759761452674866,
-0.05584608018398285,
0.8276896476745605,
0.5439636707305908,
0.04289286211133003,
0.01761038973927498,
0.20785409212112427,
0.07925856113433838,
-0.10790403932332993,
-0.31822773814201355,
0.07383478432893753,
0.0013293896336108446,
0.3556405007839203,
-0.32189425826072693,
-0.0781058743596077,
-0.5559062957763672,
0.655126690864563,
-0.6245361566543579,
0.2640076279640198,
0.45835116505622864,
0.5212611556053162,
0.8740431666374207,
-1.1378499269485474,
0.23340944945812225,
-0.012197718024253845,
-0.029720021411776543,
0.7075214982032776,
-0.29315999150276184,
-0.6408959627151489,
-0.5924098491668701,
-0.4705268442630768,
-0.7180983424186707,
0.46603402495384216,
-0.18504196405410767,
0.23462621867656708,
-0.8164796233177185,
-0.16221627593040466,
0.27538880705833435,
0.29256144165992737,
-0.17859412729740143,
0.32900887727737427,
-0.21357588469982147,
0.06650444865226746,
-0.18782854080200195,
0.13204310834407806,
0.02756733074784279,
-0.09835658222436905,
-0.4226195812225342,
-0.2493872493505478,
0.5588834881782532,
0.1937597095966339,
-0.5078084468841553,
-0.671358585357666,
-0.011642017401754856,
0.07970838993787766,
0.21413753926753998,
-0.19502350687980652,
0.47080257534980774,
0.22906994819641113,
-0.3779703974723816,
-0.655709981918335,
-0.24369394779205322,
0.09383738785982132,
0.3207097053527832,
0.4846770465373993,
0.21501262485980988,
-0.07885222136974335,
0.13542453944683075,
0.47216618061065674,
-0.7386980056762695,
-0.22994519770145416,
0.6376702189445496,
-0.9555935263633728,
-0.3669542074203491,
-0.21706834435462952,
0.056598592549562454,
-0.2827664315700531,
-0.42973488569259644,
-1.5086183547973633,
0.4017033278942108,
0.19245655834674835,
-0.08759543299674988,
-0.1314343363046646,
-0.5022280216217041,
-0.07636930793523788,
0.16855047643184662,
0.637820839881897,
0.03501319885253906,
-0.016899148002266884,
0.4540017545223236,
-0.43280819058418274,
-0.739596426486969,
0.3676992356777191,
0.7838175892829895,
0.5753944516181946,
-1.0211187601089478,
-0.08207012712955475,
0.3710537552833557,
-0.18337449431419373,
-0.32168373465538025,
0.22447708249092102,
-0.4431581497192383,
0.13166096806526184,
0.21328389644622803,
0.02191096544265747,
0.19916808605194092,
0.12512561678886414,
0.029612315818667412,
-0.1231389045715332,
-0.2573537826538086,
-0.9581589102745056,
0.07881075143814087,
-0.8423655033111572,
0.3451586067676544,
0.7186572551727295,
0.06494978070259094,
0.05049702525138855,
-0.15481434762477875,
-0.3264268934726715,
-0.43987026810646057,
-0.491315633058548,
-0.367712140083313,
-1.319926381111145,
-0.48961305618286133,
-0.7919602990150452,
0.22751709818840027,
0.20388592779636383,
0.29516905546188354,
-0.7428991794586182,
0.34859949350357056,
-0.7271071076393127,
-0.17997020483016968,
0.031551167368888855,
0.6458083987236023,
-0.0022098373156040907,
-0.9364296793937683,
-0.5462844967842102,
-0.36371666193008423,
-0.25426357984542847,
-0.3980533480644226,
-0.8955097794532776,
-0.1870368868112564,
-0.04215080291032791,
0.7860666513442993,
-0.016056587919592857,
1.3769760131835938,
-0.8620703220367432,
-1.1856483221054077,
0.019997071474790573,
0.4970318078994751,
-1.0090303421020508,
0.7323715090751648,
0.36214882135391235,
0.7899507880210876,
0.3316105306148529,
0.14412406086921692,
-0.2484763115644455,
0.18333031237125397,
-1.1488010883331299,
-0.14550413191318512,
-0.21439605951309204,
0.5052668452262878,
0.04420267418026924,
-0.6631725430488586,
0.04094075784087181,
0.20398767292499542,
-1.3196802139282227,
0.4853087365627289,
-0.7320811152458191,
0.6642786860466003,
-1.2916615009307861,
0.5856918692588806,
0.4151754379272461,
0.5345311164855957,
-0.041426897048950195,
0.6990505456924438,
-0.12996388971805573,
-0.35768258571624756,
0.23792335391044617,
0.3425293266773224,
-0.10016071051359177,
0.10099516808986664,
0.3215149939060211,
-0.3277882933616638,
-0.3825381100177765,
0.26490890979766846,
-0.26209986209869385,
0.09226329624652863,
-0.5700778365135193,
-0.2416023463010788,
-0.40078505873680115,
0.1321621686220169,
-0.8468092679977417,
0.17597821354866028,
0.723822832107544,
-0.3931410312652588,
0.13078369200229645,
-0.4776418209075928,
-0.5524578094482422,
-0.2580929696559906,
-0.6813785433769226,
-1.1297659873962402,
-0.1785723716020584,
-0.20480021834373474,
-0.025915296748280525,
0.30754292011260986,
-0.329814076423645,
-0.13411159813404083,
-0.5671623349189758,
1.0220850706100464,
0.3431881368160248,
0.01710396260023117,
-0.5995430946350098,
-0.13370920717716217,
-0.9687895178794861,
0.23871757090091705,
-0.6290463805198669,
0.09569254517555237,
-0.5671144723892212,
-0.944175660610199,
0.15997014939785004,
0.6633126735687256,
-0.07333192229270935,
0.3972681164741516,
0.03557060286402702,
0.3086276948451996,
0.0912814512848854,
0.3316824436187744,
-0.5249377489089966,
-0.07218433916568756,
-0.5829241275787354,
0.6360394358634949,
-0.1321401745080948,
-0.38499805331230164,
0.011900878511369228,
-0.004611352924257517,
0.030397385358810425,
-0.5963563919067383,
-0.15935097634792328,
1.0611127614974976,
0.6982608437538147,
-0.5111103057861328,
0.7018341422080994,
0.4612530469894409,
0.19426319003105164,
0.4699621796607971,
-0.5684611797332764,
0.1528889685869217,
0.4077117443084717,
0.105929434299469,
0.5505185127258301,
0.2910689115524292,
0.6681848168373108,
0.11464238166809082,
0.20487265288829803,
-0.15116924047470093,
0.23798562586307526,
-0.024686476215720177,
0.4425365626811981,
0.5990959405899048,
-0.6532315015792847,
0.4228293299674988,
-0.05332571268081665,
0.29347947239875793,
0.4615800082683563,
0.02725658379495144,
-0.44508957862854004,
-0.13932166993618011,
-0.02090287022292614,
0.315167635679245,
-0.5765165686607361,
-0.33342042565345764,
-0.36776670813560486,
-0.3837306797504425,
-0.11019933223724365,
0.28619813919067383,
0.05542851984500885,
0.3286080062389374,
0.7156232595443726,
0.016962314024567604,
-0.18284425139427185,
0.8921164870262146,
0.4727625548839569,
1.2316243648529053,
0.501538097858429,
0.18468737602233887,
0.6416406035423279,
0.5200392007827759,
0.5835486650466919,
-0.8739992380142212,
-0.00643891142681241,
0.11428333818912506,
-1.5303196907043457,
-0.24000263214111328,
-0.20138761401176453,
-0.013390368781983852,
-0.2353409379720688,
-0.8404704332351685,
0.22566474974155426,
-0.3123847246170044,
0.1928718090057373,
0.30577632784843445,
-0.2015804946422577,
-0.2123187780380249,
0.44091275334358215,
-0.1591530442237854,
0.18962311744689941,
0.5930227041244507,
0.2580746114253998,
0.08230967074632645,
0.6996873617172241,
1.4418755769729614,
0.08884760737419128,
0.398155152797699,
0.142112597823143,
-0.27062979340553284,
0.3131342828273773,
0.8279244303703308,
-0.5012903809547424,
0.5615646243095398,
-0.5560800433158875,
-0.4951545298099518,
-0.0696706473827362,
-0.13712987303733826,
-0.3622054159641266,
0.17533539235591888,
0.21618449687957764,
-0.1756918579339981,
-0.7143355011940002,
-0.10558465868234634,
1.1027915477752686,
0.24989956617355347,
-0.2478666752576828,
-0.3128460943698883,
-0.1277218461036682,
-0.9646252989768982,
0.02829296700656414,
-0.8577683568000793,
0.1873394399881363,
-0.4872804880142212,
-0.2725597023963928,
-0.39108049869537354,
-0.36826950311660767,
-0.3892285227775574,
-1.0364711284637451,
0.09047473967075348,
-0.5085541009902954,
0.31050434708595276,
0.47531864047050476,
-0.3282260000705719,
0.3374992311000824,
-0.30941200256347656,
-0.1884859800338745,
-0.32713091373443604,
1.2974584102630615,
0.2856834828853607,
-0.2615634799003601,
1.0548222064971924,
0.23290108144283295,
-0.5924240946769714,
0.1778506189584732,
0.6548174619674683,
-1.250565528869629,
0.772724449634552,
-0.6457329988479614,
0.7025997042655945,
0.22704817354679108,
0.10211608558893204,
0.24847930669784546,
-0.03867873549461365,
0.5855154395103455,
0.2469053864479065,
-0.6543065905570984,
-0.17676986753940582,
-0.4259708821773529,
-0.2570103406906128,
-0.8356680274009705,
0.15895360708236694,
-0.16307330131530762,
-0.351696252822876,
-0.08096057921648026,
-0.6258323192596436,
4.194911479949951,
0.6830135583877563,
0.9184034466743469,
0.8358723521232605,
0.692558228969574,
1.1865532398223877,
-0.014264478348195553,
0.20555149018764496,
0.3020671010017395,
-0.638367772102356,
-0.45725899934768677,
0.16038057208061218,
0.2366698682308197,
0.08935733139514923,
0.06573464721441269,
0.7961006164550781,
-0.3291761577129364,
-0.0030750916339457035,
-0.1559210568666458,
-1.397199273109436,
-1.0808696746826172,
-0.09145993739366531,
0.5039603114128113,
0.20557983219623566,
0.08608391135931015,
-0.15705174207687378,
-0.044374000281095505,
-0.5372098088264465,
-0.9844723343849182,
-0.552687406539917,
-0.8816641569137573,
-0.7216121554374695,
0.3460179269313812,
0.09756559133529663,
-0.9374447464942932,
0.13054248690605164,
-0.07566600292921066,
-0.20421479642391205,
0.16825610399246216,
-0.18012455105781555,
0.012711800634860992,
0.23264896869659424,
0.7509117722511292,
-0.5984250903129578,
0.1590060293674469,
1.3274110555648804,
-0.1606104075908661,
0.8271365165710449,
0.9098287224769592,
-0.08226277679204941,
0.07470855861902237,
0.008098124526441097,
0.1607779711484909,
-0.44212934374809265,
-0.19565030932426453,
-0.22916929423809052,
-0.5983462929725647,
0.09294033795595169,
-0.009118041023612022,
0.06852666288614273,
0.2902947962284088,
-0.29171186685562134,
0.04486875981092453,
0.1026054173707962,
-0.3063093423843384,
0.36056166887283325,
0.24511504173278809,
0.024590104818344116,
-0.0160989947617054,
-0.09198777377605438,
-0.46463432908058167,
-0.7822954058647156,
-0.5582581162452698,
0.41078701615333557,
0.27213892340660095,
0.5288445949554443,
0.0876573920249939,
0.30085238814353943,
0.04015373811125755,
0.2865239977836609,
-0.05538427084684372,
-0.252740740776062,
-0.2610411047935486,
0.20329003036022186,
0.2693905830383301,
0.6570312976837158,
-0.2914869487285614,
0.4027992784976959,
-0.18301092088222504,
0.6621086597442627,
0.5246351957321167,
1.6989543437957764,
0.48113951086997986,
0.4986761808395386,
-0.8989331126213074
] |
SU(N) Gauge Theories with C-Periodic Boundary Conditions: II. Small Volume Dynamics
|
The dynamics of SU(N) gauge theories, especially for N=3, in a small C-periodic box are investigated. We identify the fields that mimimize the energy---the torons---and determine which of these ``classical'' vacua are stable quantum mechanically. The stable torons break cubic symmetry, which has interesting consequences on the spectrum. At any of the stable torons there are also quartic modes. Since all C-periodic boundary conditions are gauge-equivalent, we choose a convenient version, for which the quartic modes are constant modes, and compute the effective Hamiltonian to one loop in perturbation theory.
|
A.S. Kronfeld and U.-J. Wiese
|
hep-lat hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210008
|
hep-lat/9210009
|
[
0.29534780979156494,
-0.11549744009971619,
0.7038094401359558,
0.7107500433921814,
0.39938926696777344,
-0.33582615852355957,
0.1042969673871994,
-0.2754805088043213,
-1.296451210975647,
1.5461660623550415,
1.3648687601089478,
-0.07547008991241455,
0.7086171507835388,
-0.1250583678483963,
-0.2648293972015381,
0.636094868183136,
0.19291643798351288,
-0.6381751894950867,
-1.3972066640853882,
0.20607925951480865,
0.19468185305595398,
0.005469990894198418,
-1.264731526374817,
-0.24651141464710236,
-0.6467119455337524,
0.7864255905151367,
-0.07385028153657913,
0.6785727739334106,
1.3180238008499146,
0.2889818549156189,
0.29345807433128357,
-0.3246200978755951,
-0.05757160484790802,
-0.49817198514938354,
-0.5323250889778137,
-0.38688379526138306,
0.1532907783985138,
-0.07381974905729294,
0.7323113679885864,
-0.6351831555366516,
1.4784657955169678,
0.3654201924800873,
0.5897307991981506,
0.08412230014801025,
-0.9029150605201721,
0.6629523634910583,
-0.2594749927520752,
-0.06070495769381523,
-0.0265293400734663,
-1.4444925785064697,
-0.1105947196483612,
0.19933055341243744,
0.15527582168579102,
-1.1061338186264038,
-0.1257510483264923,
-0.37275418639183044,
0.16417071223258972,
1.0161937475204468,
-0.6362791061401367,
-0.32829123735427856,
0.8110818266868591,
-0.27504560351371765,
0.6924746632575989,
-0.7551220059394836,
0.16707909107208252,
0.9700513482093811,
-0.3523287773132324,
0.861587405204773,
0.23043157160282135,
-0.7008042931556702,
-0.4986363351345062,
-0.5831456184387207,
-0.8879398703575134,
0.20689386129379272,
-0.8201926946640015,
-0.017241083085536957,
0.32751548290252686,
-0.5244368314743042,
-1.2437556982040405,
-0.29691609740257263,
-0.02071794867515564,
-0.1725742220878601,
-0.9822202920913696,
0.5003955364227295,
-0.4780157804489136,
-0.6000540256500244,
-0.10064126551151276,
0.04917455092072487,
-0.35209938883781433,
1.0104031562805176,
0.24521036446094513,
0.6728698015213013,
0.49531853199005127,
-0.357021301984787,
0.21477043628692627,
0.5567110776901245,
0.6667683124542236,
0.22599251568317413,
0.23842200636863708,
0.02525104209780693,
-0.24013055860996246,
0.6067796945571899,
-0.2604285776615143,
-0.15446552634239197,
-0.8411465883255005,
0.46493589878082275,
0.4027005732059479,
-0.1885848194360733,
-0.6309083104133606,
-0.605998158454895,
-0.172331303358078,
0.19859331846237183,
0.450952410697937,
0.3853658437728882,
0.34279578924179077,
0.3012666702270508,
0.054723937064409256,
-0.3773479759693146,
-0.7010030150413513,
-0.03457782790064812,
0.28465521335601807,
0.45358404517173767,
0.17879720032215118,
0.6800377368927002,
-0.04714355617761612,
-0.46923089027404785,
0.64583820104599,
0.8766265511512756,
-0.07042741030454636,
0.0831097811460495,
0.03325909003615379,
-0.481964111328125,
-0.3994962275028229,
0.5539602041244507,
-0.12323246896266937,
0.669745147228241,
-0.06915739923715591,
0.1983945667743683,
0.47538310289382935,
-0.36214104294776917,
0.9095816612243652,
-0.7060577869415283,
-0.019858866930007935,
0.9085801243782043,
0.06456980109214783,
-0.09360475093126297,
0.2745746374130249,
-0.32426634430885315,
-0.16996625065803528,
-0.08053750544786453,
-0.7233434915542603,
0.49288660287857056,
0.08169867098331451,
-0.08507490158081055,
0.07152502238750458,
0.6855570077896118,
-0.6441357731819153,
0.7845684885978699,
-0.6889396905899048,
-0.9607335925102234,
0.8618114590644836,
-0.3482634723186493,
-0.6169697642326355,
0.259217768907547,
-0.7293922901153564,
0.38097283244132996,
-0.5346500277519226,
0.04356129840016365,
-0.07672824710607529,
-0.5188548564910889,
0.4762967526912689,
0.4535888731479645,
-0.8988913297653198,
1.0325746536254883,
0.2991815507411957,
0.31986409425735474,
0.8293331861495972,
-0.4674408733844757,
0.020761646330356598,
0.26568737626075745,
-0.08640293031930923,
-0.22225435078144073,
0.5899995565414429,
0.4372867941856384,
-0.591749906539917,
-0.06941632181406021,
-0.5295712351799011,
-0.16556909680366516,
-0.2169283926486969,
-0.11914791166782379,
-0.2092437744140625,
0.32782986760139465,
-0.9303706288337708,
0.33662837743759155,
-0.33790549635887146,
-0.6932381391525269,
-0.944210410118103,
0.056914716958999634,
-0.49457848072052,
-0.7901151776313782,
-0.36083877086639404,
0.14156560599803925,
-1.0146318674087524,
0.21356883645057678,
-1.655399203300476,
0.6403287649154663,
0.13349531590938568,
-0.6808437705039978,
-0.7072623372077942,
-0.19791418313980103,
0.4692952632904053,
-0.2821495532989502,
0.5512778759002686,
-0.22972820699214935,
-0.4675835371017456,
0.5635957717895508,
0.2316892445087433,
0.30856063961982727,
0.46700263023376465,
-0.3005949556827545,
0.7051551938056946,
0.20075048506259918,
-0.5522377490997314,
1.1305630207061768,
-0.09273441880941391,
-0.4764088988304138,
0.6010568737983704,
0.12821552157402039,
0.3351615369319916,
-0.4656476676464081,
0.058107439428567886,
0.4106472432613373,
0.05190635100007057,
0.04123811796307564,
0.6682189106941223,
1.147430658340454,
1.4799017906188965,
0.681242048740387,
-0.05788125470280647,
0.032775379717350006,
-0.38430270552635193,
0.0074482811614871025,
0.5577602982521057,
-0.4405561685562134,
0.35890087485313416,
0.542357325553894,
-0.41192764043807983,
-0.012243547476828098,
-0.8015691637992859,
0.6850546598434448,
0.4158211946487427,
0.7191222310066223,
0.5937692523002625,
0.21517036855220795,
-0.7490907907485962,
0.10437272489070892,
-0.2563338577747345,
0.5188636779785156,
-0.6632139682769775,
0.13932137191295624,
-0.12700700759887695,
0.023952312767505646,
0.2718653082847595,
-0.47744041681289673,
-1.0343257188796997,
1.0117568969726562,
0.36272361874580383,
0.05911094695329666,
0.5965871214866638,
-0.2217772901058197,
-0.8861318230628967,
-0.07492046803236008,
-0.7163570523262024,
-0.015709875151515007,
0.020003223791718483,
0.42369207739830017,
1.0637420415878296,
-0.4592658579349518,
0.36065608263015747,
0.3623688220977783,
-0.42172229290008545,
1.0563448667526245,
0.11894548684358597,
0.1602765917778015,
0.863425612449646,
-0.3616243302822113,
-0.9939796328544617,
-0.06118312105536461,
-0.6923747658729553,
-0.2363688051700592,
0.4394567906856537,
0.24195872247219086,
0.643836259841919,
-0.25765782594680786,
-0.043931763619184494,
0.29239916801452637,
-1.0686808824539185,
0.18454943597316742,
0.2851598560810089,
-0.7915493249893188,
0.009643815457820892,
0.44706669449806213,
-0.5193712115287781,
-0.6338480710983276,
-0.8235306143760681,
0.7478412985801697,
0.34214669466018677,
-0.37336859107017517,
0.8960937857627869,
0.1372060626745224,
0.27458521723747253,
0.28169184923171997,
-0.8770688772201538,
0.2272665947675705,
-0.0060846866108477116,
0.7007113099098206,
0.369981050491333,
0.19239866733551025,
-0.2645973563194275,
-0.9813178777694702,
0.06908717751502991,
-0.17522089183330536,
0.3954540193080902,
-0.6834328770637512,
-0.26828867197036743,
0.6480453014373779,
-0.2552400827407837,
-0.9365330934524536,
0.35429027676582336,
-0.9707021117210388,
-0.7918536067008972,
-0.08548153191804886,
-0.7620747685432434,
0.20231182873249054,
-0.1716030389070511,
0.05375021696090698,
-0.7548027038574219,
0.08629584312438965,
-0.2205285280942917,
0.5378879904747009,
0.6275954842567444,
-0.4953848123550415,
0.43936872482299805,
0.6405030488967896,
0.5250939726829529,
0.34019291400909424,
0.4909684956073761,
0.09081459790468216,
-0.7366430759429932,
0.8148919343948364,
-0.9523184895515442,
0.5434651374816895,
0.6887598633766174,
0.3019392490386963,
-0.1412888616323471,
0.02108810842037201,
-0.5229591727256775,
-0.36039137840270996,
-0.8586111664772034,
-0.7389432191848755,
0.1312292516231537,
0.5957214832305908,
-0.6467671990394592,
-0.10054384171962738,
-0.5526646375656128,
0.14914129674434662,
0.4289899170398712,
-0.061098262667655945,
0.7845771908760071,
-1.1076425313949585,
0.2575039565563202,
0.02040916495025158,
-0.49089503288269043,
0.3140265941619873,
-0.3553621172904968,
0.4238656461238861,
0.1604837030172348,
0.31169354915618896,
0.8280362486839294,
-0.6501607298851013,
-1.0655514001846313,
-0.4930402636528015,
1.0304204225540161,
1.074929118156433,
1.1114939451217651,
0.8597481846809387,
-0.42537862062454224,
0.21363510191440582,
-0.6481831073760986,
-0.23673978447914124,
0.24071384966373444,
-0.2254607379436493,
-0.09136928617954254,
-0.06219872832298279,
-0.10978176444768906,
-0.48223671317100525,
-0.05259290710091591,
0.8539427518844604,
0.4080447852611542,
0.03165297582745552,
0.3763192296028137,
0.26931002736091614,
0.6862497329711914,
0.9714115858078003,
0.05751046538352966,
0.14895915985107422,
-1.182921051979065,
0.7113765478134155,
0.20411427319049835,
0.549736499786377,
-0.31272265315055847,
-0.7695273160934448,
-0.308810830116272,
-1.2280598878860474,
0.7547385692596436,
0.3035569489002228,
-0.3600359857082367,
0.38985732197761536,
-0.1272994577884674,
-0.28601133823394775,
0.2312256395816803,
-0.5997869372367859,
0.3208352029323578,
-0.29075849056243896,
0.36105018854141235,
-0.8671006560325623,
0.19994930922985077,
0.15653648972511292,
0.5709053874015808,
0.9235435128211975,
-0.44165557622909546,
-1.2880632877349854,
-0.7839709520339966,
0.4707929193973541,
-0.5225710868835449,
-0.2141808122396469,
0.6415042281150818,
0.25787925720214844,
0.34600698947906494,
-0.659053385257721,
0.13702501356601715,
0.6727977991104126,
-0.6933426856994629,
-0.266446590423584,
0.38767892122268677,
-0.28786665201187134,
-0.0644020289182663,
0.8248260617256165,
0.0842709168791771,
-0.7728732824325562,
0.10788249969482422,
-0.28883618116378784,
-0.5504667162895203,
-0.046803973615169525,
-0.49306148290634155,
-0.49970030784606934,
-0.7938437461853027,
-0.18361318111419678,
0.9828824996948242,
0.2394561767578125,
-0.19132663309574127,
0.060447461903095245,
0.14762572944164276,
-0.4558206796646118,
-0.018483562394976616,
0.43292802572250366,
0.7858315110206604,
0.7061236500740051,
1.0314409732818604,
0.8164225816726685,
-0.012945780530571938,
0.5496100783348083,
-0.11987689137458801,
-0.2243817150592804,
0.36918044090270996,
-0.19868676364421844,
-0.3789089024066925,
-0.6583830714225769,
-0.009084086865186691,
-0.9198300838470459,
-0.5161592960357666,
0.5464684963226318,
-0.5122475028038025,
1.105020523071289,
0.3666127920150757,
-1.2684218883514404,
-0.09171778708696365,
-0.6279853582382202,
-0.43687498569488525,
0.5991878509521484,
-0.269788920879364,
-0.31307607889175415,
0.13749103248119354,
-0.7439578771591187,
0.5063919425010681,
0.4772726893424988,
0.09524773061275482,
-0.010479798540472984,
0.4373950958251953,
0.5173848271369934,
-0.04594586044549942,
0.8793357610702515,
-1.0129544734954834,
0.3962695598602295,
-0.6464138031005859,
0.3546958565711975,
-0.12182159721851349,
-0.4869115650653839,
-0.4569057822227478,
-0.20338399708271027,
0.2620612680912018,
-0.4545888900756836,
0.45193982124328613,
-0.03129931539297104,
-0.0793670117855072,
0.10946757346391678,
0.08287046104669571,
-0.5960639119148254,
-0.17181327939033508,
0.8404524922370911,
0.01660873368382454,
-0.5163947939872742,
0.13148851692676544,
1.0500062704086304,
0.0396253801882267,
-0.4479753077030182,
-0.14966675639152527,
-0.3757777810096741,
0.22433501482009888,
-0.7716929912567139,
-0.2757187783718109,
-0.9095398187637329,
-0.31364527344703674,
0.09569687396287918,
-0.47649291157722473,
0.20263232290744781,
0.1830054074525833,
-0.06234213337302208,
0.42749300599098206,
-0.21249139308929443,
-0.8431410193443298,
-0.13372278213500977,
-0.23544402420520782,
-0.7618109583854675,
-0.5132261514663696,
0.12716680765151978,
-0.816316545009613,
0.38994261622428894,
-0.05032142996788025,
0.2661231458187103,
0.22157883644104004,
-0.23220379650592804,
0.025400128215551376,
0.7325575947761536,
0.12892228364944458,
0.24072660505771637,
0.34908536076545715,
0.39167606830596924,
0.24021485447883606,
0.36099594831466675,
-0.9013802409172058,
0.7813243269920349,
-0.9723886251449585,
1.128326416015625,
-0.6499126553535461,
-0.16557593643665314,
-0.3386191427707672,
-0.010063298046588898,
0.6455617547035217,
-0.6356870532035828,
0.27142664790153503,
0.029217218980193138,
0.19177059829235077,
0.8354042768478394,
0.49595823884010315,
-0.858675479888916,
-0.414214551448822,
-0.22627827525138855,
-1.0990114212036133,
0.57082599401474,
-0.03956270590424538,
-0.39615124464035034,
-0.6933563351631165,
-1.1437108516693115,
-0.12357070297002792,
0.10710650682449341,
0.1356237828731537,
0.5623076558113098,
-0.30959635972976685,
-0.13682955503463745,
0.025799307972192764,
0.6813066601753235,
-0.45187148451805115,
-0.2705577313899994,
0.4627332389354706,
-0.14904023706912994,
0.013278894126415253,
-0.4713200628757477,
-0.9084354639053345,
-0.9944607615470886,
-0.5106008052825928,
0.2756764590740204,
0.43938642740249634,
-0.1695481240749359,
0.6103206276893616,
-0.3324972093105316,
-0.6106403470039368,
-0.10155759006738663,
-0.3086225986480713,
0.16345524787902832,
-0.1843273937702179,
0.3332398235797882,
-0.0054094488732516766,
0.14019013941287994,
0.128018319606781,
0.35448262095451355,
-0.43401241302490234,
-0.5179978609085083,
0.9080424904823303,
-0.3762715756893158,
-0.49307066202163696,
0.6198936700820923,
0.32796815037727356,
-0.705865204334259,
-0.20451627671718597,
-1.6304057836532593,
-0.28720566630363464,
-0.3461439311504364,
-0.6519024968147278,
0.23268555104732513,
-0.12065565586090088,
-0.46960946917533875,
1.0626723766326904,
0.4592278003692627,
-0.05018766224384308,
0.10879174619913101,
0.054606396704912186,
-0.3454076647758484,
-0.9673017263412476,
-0.09493283182382584,
0.8878957629203796,
-0.6547428965568542,
-0.9966228604316711,
0.19120986759662628,
0.33834531903266907,
-0.4034923017024994,
0.3724672496318817,
0.05917038768529892,
-0.5286164283752441,
-0.05111042782664299,
-0.19008991122245789,
0.25167009234428406,
-0.04959958791732788,
-0.18895785510540009,
0.6596344709396362,
-0.21766993403434753,
-0.3737657964229584,
-0.7444020509719849,
-0.5715022683143616,
-0.02218022756278515,
0.20851574838161469,
0.782142162322998,
-0.10628872364759445,
0.5605559945106506,
-0.567564845085144,
-0.7716193199157715,
-0.23022089898586273,
-1.0850250720977783,
0.19885919988155365,
-1.2641839981079102,
-0.5037158727645874,
-0.9456249475479126,
-0.6119294762611389,
0.640375018119812,
0.11246192455291748,
-0.21225085854530334,
0.18192967772483826,
-1.2259315252304077,
-0.15303362905979156,
0.5105873346328735,
-0.19096463918685913,
-0.06921007484197617,
-0.4488506615161896,
-0.2704983651638031,
0.20373457670211792,
-0.5507635474205017,
-0.14898183941841125,
-0.0015406650491058826,
0.4374774396419525,
-0.5763935446739197,
0.4766169786453247,
-0.5426071882247925,
0.5486445426940918,
-0.8636544346809387,
-0.4627930223941803,
-0.05722060054540634,
-0.47461140155792236,
-0.6300821304321289,
0.41693535447120667,
0.27940458059310913,
0.13021378219127655,
-0.04389940947294235,
-0.08994549512863159,
-0.7066397666931152,
-0.07096850126981735,
-0.7148875594139099,
-0.5308064818382263,
-0.40401893854141235,
0.3798666298389435,
-0.16585732996463776,
-0.4540090262889862,
0.03948120027780533,
0.15855275094509125,
-0.9967419505119324,
0.7350863814353943,
-0.837109386920929,
0.07129178941249847,
-0.4445260763168335,
0.16498522460460663,
0.4356558620929718,
0.1801653355360031,
-0.5660445094108582,
0.6206904053688049,
-0.30212172865867615,
-0.11877068132162094,
-0.025990523397922516,
0.5734856128692627,
-0.20643365383148193,
0.4244254231452942,
0.32376956939697266,
-0.5440701246261597,
0.16396278142929077,
0.6457776427268982,
0.1177198588848114,
-0.15901564061641693,
-0.6395038366317749,
-0.6411168575286865,
0.11516014486551285,
0.08380025625228882,
-0.7288443446159363,
0.8665103316307068,
0.17823554575443268,
-0.3538159132003784,
-0.873361349105835,
-0.4075419008731842,
-0.5448184013366699,
0.005645249970257282,
-0.6224132776260376,
0.3142944872379303,
-0.07405462861061096,
-0.08055634796619415,
0.008719975128769875,
0.15800854563713074,
0.048405688256025314,
-0.0013960362412035465,
0.16962918639183044,
-0.21250809729099274,
-0.23388232290744781,
0.10781659185886383,
-0.4039108157157898,
0.14536607265472412,
-1.0220162868499756,
-0.565104067325592,
-0.04821610823273659,
1.051448941230774,
-1.0456372499465942,
-0.28611359000205994,
-0.6263039708137512,
0.6129100918769836,
-0.22383305430412292,
-0.24198946356773376,
0.2545285224914551,
-0.08625633269548416,
0.1820654422044754,
0.1500362753868103,
-0.5865431427955627,
0.09709536284208298,
0.27195096015930176,
0.7368748784065247,
0.3202040493488312,
-0.9785745739936829,
0.40739911794662476,
-0.1740100085735321,
-0.0015524649061262608,
0.017659932374954224,
0.4479588568210602,
0.6831573843955994,
0.332666277885437,
-0.9695038795471191,
0.706031084060669,
-0.329449325799942,
0.8925216794013977,
0.5555499792098999,
-0.38005557656288147,
0.1776946485042572,
0.5771889686584473,
0.49018967151641846,
0.09050683677196503,
0.30456480383872986,
-0.14907924830913544,
0.2736283540725708,
0.015134002082049847,
0.1326727569103241,
0.12125438451766968,
0.6588667631149292,
0.39755702018737793,
0.5185239315032959,
-0.2632431387901306,
0.03778795897960663,
0.2340003252029419,
-0.0996788814663887,
-0.4617830812931061,
-0.05848770588636398,
-0.02095261588692665,
0.013947867788374424,
0.7366428375244141,
0.554808497428894,
-0.5741205811500549,
-0.7767176032066345,
-0.175554558634758,
0.6792321801185608,
0.22852236032485962,
0.31120559573173523,
-0.05976315215229988,
1.2009512186050415,
0.4107001721858978,
0.010480144061148167,
0.36452433466911316,
0.4490259289741516,
0.30070415139198303,
0.3678416311740875,
0.4320473372936249,
0.5558437705039978,
1.1031877994537354,
0.03710757941007614,
0.36998414993286133,
-0.702233612537384,
0.14387916028499603,
0.8099073767662048,
-1.8038092851638794,
0.1977306753396988,
-0.38787370920181274,
-0.35616335272789,
-0.5473544001579285,
-0.806464672088623,
0.32449230551719666,
-0.685964822769165,
0.5829504728317261,
1.0318764448165894,
-0.43348750472068787,
1.0865731239318848,
0.546901524066925,
-0.13888773322105408,
0.36117419600486755,
0.882192075252533,
-0.2322125881910324,
-0.29450637102127075,
1.0879628658294678,
1.7631546258926392,
-0.11418057978153229,
0.17962180078029633,
0.04333864152431488,
-0.745087206363678,
0.6217896938323975,
0.012404308654367924,
0.05252408608794212,
1.155723214149475,
-0.5775353908538818,
-0.46040645241737366,
0.1568954437971115,
0.03375623747706413,
0.06372188031673431,
-0.3712064027786255,
-0.144847571849823,
0.15123505890369415,
-0.2744728624820709,
-0.8621036410331726,
1.7145358324050903,
0.8884410858154297,
-0.5648087859153748,
0.006446763873100281,
-0.036247290670871735,
-0.09538422524929047,
-0.45953717827796936,
-0.09461425989866257,
0.5258028507232666,
0.3168296813964844,
0.4063786268234253,
0.14889265596866608,
-0.7353612184524536,
-0.6644763350486755,
-1.421314001083374,
0.42606499791145325,
-0.6411856412887573,
0.8917924165725708,
0.34436237812042236,
0.3136405646800995,
0.7366138100624084,
-0.7175913453102112,
0.3660217821598053,
0.5955102443695068,
1.0153701305389404,
-0.05420372262597084,
-0.5888209939002991,
0.5525515079498291,
0.5003281831741333,
-0.9070850610733032,
0.6297321319580078,
0.7434564828872681,
-0.5446473360061646,
0.4998621642589569,
-0.3675704002380371,
-0.028227154165506363,
0.6367512345314026,
0.0369739793241024,
0.800011157989502,
-0.15706707537174225,
0.5478156805038452,
-0.323371946811676,
-0.4635172188282013,
-0.7851957082748413,
-1.2308387756347656,
0.14076246321201324,
-0.8526811599731445,
0.538523256778717,
-0.4266834557056427,
1.0203237533569336,
0.5030339360237122,
-0.405467689037323,
3.821526527404785,
1.407262921333313,
0.2555965185165405,
0.2622337341308594,
0.7317358255386353,
0.5927837491035461,
-0.22902508080005646,
-0.38529738783836365,
0.6626695394515991,
-1.1804172992706299,
-0.4286344051361084,
0.8022310137748718,
0.15664716064929962,
-0.33838769793510437,
0.06655828654766083,
0.8166026473045349,
-0.021724151447415352,
0.4884442985057831,
0.10171904414892197,
-0.8233962655067444,
-0.44580304622650146,
0.22844207286834717,
0.7156226634979248,
0.3360025882720947,
0.2176746129989624,
0.23325075209140778,
0.1725970357656479,
-0.42816126346588135,
-0.25454825162887573,
-0.3614215552806854,
-0.84132319688797,
-0.9018744230270386,
0.2596571147441864,
-0.582933247089386,
-0.593386709690094,
0.4889887571334839,
-0.3126493990421295,
-0.7125275135040283,
0.4409789741039276,
0.1053130179643631,
0.026790911331772804,
-0.004908138886094093,
-0.4069996476173401,
-0.4635918140411377,
-1.0877412557601929,
1.4424147605895996,
0.24486491084098816,
0.592440128326416,
-0.022685719653964043,
-0.4547259211540222,
0.7729710340499878,
-0.27418774366378784,
0.6386435627937317,
-0.16689138114452362,
-1.145045280456543,
-0.045696455985307693,
-0.379946768283844,
-0.35669729113578796,
0.053255386650562286,
0.06830672919750214,
0.7343876361846924,
-0.1255873441696167,
-0.1811942309141159,
0.3323056995868683,
0.14340227842330933,
1.0440138578414917,
0.024743786081671715,
-0.06784801185131073,
-0.4963136911392212,
-0.18948350846767426,
-0.29627540707588196,
0.053553078323602676,
-0.4730220437049866,
-0.45990779995918274,
0.4544329345226288,
0.09053495526313782,
0.05480339750647545,
0.766236424446106,
-0.11755970865488052,
0.45713526010513306,
-0.03481144458055496,
-0.5725724101066589,
-0.5495127439498901,
0.18989033997058868,
0.04877772182226181,
0.42761704325675964,
-0.2527226209640503,
0.40466979146003723,
0.36316514015197754,
0.2829558551311493,
0.5062251687049866,
1.6332731246948242,
0.035374563187360764,
0.1958998590707779,
-0.9061354994773865
] |
Renormalization Group Analysis of Finite-Size Scaling in the $\Phi^4_4$ Model
|
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions.
|
R. Kenna and C.B. Lang
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210009
|
hep-lat/9210010
|
[
0.6406657099723816,
-0.46485280990600586,
0.33346474170684814,
-0.009588230401277542,
0.23180726170539856,
-0.3479602336883545,
-0.06988479942083359,
-0.48470333218574524,
-0.8696011900901794,
1.5338592529296875,
1.006417989730835,
-0.07205425947904587,
0.07805225253105164,
-0.49704626202583313,
-0.2951427400112152,
0.5396340489387512,
0.10879456251859665,
-0.6081069707870483,
-1.376869559288025,
-0.006672261748462915,
0.13320475816726685,
-0.38813912868499756,
-1.496424674987793,
-0.44906437397003174,
-0.3438349664211273,
0.5500177145004272,
-0.19827111065387726,
0.1442020833492279,
1.139896273612976,
0.4951867461204529,
0.5065342783927917,
-0.5670710802078247,
0.3615832030773163,
-0.31871330738067627,
-0.5639030933380127,
-0.13596774637699127,
0.01802985742688179,
-0.009329685941338539,
0.8357608914375305,
-0.20792493224143982,
1.1916531324386597,
-0.7026528120040894,
0.24265940487384796,
-0.12302784621715546,
-0.6863710880279541,
0.34249505400657654,
-0.2354567050933838,
-0.034890178591012955,
-0.17335747182369232,
-1.3139554262161255,
0.21764972805976868,
0.15293559432029724,
0.5066995024681091,
-0.51357102394104,
-0.25174495577812195,
-0.3439748287200928,
0.09777162969112396,
0.33840134739875793,
-0.517509937286377,
-0.6430080533027649,
0.8785802125930786,
-0.11633660644292831,
0.37711554765701294,
-1.1668037176132202,
0.16978727281093597,
0.2012576162815094,
-0.3786337673664093,
0.5779701471328735,
0.3536885678768158,
-0.4310450553894043,
-0.22362969815731049,
-0.5826888680458069,
-0.7224392294883728,
0.21142010390758514,
-0.39776405692100525,
0.5474647283554077,
-0.01775774359703064,
-0.8721438646316528,
-1.5080336332321167,
-0.27921390533447266,
-0.25275152921676636,
-0.519437849521637,
-0.5642644762992859,
0.0036442189011722803,
-0.5583910346031189,
-0.7031664848327637,
0.07012913376092911,
-0.035543765872716904,
0.10887748748064041,
0.8977689743041992,
0.06757082045078278,
0.7419708967208862,
-0.23989786207675934,
0.16098728775978088,
0.7351057529449463,
0.7834279537200928,
0.666147768497467,
0.6537252068519592,
0.6101377010345459,
0.3701463043689728,
0.1035960465669632,
0.616738498210907,
-0.4791008234024048,
0.5973563194274902,
-0.9408050179481506,
0.5175309181213379,
0.24103879928588867,
0.0518219992518425,
-0.202727273106575,
-0.7191182971000671,
0.5393018126487732,
-0.11246398836374283,
0.18381021916866302,
0.9189049601554871,
-0.05690731480717659,
0.5555828809738159,
-0.09677914530038834,
0.02474869415163994,
-0.6281874775886536,
-0.45460203289985657,
0.056373123079538345,
0.045931342989206314,
0.26605671644210815,
0.6487399935722351,
0.31889021396636963,
0.10092255473136902,
0.029654590412974358,
0.763054609298706,
-0.5770582556724548,
-0.19312097132205963,
0.3182399272918701,
-0.005034330300986767,
0.15213589370250702,
0.6345466375350952,
-0.43897199630737305,
0.3152143061161041,
-0.47507238388061523,
0.5103719830513,
0.3282795250415802,
-0.2533032298088074,
0.8770673274993896,
-0.814435601234436,
0.16429398953914642,
1.0966615676879883,
0.26945164799690247,
0.08016525954008102,
0.29483816027641296,
-0.3842582106590271,
0.22143104672431946,
0.324375718832016,
-0.609201192855835,
0.4739677906036377,
-0.0644998848438263,
0.5908190608024597,
0.3319147229194641,
0.4519454538822174,
0.06653493642807007,
0.4112122058868408,
-0.8481248021125793,
-0.789077639579773,
0.9101841449737549,
-0.40265077352523804,
-0.5382580757141113,
0.23675769567489624,
-0.7665295004844666,
0.25123831629753113,
-0.7599822282791138,
0.34563082456588745,
0.06672275066375732,
-0.7899957895278931,
-0.012566406279802322,
0.5042999386787415,
-0.3556932806968689,
1.1025375127792358,
-0.058515746146440506,
0.2984163463115692,
0.45981207489967346,
-0.7740423679351807,
0.5654962062835693,
0.038453273475170135,
-0.55172199010849,
-0.392008900642395,
0.6778268814086914,
0.01465491484850645,
-0.023428594693541527,
-0.3100024163722992,
-0.38462674617767334,
-0.279773473739624,
0.12657397985458374,
0.24979837238788605,
-0.4544358551502228,
0.42466261982917786,
-0.334751695394516,
0.6262673735618591,
-0.5955858826637268,
-0.24806621670722961,
-1.0979971885681152,
0.4329640865325928,
-1.1369078159332275,
-0.3901512622833252,
-0.04888949543237686,
0.38445380330085754,
-1.1093729734420776,
0.40817373991012573,
-1.263181209564209,
0.08743170648813248,
0.5065755844116211,
-0.19292791187763214,
-0.6302946209907532,
-0.34622955322265625,
0.3921777904033661,
-0.2986599802970886,
1.054099678993225,
-0.5764268636703491,
0.3688078224658966,
0.16468621790409088,
-0.002561559434980154,
0.2552748918533325,
0.772265613079071,
0.20986811816692352,
0.7629448175430298,
0.44065946340560913,
-0.24421297013759613,
0.9489995241165161,
-0.42528417706489563,
-0.47695744037628174,
0.4597192406654358,
0.5667057037353516,
0.4635535180568695,
-0.08360558748245239,
-0.17566870152950287,
0.37572404742240906,
-0.3974798023700714,
0.18864984810352325,
0.8351770639419556,
0.4696171283721924,
0.9702731370925903,
0.30773356556892395,
0.3714228570461273,
0.3420741856098175,
-0.318080872297287,
0.233184352517128,
0.33626919984817505,
0.1736273169517517,
0.34308522939682007,
0.4193422198295593,
-0.536000669002533,
0.3124374747276306,
-0.48906275629997253,
0.50186687707901,
-0.15258252620697021,
1.0650181770324707,
-0.03692298009991646,
0.26144054532051086,
-1.1067479848861694,
0.1576278656721115,
-0.1572730541229248,
0.16016869246959686,
0.04606474190950394,
-0.3005351126194,
-0.04227623715996742,
-0.4034189283847809,
-0.41190454363822937,
-0.6104651093482971,
-0.20375265181064606,
0.9355766773223877,
0.30047133564949036,
0.41947412490844727,
0.6909171938896179,
-0.20436391234397888,
-1.4129600524902344,
0.22667469084262848,
-0.9635695219039917,
-0.37891027331352234,
-0.5735058784484863,
-0.18523569405078888,
0.6811911463737488,
-0.6643723845481873,
0.3007073402404785,
-0.3192968964576721,
-0.46563267707824707,
0.6754425168037415,
-0.3780573606491089,
0.5764973163604736,
0.5322635173797607,
-0.158633753657341,
-0.9621769189834595,
0.31625524163246155,
-0.763708770275116,
-0.045724209398031235,
0.20858646929264069,
0.7663099765777588,
0.8619599938392639,
-0.7128124833106995,
-0.050454821437597275,
-0.36425092816352844,
-0.7936881184577942,
0.44299960136413574,
0.05482954904437065,
-0.505479097366333,
-0.39567723870277405,
0.449859619140625,
-0.20126941800117493,
-0.5249423384666443,
-1.0910612344741821,
0.7070490717887878,
0.6788056492805481,
-0.18696583807468414,
0.5184550881385803,
0.21388353407382965,
-0.5283980965614319,
0.3703535199165344,
0.16373887658119202,
0.22470970451831818,
0.044552288949489594,
0.8769515752792358,
0.7081981897354126,
0.46561387181282043,
0.17020893096923828,
-0.5997825860977173,
-0.07041652500629425,
0.6414815783500671,
-0.32153189182281494,
0.02513379044830799,
-0.3508176803588867,
1.1496084928512573,
-0.12357280403375626,
-0.7670857310295105,
-0.2560011148452759,
-0.9221664071083069,
-0.6878912448883057,
0.3732772469520569,
-0.49959614872932434,
0.6686743497848511,
0.04388876259326935,
0.046196237206459045,
-0.66087806224823,
-0.17850199341773987,
-0.21318690478801727,
0.2878325581550598,
0.5913019776344299,
-0.6083544492721558,
0.5769193768501282,
0.5462106466293335,
0.5268234610557556,
0.14377468824386597,
0.1426551640033722,
-0.35584938526153564,
0.09959577023983002,
0.6684852838516235,
-0.7374118566513062,
0.15024356544017792,
0.6156717538833618,
-0.08519764989614487,
0.056562986224889755,
0.5968664884567261,
-0.4556819796562195,
-0.4690854847431183,
-0.7802658677101135,
-0.33869802951812744,
0.1421751230955124,
0.743500828742981,
-0.28833913803100586,
-0.11844756454229355,
-0.41017797589302063,
0.3033807575702667,
0.6598154902458191,
-0.4242068827152252,
0.7848513126373291,
-1.2077666521072388,
0.2652687132358551,
-0.07795508950948715,
-0.3048170208930969,
0.39171186089515686,
-0.052220653742551804,
-0.0291033573448658,
-0.14811675250530243,
0.0838313028216362,
1.0294829607009888,
-0.5665490627288818,
-0.7025780081748962,
-0.19014376401901245,
1.0126984119415283,
0.3171563148498535,
0.8440954089164734,
0.675540030002594,
-0.2422184944152832,
-0.3754737079143524,
-0.23026177287101746,
-0.09858061373233795,
-0.4830852150917053,
-0.6431787610054016,
-0.5408569574356079,
-0.18841885030269623,
-0.07451082766056061,
-0.18878525495529175,
0.7229255437850952,
0.28735825419425964,
0.7886173129081726,
0.20785661041736603,
0.3035539984703064,
0.3645944893360138,
0.9210971593856812,
0.7476662993431091,
0.11919337511062622,
0.7306336164474487,
-1.0088704824447632,
0.1444031000137329,
-0.05539162456989288,
0.2165401130914688,
-0.2632787823677063,
-0.2959294617176056,
-0.24179235100746155,
-0.8328846096992493,
0.49276062846183777,
0.28542983531951904,
-0.5807267427444458,
0.6923434734344482,
-0.5784363150596619,
0.4649573862552643,
-0.16476646065711975,
-0.09875492751598358,
0.3960188925266266,
0.46764934062957764,
0.24178197979927063,
-0.8235629796981812,
0.32190996408462524,
0.07693801075220108,
0.9217978119850159,
0.5474159717559814,
-1.0930559635162354,
-0.6571781635284424,
-0.9531474709510803,
0.0177948996424675,
0.09253839403390884,
-0.3452712595462799,
1.0804256200790405,
-0.03992025926709175,
0.5382741689682007,
-0.4768613576889038,
-0.11327730864286423,
0.454265832901001,
-0.7297438383102417,
-0.3474210500717163,
0.3820188045501709,
-0.04697112366557121,
-0.20947937667369843,
0.5822156071662903,
0.12540578842163086,
-0.4475570619106293,
-0.31069526076316833,
-0.11985495686531067,
-0.28049424290657043,
-0.35608458518981934,
-0.406666100025177,
0.1017131581902504,
-0.45080581307411194,
-0.24450622498989105,
0.5497888326644897,
0.1340915709733963,
0.135357066988945,
-0.26092448830604553,
0.061279647052288055,
-0.19353929162025452,
0.0010796970454975963,
0.016331586986780167,
0.19549508392810822,
0.786727786064148,
1.1402298212051392,
0.04623401165008545,
0.36077991127967834,
0.08898928761482239,
0.24732017517089844,
-0.18211404979228973,
0.39368000626564026,
0.23779286444187164,
-0.5042672753334045,
-0.1589258760213852,
0.28731945157051086,
-0.8833469152450562,
-0.6695576310157776,
-0.18262715637683868,
-0.02409168891608715,
0.4783017039299011,
-0.08209228515625,
-0.4693322777748108,
-0.4296477735042572,
-0.16301216185092926,
-0.5611796975135803,
0.4485057592391968,
-0.1665448546409607,
-0.5438410043716431,
0.7007284164428711,
-0.3604431748390198,
-0.26270627975463867,
0.21586096286773682,
-0.30601656436920166,
-0.013856886886060238,
0.3962710201740265,
0.5509613156318665,
0.5308628678321838,
0.792599618434906,
-0.4466886818408966,
0.09021379053592682,
-0.2551514506340027,
0.40025758743286133,
-0.11432959884405136,
-0.28133538365364075,
-0.22645415365695953,
-0.2347889095544815,
-0.28162050247192383,
-0.413429319858551,
-0.19624480605125427,
-0.2951441705226898,
-0.024186236783862114,
-0.15965977311134338,
-0.21831771731376648,
-0.4591703712940216,
-0.37891900539398193,
0.39836856722831726,
0.25158947706222534,
-0.9036444425582886,
0.3718574047088623,
0.6480461359024048,
0.0915815457701683,
0.36174672842025757,
-0.1746729612350464,
-0.25074267387390137,
0.1386638730764389,
-0.5225712060928345,
-0.15897203981876373,
-1.1259735822677612,
-0.5248855352401733,
-0.11828901618719101,
-0.8181155323982239,
0.6327748894691467,
0.3831365704536438,
0.130618616938591,
0.5208828449249268,
-0.20782388746738434,
-0.461965948343277,
0.061402011662721634,
-1.0510053634643555,
-0.41755905747413635,
-0.10129435360431671,
-0.3460918068885803,
-0.5945143699645996,
0.3792661130428314,
0.376865029335022,
0.46779516339302063,
0.41943395137786865,
-0.09085676074028015,
0.3592919409275055,
0.49672964215278625,
-0.0667765885591507,
-0.1654207706451416,
0.05798054113984108,
0.4182761609554291,
-0.07586938887834549,
0.21765738725662231,
-0.7551020383834839,
0.6774312257766724,
-0.9393314719200134,
1.0442798137664795,
-0.2915378212928772,
-0.8802148699760437,
0.11648308485746384,
0.5624544024467468,
0.3625729978084564,
-0.5180553197860718,
0.221243217587471,
0.31838464736938477,
-0.279773473739624,
0.6840082406997681,
-0.03060215152800083,
-0.5436403155326843,
-0.4412768483161926,
-0.44278234243392944,
-0.88874351978302,
0.5680423378944397,
0.2608555853366852,
-0.10641086846590042,
-1.0403048992156982,
-0.30072689056396484,
0.06446529179811478,
0.05377437546849251,
0.47086867690086365,
0.33063122630119324,
-0.31884831190109253,
0.4940466284751892,
0.20220528542995453,
0.056338828057050705,
-0.48466920852661133,
0.033950503915548325,
0.24156755208969116,
-0.01442129909992218,
-0.1066899448633194,
-0.027560504153370857,
-0.5937916040420532,
-1.0533353090286255,
-0.4581182897090912,
0.3239108920097351,
0.0014836605405434966,
-0.24269160628318787,
0.42098525166511536,
-0.37499183416366577,
-0.23567011952400208,
-0.18515142798423767,
0.3156464397907257,
-0.279343843460083,
0.03003830462694168,
0.438764363527298,
0.07566522061824799,
0.21252334117889404,
0.14200711250305176,
0.8439338803291321,
-0.4310636520385742,
-0.06997454166412354,
0.32626765966415405,
-0.3122779428958893,
-0.5387572646141052,
0.5920449495315552,
-0.19857478141784668,
-0.3277721107006073,
0.03299064189195633,
-1.025111436843872,
-0.6563845872879028,
-0.25033003091812134,
-0.4919402301311493,
0.39081209897994995,
0.03991159424185753,
-0.10132059454917908,
0.9667890667915344,
0.1589977741241455,
-0.6501738429069519,
0.35767868161201477,
-0.21839748322963715,
-0.4180293381214142,
-0.44288256764411926,
0.0890081450343132,
1.2867759466171265,
-0.1724480539560318,
-0.6092578172683716,
0.41401100158691406,
-0.4175132215023041,
-0.4580842852592468,
0.4109775722026825,
0.27893373370170593,
-0.41922661662101746,
0.6850525736808777,
0.4847337603569031,
0.7316377758979797,
0.3436371684074402,
0.5364283323287964,
0.17134089767932892,
0.19350671768188477,
-0.14873671531677246,
-0.7912041544914246,
-0.4085846245288849,
-0.23550724983215332,
0.15680834650993347,
1.2110791206359863,
-0.06244635954499245,
0.33418112993240356,
0.032887302339076996,
-0.6141825318336487,
-0.31508803367614746,
-0.8190546035766602,
0.33515653014183044,
-0.948414146900177,
-0.4064876139163971,
-0.40857186913490295,
-0.4052193760871887,
0.8111192584037781,
0.3309524357318878,
-0.07726092636585236,
-0.25070175528526306,
-0.8577101230621338,
0.01248505525290966,
0.4592406153678894,
-0.42611512541770935,
-0.1615883857011795,
-0.6328127980232239,
-0.8089072704315186,
-0.25223425030708313,
-0.05443202704191208,
-0.15866996347904205,
-0.5509845614433289,
-0.3751150667667389,
0.011853117495775223,
0.3568766117095947,
-0.44769027829170227,
0.36519861221313477,
-0.8904460072517395,
-1.0520639419555664,
-0.03779372200369835,
-0.5845087170600891,
-0.9868298768997192,
0.16996535658836365,
-0.07855834811925888,
0.6815126538276672,
0.14424972236156464,
-0.15201570093631744,
-0.3983004093170166,
0.2664932608604431,
-0.8825538158416748,
-0.06911522150039673,
0.16819457709789276,
-0.004345428664237261,
-0.42847970128059387,
-0.3711889088153839,
0.042634401470422745,
-0.004512408748269081,
-1.149682879447937,
0.31095606088638306,
-0.4253157675266266,
-0.11265379190444946,
-0.6788848042488098,
0.1660490483045578,
0.5208231210708618,
0.2926996946334839,
-0.38247188925743103,
0.8420259952545166,
-0.3430764079093933,
-0.22740615904331207,
-0.30629563331604004,
0.02444138377904892,
-0.09431461989879608,
0.6036167740821838,
0.37347277998924255,
-0.4509254992008209,
0.02606641873717308,
0.28687357902526855,
-0.5965555310249329,
0.3373804986476898,
-0.09755121916532516,
-0.29415586590766907,
-0.14310018718242645,
0.015246647410094738,
-0.6487536430358887,
0.46575599908828735,
0.3396260738372803,
-0.6917874217033386,
-0.9214969873428345,
-0.37181931734085083,
-0.9477973580360413,
0.39314448833465576,
-0.8620986342430115,
-0.1967906951904297,
-0.1407783329486847,
-0.5713521838188171,
0.18554255366325378,
0.02321365848183632,
-0.46734923124313354,
0.3970107138156891,
0.24147094786167145,
0.018816161900758743,
-0.2146267592906952,
-0.1380392611026764,
-0.4515690803527832,
0.2443293035030365,
-0.894011914730072,
-0.5741739273071289,
-0.5719074010848999,
0.3367283344268799,
-0.7602855563163757,
-0.49720075726509094,
-0.7387574315071106,
0.7894051671028137,
-0.15013809502124786,
-0.25809216499328613,
-0.01852506585419178,
-0.16304942965507507,
0.11626289039850235,
0.24792391061782837,
-0.6549059748649597,
0.2538353204727173,
0.0443757064640522,
0.5496653318405151,
-0.15571898221969604,
-0.9117746949195862,
0.6296983957290649,
0.11651191860437393,
0.17413443326950073,
-0.17718255519866943,
-0.24552808701992035,
0.9037981629371643,
-0.00990535318851471,
-0.5915020108222961,
0.9610893130302429,
-0.04242844879627228,
0.3577340543270111,
0.46955302357673645,
-0.46816545724868774,
0.3961314558982849,
0.13138513267040253,
0.3717407286167145,
0.5040434002876282,
0.8250698447227478,
0.15754824876785278,
0.5569819808006287,
0.3634650409221649,
-0.017948292195796967,
-0.02491731010377407,
0.5987424850463867,
0.42082443833351135,
0.4077335000038147,
-0.3642987310886383,
0.32076722383499146,
0.4072357714176178,
0.20835630595684052,
-0.22555746138095856,
-0.13708825409412384,
0.0657772347331047,
-0.15439286828041077,
0.10681022703647614,
0.5942991971969604,
-0.8706225156784058,
-0.3535788953304291,
-0.5505796074867249,
0.615657389163971,
-0.2866427004337311,
0.3216952085494995,
-0.10000156611204147,
0.809429407119751,
0.6841194033622742,
-0.029454071074724197,
0.10768932104110718,
0.5463709831237793,
0.05731935054063797,
0.970458984375,
0.4968201518058777,
0.3406427204608917,
0.6058849096298218,
0.11142188310623169,
0.29266732931137085,
-0.9062031507492065,
0.18618297576904297,
0.7717454433441162,
-1.421342372894287,
0.3638017475605011,
-0.625313937664032,
-0.2971567213535309,
-0.423316091299057,
-0.7196323871612549,
0.23945187032222748,
-0.6594693660736084,
0.2835038900375366,
0.9731346368789673,
-0.6605029702186584,
0.3231963515281677,
0.8295920491218567,
-0.0635576993227005,
0.30765286087989807,
0.8850879669189453,
-0.02717091515660286,
0.4132995903491974,
1.6641325950622559,
1.1577215194702148,
0.042150285094976425,
0.0032385860104113817,
0.5108550190925598,
-0.36933988332748413,
0.42764976620674133,
0.614626407623291,
-0.6391952037811279,
1.0445808172225952,
-0.4634184241294861,
-1.0265212059020996,
0.5137226581573486,
0.4610201418399811,
-0.10006216913461685,
-0.3689505457878113,
0.14089146256446838,
0.2653302252292633,
-0.5410630106925964,
-0.5598989129066467,
1.3099501132965088,
0.5981836915016174,
-0.2386574149131775,
-0.44491034746170044,
-0.03847956657409668,
-0.35392123460769653,
-0.15670059621334076,
-0.7433930039405823,
-0.18329159915447235,
0.2921605110168457,
0.5045539140701294,
-0.12770381569862366,
-0.8660217523574829,
-0.3124738335609436,
-1.0640125274658203,
0.1047830879688263,
-0.6349939703941345,
0.26989707350730896,
0.0632135197520256,
0.48382851481437683,
0.4941997528076172,
-0.6265395283699036,
0.15215474367141724,
0.07897644490003586,
1.0156878232955933,
-0.48317015171051025,
-0.1847577542066574,
0.7797182202339172,
1.0002403259277344,
-0.5833373069763184,
0.8674310445785522,
0.7738714814186096,
-0.7625753283500671,
0.8375489115715027,
-0.38425779342651367,
0.5114005208015442,
0.7298277020454407,
0.14368519186973572,
0.5044809579849243,
0.2433842420578003,
0.516577422618866,
-0.010611931793391705,
-0.44190216064453125,
-0.729080855846405,
-0.7625858783721924,
0.18788406252861023,
-0.9693632125854492,
-0.060886625200510025,
-0.4492647647857666,
0.3123863935470581,
0.28810057044029236,
-0.5383928418159485,
4.177175998687744,
0.6702686548233032,
0.3434465229511261,
0.1925377994775772,
0.49798980355262756,
0.4301197826862335,
-0.09811610728502274,
-0.3320521414279938,
0.2543557584285736,
-0.8536440134048462,
-0.5811294913291931,
0.19907766580581665,
0.13395480811595917,
-0.06919495761394501,
-0.5822830200195312,
0.5211842060089111,
-0.7340372204780579,
0.011066352017223835,
0.1849026083946228,
-1.0021528005599976,
-0.6161670684814453,
0.4031275808811188,
0.12247107923030853,
-0.25148454308509827,
0.1863781064748764,
-0.14771832525730133,
0.2789626717567444,
-0.7867805361747742,
-0.5198246240615845,
-0.6683416366577148,
-0.5529772639274597,
-0.8547095060348511,
-0.021091675385832787,
-0.5598021745681763,
-0.8139601945877075,
-0.12873128056526184,
-0.27843356132507324,
-0.46825575828552246,
-0.0896124541759491,
0.3140319883823395,
0.02843993715941906,
0.44332531094551086,
0.08624880015850067,
-0.5962945818901062,
-0.9091968536376953,
0.8214517831802368,
-0.2832058072090149,
0.7650807499885559,
0.09931647777557373,
-0.4328535497188568,
0.8430150151252747,
-0.10826827585697174,
0.8208521604537964,
0.1981991082429886,
-0.9100531339645386,
-0.10066830366849899,
-0.42219769954681396,
0.08927904069423676,
0.2503131926059723,
0.5011339783668518,
0.29719972610473633,
-0.24991796910762787,
-0.08735876530408859,
-0.3166753351688385,
-0.1451646089553833,
0.45698732137680054,
0.07087392359972,
0.40193864703178406,
-0.23803146183490753,
0.23224472999572754,
-0.07200036197900772,
-0.8293678760528564,
-0.1486719399690628,
0.07898959517478943,
0.23171599209308624,
0.23813998699188232,
-0.10398555546998978,
0.7241626381874084,
-0.1511184126138687,
0.016997408121824265,
-0.17063112556934357,
-0.13523145020008087,
-0.14166124165058136,
0.4018915891647339,
-0.3782818615436554,
1.193994164466858,
-0.40604355931282043,
0.35707372426986694,
0.460083544254303,
0.4991718828678131,
0.35093098878860474,
1.4512004852294922,
0.008867088705301285,
-0.04575295373797417,
-1.0569931268692017
] |
Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models
|
Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$. Several lattice formulations are compared and shown to enjoy scaling for $\xi$ as small as $2.5$. Asymptotic scaling is investigated using as bare coupling constant both the usual $\beta$ and $\beta_E$ (related to the internal energy); the latter is shown to improve asymptotic scaling properties. Studies of finite size effects show their $N$-dependence to be highly non-trivial, due to the increasing radius of the $\bar z z$ bound states at large $N$.
|
Massimo Campostrini, Paolo Rossi, and Ettore Vicari
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210010
|
hep-lat/9210011
|
[
0.13191168010234833,
-0.23563914000988007,
-0.025974612683057785,
-0.09083102643489838,
0.41042429208755493,
-0.18255868554115295,
0.01912005990743637,
-0.341206818819046,
-0.9380695223808289,
1.6451414823532104,
1.0665634870529175,
-0.15557856857776642,
-0.055732060223817825,
-0.5909604430198669,
0.14154134690761566,
0.5321634411811829,
-0.4695763885974884,
-1.1789793968200684,
-1.0516215562820435,
0.3934346139431,
0.4577387273311615,
-0.3329960107803345,
-0.9824001789093018,
-0.9794540405273438,
-0.34181538224220276,
0.6385318040847778,
0.018769532442092896,
0.056176066398620605,
1.3536769151687622,
1.0673167705535889,
0.7346370816230774,
-0.47033172845840454,
-0.25869160890579224,
-0.2212633341550827,
-0.6961502432823181,
-0.2378174215555191,
-0.20236903429031372,
-0.09158521145582199,
0.6833095550537109,
-0.17165420949459076,
0.8391356468200684,
-0.3229503035545349,
0.9465897083282471,
0.27874332666397095,
-0.8114772439002991,
0.31969550251960754,
-0.12227445840835571,
-0.5159562230110168,
-0.25525781512260437,
-0.9434236884117126,
0.06933353841304779,
0.22240841388702393,
0.4680623710155487,
-1.022032618522644,
-0.11151084303855896,
-0.2529968321323395,
0.6751514673233032,
0.24148209393024445,
-0.40748292207717896,
-0.31087005138397217,
1.035928726196289,
-0.10818470269441605,
0.6495938301086426,
-1.0960074663162231,
0.2725067138671875,
0.6537936925888062,
-0.624465823173523,
0.5500362515449524,
-0.14980405569076538,
-0.85858553647995,
-0.08131840080022812,
-0.3948432505130768,
-0.28898242115974426,
0.053635381162166595,
-0.6041660308837891,
0.48577648401260376,
0.09587147831916809,
-0.6948111057281494,
-1.4500904083251953,
-0.2182251513004303,
-0.11107765138149261,
-0.05169013887643814,
-0.2795047163963318,
0.26798033714294434,
-0.4485253095626831,
-0.40090757608413696,
-0.20675282180309296,
-0.4909096658229828,
0.13747820258140564,
0.6153324246406555,
0.29840710759162903,
1.0660992860794067,
0.14877451956272125,
-0.044567517936229706,
0.27191534638404846,
0.977526068687439,
0.1392602026462555,
0.4903786778450012,
0.1686914563179016,
0.09272655844688416,
-0.21507766842842102,
0.32221755385398865,
-0.6630368828773499,
0.1712012141942978,
-0.913196861743927,
1.0274540185928345,
0.42761778831481934,
-0.08353591710329056,
-0.08778779953718185,
-0.6670300960540771,
0.3839901387691498,
0.2000766098499298,
0.5833680629730225,
0.5203737020492554,
0.26299411058425903,
0.6320253014564514,
-0.11129497736692429,
-0.33951935172080994,
-0.6923587918281555,
-0.2523861527442932,
-0.2389105260372162,
-0.10161267220973969,
0.43202146887779236,
0.21872544288635254,
0.13170991837978363,
-0.2821168303489685,
0.5090250372886658,
0.8794116973876953,
-0.6950125694274902,
-0.4106774926185608,
-0.1393769085407257,
-0.37004658579826355,
-0.06762272119522095,
0.9031277298927307,
0.021922605112195015,
0.05309027433395386,
-0.8214213252067566,
0.12097280472517014,
0.565397322177887,
-0.5064180493354797,
1.063504695892334,
-0.7006195783615112,
0.49701350927352905,
0.989037036895752,
0.231431782245636,
0.0452989898622036,
0.4249885380268097,
-0.1489122062921524,
-0.17002058029174805,
0.5089957118034363,
-0.48215681314468384,
0.015581111423671246,
-0.8328895568847656,
0.47754937410354614,
-0.06157829612493515,
0.3692062199115753,
-0.6688012480735779,
0.0736631527543068,
-0.6749154925346375,
-0.5965997576713562,
0.8009811043739319,
-0.6049022674560547,
-0.6490361094474792,
0.36249759793281555,
-1.127699851989746,
0.24669018387794495,
-0.43734338879585266,
-0.2041947990655899,
0.04511826112866402,
-0.5282691121101379,
0.15423442423343658,
0.28995800018310547,
-0.6342893242835999,
0.6452843546867371,
0.12614920735359192,
0.6790935397148132,
0.7021030187606812,
-0.44305333495140076,
0.8171519041061401,
0.15889057517051697,
-0.44673624634742737,
-0.3512292802333832,
0.44193416833877563,
0.18696333467960358,
-0.5240036845207214,
-0.1894570142030716,
0.15855911374092102,
-0.31232672929763794,
0.08065161108970642,
-0.013991694897413254,
-0.025116674602031708,
0.04256425052881241,
-0.49257591366767883,
0.38781625032424927,
-0.7089625000953674,
-0.31166699528694153,
-0.7954713702201843,
-0.2602000832557678,
-0.8446304202079773,
-0.9825804829597473,
-0.14836591482162476,
-0.24562790989875793,
-0.787202775478363,
0.5214059948921204,
-1.3504973649978638,
-0.02900736778974533,
0.7414221167564392,
-0.062135960906744,
-0.8464027047157288,
-0.004430149216204882,
0.6511000990867615,
-0.2384749948978424,
0.8420475721359253,
-0.22551338374614716,
0.18581615388393402,
0.3743709921836853,
-0.16503767669200897,
0.63979172706604,
1.0311208963394165,
0.08134202659130096,
0.7720653414726257,
0.32710155844688416,
-0.22094927728176117,
1.0557245016098022,
-0.16438686847686768,
-0.7130102515220642,
0.6245815753936768,
0.7764957547187805,
0.054947998374700546,
0.07095969468355179,
-0.5939568281173706,
0.22109881043434143,
-0.3599690794944763,
0.2569552958011627,
0.7899758815765381,
0.5443084239959717,
0.5411802530288696,
0.4356931149959564,
0.30091434717178345,
0.4493424594402313,
-0.40537014603614807,
0.13056902587413788,
0.5442864298820496,
-0.26650556921958923,
0.041048698127269745,
0.40231576561927795,
-0.44777655601501465,
-0.3511926233768463,
-0.3986850380897522,
0.6112191677093506,
-0.3016515076160431,
0.9151425957679749,
0.3440617620944977,
0.1828813999891281,
-1.1985321044921875,
0.17426642775535583,
-0.2803182601928711,
-0.002045955043286085,
-0.39728134870529175,
-0.3383583724498749,
0.4494536817073822,
-0.07981345057487488,
-0.4299345910549164,
-0.46971097588539124,
-0.07507443428039551,
0.6126238107681274,
-0.10292764753103256,
0.24697692692279816,
0.351109117269516,
0.02792433090507984,
-0.804282546043396,
0.1408003866672516,
-1.1577192544937134,
-0.13684341311454773,
-0.5672374963760376,
0.02976241707801819,
0.8861837983131409,
-0.6584467887878418,
0.03552509471774101,
-0.1556168496608734,
-0.35453730821609497,
0.9356438517570496,
-0.8685747981071472,
0.6836066842079163,
0.8292415738105774,
0.06998308002948761,
-1.0754936933517456,
-0.059397853910923004,
-0.31082093715667725,
-0.15720133483409882,
0.26497912406921387,
0.4412975311279297,
0.9893863797187805,
-0.3396349847316742,
0.213909313082695,
-0.12580740451812744,
-0.9642040133476257,
0.5120740532875061,
0.10333047807216644,
-0.5073065757751465,
-0.2551642060279846,
0.3076695203781128,
-0.056486599147319794,
-0.3975614607334137,
-0.8073770999908447,
1.1314465999603271,
0.5302611589431763,
-0.682334840297699,
0.6441972255706787,
-0.08321691304445267,
-0.17123253643512726,
0.6838994026184082,
0.12481215596199036,
0.25769028067588806,
0.31869640946388245,
0.9059875011444092,
0.4552464187145233,
0.04240402206778526,
-0.3891436457633972,
-0.8604210615158081,
0.35188567638397217,
0.1846311390399933,
-0.32420745491981506,
0.06791069358587265,
-0.34729501605033875,
0.46858862042427063,
0.0618126206099987,
-0.8727408647537231,
0.30587735772132874,
-0.7069929242134094,
-0.4424959421157837,
0.16277377307415009,
-0.624922513961792,
0.7041776776313782,
-0.058701302856206894,
0.41435107588768005,
-1.1571972370147705,
0.008379869163036346,
0.2172223925590515,
0.3966902792453766,
0.7854776382446289,
-0.2772567868232727,
0.45754626393318176,
0.3090865910053253,
0.5628930926322937,
0.38669970631599426,
-0.015413274057209492,
-0.031348470598459244,
-0.10052324086427689,
0.7726626396179199,
-0.5732734203338623,
0.25265851616859436,
0.579868495464325,
0.25703153014183044,
0.37117815017700195,
0.24778646230697632,
-0.027381468564271927,
-0.17896810173988342,
-0.6579593420028687,
-0.4582841396331787,
0.8628482222557068,
0.4806199371814728,
-0.2024189829826355,
-0.28332000970840454,
-0.7418395280838013,
0.009243914857506752,
0.5484709739685059,
0.11124065518379211,
0.5559656023979187,
-1.1398214101791382,
-0.14661449193954468,
-0.279712975025177,
-0.4938376545906067,
0.03441920503973961,
0.05994804948568344,
0.19066910445690155,
0.11172664165496826,
0.3186480700969696,
0.7164830565452576,
-0.5044453144073486,
-0.5830643773078918,
0.06337084621191025,
1.0839333534240723,
0.6747986078262329,
1.1339154243469238,
0.5261853933334351,
-0.5242324471473694,
-0.21318382024765015,
-0.4698132872581482,
-0.6617950797080994,
-0.32813042402267456,
0.09373562037944794,
-0.057931918650865555,
-0.34864598512649536,
-0.25454720854759216,
-0.02693072333931923,
0.506602942943573,
0.6899041533470154,
0.9201408624649048,
0.1009918674826622,
0.1712450385093689,
0.30897074937820435,
0.7393872141838074,
0.6931962966918945,
-0.17167530953884125,
0.09891551733016968,
-1.305625319480896,
0.3981192111968994,
0.016393257305026054,
0.8152315616607666,
-0.013435207307338715,
-0.26219186186790466,
-0.21481846272945404,
-1.0293503999710083,
0.2613416612148285,
0.0384695939719677,
-0.3376849889755249,
0.43274104595184326,
-0.10599655658006668,
0.5404238104820251,
0.05422564595937729,
-0.10905200988054276,
0.43755918741226196,
0.2001114785671234,
0.3857359290122986,
-1.1169404983520508,
0.5497498512268066,
-0.5538877248764038,
0.864714503288269,
0.6894374489784241,
-0.9928817749023438,
-0.698247492313385,
-0.6031890511512756,
0.2353811413049698,
0.2313688099384308,
-0.2938132882118225,
0.8716551661491394,
0.14246734976768494,
0.3500663638114929,
-0.5897184610366821,
-0.21631869673728943,
0.3725241422653198,
-0.6695361137390137,
-0.34447407722473145,
-0.018556924536824226,
-0.3779676854610443,
0.03023824840784073,
0.16302737593650818,
0.2973913848400116,
-0.7479355931282043,
0.08088211715221405,
-0.31344079971313477,
-0.2600744366645813,
-0.2967444658279419,
-0.7798062562942505,
-0.738639771938324,
-0.7370449900627136,
0.044583335518836975,
0.17254851758480072,
0.5394178628921509,
0.04407201334834099,
-0.3565814197063446,
0.23067571222782135,
0.006006759591400623,
-0.34698712825775146,
0.23033583164215088,
0.12726348638534546,
0.7838733196258545,
0.9730112552642822,
0.6716141700744629,
0.554070234298706,
0.026447368785738945,
0.3815545439720154,
-0.044352296739816666,
0.29819226264953613,
0.4460303783416748,
-0.47246164083480835,
-0.016492905095219612,
0.26064053177833557,
-1.2466864585876465,
-0.5598616003990173,
-0.15153688192367554,
0.01571454294025898,
1.019469976425171,
0.26091524958610535,
-1.0210710763931274,
-0.10617053508758545,
-0.6052761077880859,
-0.692554235458374,
0.5965030193328857,
0.26183730363845825,
-0.03461093828082085,
0.9364822506904602,
-0.5038788318634033,
0.2645917236804962,
-0.2559325098991394,
-0.5608406662940979,
-0.6049727201461792,
0.2441997081041336,
0.4897610545158386,
0.6498746871948242,
0.7528144121170044,
-0.35666245222091675,
-0.2323060929775238,
-0.6507420539855957,
0.35771140456199646,
-0.09789364039897919,
-0.08636362850666046,
-0.03533366695046425,
0.04810519143939018,
-0.04464242607355118,
-0.602885901927948,
-0.1707284301519394,
0.2507726848125458,
0.34608834981918335,
-0.5788509249687195,
-0.18389634788036346,
-0.12669453024864197,
-0.2535095512866974,
0.5172123908996582,
0.17689763009548187,
-0.7762647867202759,
-0.1364527940750122,
0.9298082590103149,
0.17565837502479553,
-0.17063739895820618,
-0.2588005065917969,
-0.20839594304561615,
-0.14038360118865967,
-0.5531841516494751,
0.35546332597732544,
-1.081346035003662,
-0.5615170001983643,
-0.21484605967998505,
-0.77467942237854,
0.5304460525512695,
0.16141758859157562,
0.4258215129375458,
0.49348729848861694,
-0.1274809092283249,
-0.1117151528596878,
0.05018438398838043,
-0.968346118927002,
-0.39502066373825073,
-0.5351446270942688,
-0.36496585607528687,
-0.3710440695285797,
0.25311991572380066,
0.01685476489365101,
0.29349830746650696,
0.3062494993209839,
-0.13691627979278564,
0.0841050073504448,
0.2246975153684616,
-0.11549308151006699,
-0.2938043475151062,
0.073104627430439,
0.4716458022594452,
0.2852005660533905,
-0.1959812492132187,
-0.378917396068573,
0.6267300248146057,
-0.7137526869773865,
1.1224714517593384,
-0.14072731137275696,
-0.6359885334968567,
-0.10651189088821411,
0.10787684470415115,
0.18691486120224,
-0.6675710678100586,
0.018755031749606133,
0.37856993079185486,
0.01972113735973835,
0.4191231429576874,
0.021817924454808235,
-0.7731111645698547,
-0.21641208231449127,
-0.3538821041584015,
-0.9132499694824219,
0.23187531530857086,
0.004776409361511469,
-0.34739717841148376,
-0.9335295557975769,
-0.963882327079773,
0.11588167399168015,
0.20899328589439392,
0.41804176568984985,
0.233927920460701,
-0.01595623791217804,
0.6423425674438477,
0.021742181852459908,
0.02695179171860218,
-0.440493106842041,
0.17618267238140106,
0.15498435497283936,
-0.4439609944820404,
-0.24287165701389313,
0.050009407103061676,
-0.6408362984657288,
-1.0841830968856812,
-0.22298528254032135,
0.5203514099121094,
-0.04932185262441635,
-0.07760287076234818,
0.08582466840744019,
-0.6996119022369385,
-0.13876104354858398,
-0.4247943162918091,
0.5253578424453735,
0.09702637046575546,
-0.12623551487922668,
0.15590019524097443,
0.12101203203201294,
0.24659375846385956,
0.3615416884422302,
0.560217559337616,
-0.1650722622871399,
0.06328397989273071,
0.2186965048313141,
-0.6083613634109497,
-0.46295011043548584,
0.4126764237880707,
-0.02924996241927147,
-0.41977572441101074,
0.15551696717739105,
-0.6649081707000732,
-0.5020143389701843,
-0.4688538610935211,
-0.2865241467952728,
0.1933065503835678,
0.33595412969589233,
0.02030300162732601,
1.0130443572998047,
0.3681364953517914,
-0.4100518524646759,
0.20573224127292633,
-0.22465527057647705,
-0.11845488846302032,
-0.29923734068870544,
0.027914438396692276,
1.3097070455551147,
-0.1293184608221054,
-0.6195016503334045,
0.19097548723220825,
-0.09599809348583221,
-0.08262314647436142,
0.5240083932876587,
0.08421371877193451,
-0.370720237493515,
0.7166121602058411,
0.8382185697555542,
0.7436379194259644,
-0.2107398957014084,
-0.05067337304353714,
0.009656156413257122,
0.2948829233646393,
0.015259199775755405,
-0.8613439202308655,
-0.6128213405609131,
-0.6764176487922668,
0.19201213121414185,
0.9922568798065186,
-0.012508844025433064,
0.25146523118019104,
0.22736647725105286,
-0.3991416096687317,
-0.6053135395050049,
-0.8755218386650085,
0.11926979571580887,
-1.1548795700073242,
-0.277835875749588,
-0.52920001745224,
-0.19909608364105225,
0.836020290851593,
0.22407454252243042,
0.3070562779903412,
-0.5760317444801331,
-0.6460572481155396,
-0.29470065236091614,
0.5662550926208496,
-0.3253153860569,
-0.047826942056417465,
-0.3000308871269226,
-0.06822635233402252,
-0.09864164888858795,
0.19153571128845215,
-0.055466022342443466,
0.27925992012023926,
-0.697800874710083,
0.1189650446176529,
0.5304117798805237,
-0.10751296579837799,
0.3679575026035309,
-0.2326306253671646,
-0.6066765785217285,
-0.3730705976486206,
-0.3905166983604431,
-0.7369928956031799,
0.18847627937793732,
-0.04122134670615196,
0.5590039491653442,
-0.06454121321439743,
0.15738727152347565,
-0.38363125920295715,
0.4737039804458618,
-1.031088948249817,
-0.17052197456359863,
-0.1286177933216095,
-0.08580444753170013,
-0.19708581268787384,
-0.8371261358261108,
-0.15350797772407532,
-0.18564707040786743,
-0.8301358222961426,
-0.09304144978523254,
-0.8731083869934082,
-0.3619430959224701,
-0.6863279938697815,
0.2422368973493576,
0.5019094944000244,
0.4879177510738373,
-0.26484644412994385,
0.32603025436401367,
0.1798342913389206,
-0.5207912921905518,
0.14076413214206696,
0.5327073335647583,
0.2588459849357605,
0.45392581820487976,
-0.009201728738844395,
-0.9310320615768433,
-0.2238878607749939,
0.24826550483703613,
-0.012971222400665283,
0.09118787199258804,
-0.2478453516960144,
-1.0472931861877441,
-0.20428156852722168,
0.15467137098312378,
-0.7136698365211487,
0.5960553288459778,
0.5557968616485596,
-0.43214672803878784,
-0.9640394449234009,
-0.5187562704086304,
-0.6284669637680054,
0.18043872714042664,
-0.8962693214416504,
-0.1601213663816452,
0.41012293100357056,
-0.4705740213394165,
0.11221575736999512,
-0.09439253807067871,
-0.307979553937912,
1.0592328310012817,
-0.07741664350032806,
-0.21935953199863434,
-0.06222432479262352,
-0.16030248999595642,
-0.0048965648747980595,
0.16494083404541016,
-0.9519811272621155,
-0.12860098481178284,
-0.6311309337615967,
0.31939759850502014,
-0.8431801199913025,
-0.5559867024421692,
-0.8431887030601501,
0.4383023679256439,
-0.050772760063409805,
-0.3486160635948181,
-0.07009833306074142,
-0.6959730982780457,
0.4996301531791687,
0.07128429412841797,
-0.6484324932098389,
0.16497229039669037,
-0.15782804787158966,
0.9035564064979553,
0.01833776943385601,
-1.0662347078323364,
0.355538547039032,
-0.11890386790037155,
0.07148079574108124,
0.004517620895057917,
-0.021898070350289345,
0.9032799601554871,
0.49363869428634644,
-0.3309982419013977,
1.2577654123306274,
-0.16164898872375488,
0.4914298951625824,
0.29072439670562744,
-0.46971452236175537,
0.24163612723350525,
0.19700880348682404,
0.5781514644622803,
0.08646521717309952,
0.8187268376350403,
0.06981593370437622,
0.3357384502887726,
0.09704770147800446,
0.33852893114089966,
0.03442717343568802,
0.3226569890975952,
0.8873162865638733,
0.33871540427207947,
-0.5335636138916016,
0.3256243169307709,
-0.056162264198064804,
0.08247268199920654,
-0.12734609842300415,
0.04682622104883194,
-0.026131991297006607,
-0.2317521870136261,
0.8565091490745544,
0.3728727400302887,
-0.6432418823242188,
-0.7560635209083557,
-0.44302991032600403,
-0.15569160878658295,
0.38215315341949463,
0.20046065747737885,
0.369808554649353,
0.6690465807914734,
0.7842997312545776,
-0.16236820816993713,
0.15102697908878326,
0.39962974190711975,
0.32706761360168457,
0.8939124345779419,
0.9100407958030701,
0.5415463447570801,
0.3473184406757355,
-0.12069955468177795,
0.38940489292144775,
-0.9012671709060669,
0.4927414059638977,
0.529549241065979,
-1.36867356300354,
-0.11810417473316193,
-0.4994756579399109,
-0.05451808497309685,
-0.45978763699531555,
-0.41538742184638977,
0.7245428562164307,
-1.1188580989837646,
0.3072240650653839,
0.8310238122940063,
-0.5675250291824341,
0.5324669480323792,
1.0007513761520386,
-0.06032407656311989,
0.15755966305732727,
0.4012090265750885,
0.02858145721256733,
-0.04372098296880722,
1.0003204345703125,
1.404302954673767,
0.5149364471435547,
0.24836218357086182,
0.23672263324260712,
-0.7846390008926392,
0.4775986075401306,
0.32341787219047546,
-0.32815492153167725,
0.7924732565879822,
-0.4537188410758972,
-0.5677414536476135,
0.28170403838157654,
0.3483017086982727,
0.08630266785621643,
-0.21534384787082672,
0.4137541353702545,
0.3828619420528412,
-0.32517871260643005,
-0.45168519020080566,
0.99278324842453,
1.1174451112747192,
-0.7341974973678589,
-0.7488171458244324,
0.3315754532814026,
-0.47227969765663147,
-0.36640703678131104,
-1.2203896045684814,
0.12117791175842285,
0.0841783806681633,
0.348800927400589,
-0.06801265478134155,
-0.8050350546836853,
-0.38667750358581543,
-0.8710976839065552,
0.41172078251838684,
-0.5823639035224915,
0.36135637760162354,
-0.3147149682044983,
0.11299730092287064,
0.25406625866889954,
-0.5099093317985535,
0.2241193950176239,
0.18806447088718414,
0.9511858224868774,
-0.11106391251087189,
0.3899724781513214,
0.5940176248550415,
0.7253382205963135,
-0.7081359624862671,
0.9380324482917786,
0.8583624958992004,
-0.9196854829788208,
0.4242950677871704,
-0.6411792635917664,
0.6495741009712219,
0.27543729543685913,
0.12752671539783478,
0.8184762597084045,
-0.020876266062259674,
0.6561112403869629,
-0.04180145263671875,
-0.13621461391448975,
-0.5400060415267944,
-1.1744388341903687,
0.17563830316066742,
-0.6214813590049744,
0.0864129513502121,
-0.45668408274650574,
0.3470977246761322,
0.4090166985988617,
-0.1553105115890503,
4.107909679412842,
1.278902530670166,
0.5245409607887268,
0.4587685465812683,
0.4251382052898407,
0.9359236359596252,
-0.37651896476745605,
-0.2636775076389313,
-0.12250011414289474,
-1.4412492513656616,
-0.5445263385772705,
0.3935304582118988,
0.026318224146962166,
-0.30776074528694153,
-0.03131720423698425,
0.7287845611572266,
-0.42020076513290405,
0.08799668401479721,
-0.08220423012971878,
-0.97562175989151,
-0.9397193789482117,
0.5002171993255615,
-0.1552528440952301,
0.023444680497050285,
0.5235410332679749,
0.24641470611095428,
0.03487738221883774,
-0.30585360527038574,
-0.3542185425758362,
-0.22773657739162445,
-0.67793869972229,
-1.070974349975586,
0.14813604950904846,
-0.4642200767993927,
-0.771309494972229,
0.26291269063949585,
-0.49012866616249084,
-0.5143288373947144,
0.3938997983932495,
0.22194097936153412,
-0.05943409726023674,
0.11021063476800919,
-0.2247374951839447,
-0.18186403810977936,
-0.9658637642860413,
1.0185126066207886,
0.14504271745681763,
0.7841454148292542,
0.05737229064106941,
-0.5635862946510315,
0.9267005324363708,
-0.22842776775360107,
0.6013034582138062,
-0.46828359365463257,
-0.9333357214927673,
0.16811025142669678,
-0.5252669453620911,
-0.03235643357038498,
0.7251676321029663,
0.7343892455101013,
0.6642366051673889,
-0.2735070586204529,
-0.46653375029563904,
-0.10323743522167206,
0.5329281091690063,
0.41247299313545227,
-0.23989702761173248,
0.5523561835289001,
-0.22284604609012604,
-0.16671590507030487,
-0.1838458627462387,
-0.4902661442756653,
-0.39238110184669495,
0.08936482667922974,
0.8114510774612427,
0.1553596556186676,
-0.221268892288208,
0.5300872921943665,
-0.5507273077964783,
-0.11569354683160782,
-0.11072991043329239,
-0.4220944941043854,
0.021640954539179802,
0.02326332964003086,
-0.3296625018119812,
0.9670659303665161,
-0.4594840407371521,
0.15761873126029968,
-0.13094240427017212,
0.1801041215658188,
0.015756826847791672,
1.5429669618606567,
0.3703063130378723,
-0.5028308033943176,
-0.9990600943565369
] |
$1/N$ Expansion of Two-Dimensional Models in the Scaling Region
|
The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with standard and improved lattice actions. We show how to perform the asymptotic expansion of effective propagators for small values of the mass gap and how to employ this result in the evaluation of physical quantities in the scaling regime. The lattice renormalization group $\beta$ function is constructed explicitly and exactly to $O({1/N})$.
|
Massimo Campostrini and Paolo Rossi
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210011
|
hep-lat/9210012
|
[
0.7738994359970093,
-0.3898041248321533,
-0.18271812796592712,
0.5519511699676514,
0.6132097840309143,
0.024873407557606697,
0.051057565957307816,
-0.55584317445755,
-0.12900914251804352,
1.8187252283096313,
0.9589800834655762,
-0.24857360124588013,
0.16169007122516632,
-0.7802013158798218,
-0.06859897077083588,
1.2276593446731567,
0.1214623749256134,
-0.747582733631134,
-1.175434947013855,
0.13973453640937805,
0.2592715919017792,
-0.23839259147644043,
-0.8078821301460266,
-0.8027797341346741,
-0.90007084608078,
0.9557744860649109,
0.02573808655142784,
0.41941797733306885,
0.9846392273902893,
0.834191620349884,
0.4440353214740753,
-0.45937955379486084,
-0.06665229052305222,
-0.3441242575645447,
-0.7115872502326965,
-0.20850615203380585,
-0.296186238527298,
-0.09608567506074905,
0.8428001403808594,
-0.40443363785743713,
0.8303614854812622,
-0.7146449089050293,
0.35913535952568054,
-0.3531920909881592,
-0.5897596478462219,
0.49829691648483276,
0.0729089006781578,
0.4594128429889679,
0.01972012221813202,
-1.5581748485565186,
-0.06563811749219894,
0.32496240735054016,
0.4546222388744354,
-0.6097036004066467,
0.18926620483398438,
0.31918641924858093,
0.05715592950582504,
0.42518699169158936,
-0.5451063513755798,
-0.6549164056777954,
0.5775452256202698,
0.05856189876794815,
0.11096595972776413,
-1.0247139930725098,
-0.294034481048584,
0.2730973958969116,
-0.22478444874286652,
0.7676361203193665,
0.09785357862710953,
-0.8421816229820251,
-0.3159530460834503,
-0.02411506697535515,
-0.7919785976409912,
0.027667222544550896,
-0.7229816913604736,
0.2514723241329193,
-0.2309165894985199,
-0.2998165488243103,
-0.858553409576416,
-0.19313488900661469,
0.03001386672258377,
0.13134068250656128,
-0.6396761536598206,
0.25711798667907715,
-0.642110288143158,
-0.4739235043525696,
-0.0988941416144371,
-0.19644410908222198,
-0.15662240982055664,
0.8798889517784119,
0.21192102134227753,
0.8060675263404846,
-0.7828562259674072,
0.21552200615406036,
0.23589685559272766,
0.7948955297470093,
0.06402264535427094,
0.540295422077179,
0.16022196412086487,
0.3894743323326111,
0.309384822845459,
0.6741369366645813,
-0.08736097067594528,
0.34509751200675964,
-0.9404789805412292,
0.6465855240821838,
0.10537739843130112,
0.3981327414512634,
0.022457178682088852,
-0.48947641253471375,
0.30614811182022095,
-0.4760712683200836,
0.025585515424609184,
0.7673032283782959,
-0.19553981721401215,
0.1266542226076126,
-0.03228567913174629,
-0.2555024027824402,
-0.9232577085494995,
-0.07797379046678543,
-0.0420951321721077,
-0.11379451304674149,
0.36357855796813965,
0.36862221360206604,
-0.4901365637779236,
-0.026390140876173973,
0.27334296703338623,
0.7295953035354614,
-0.16158682107925415,
0.3069049119949341,
0.30637261271476746,
0.5761398077011108,
0.1529475599527359,
0.19004645943641663,
-0.1623598337173462,
0.17575524747371674,
-0.2320839762687683,
0.7028124928474426,
0.7826412916183472,
-0.12387865036725998,
0.716010570526123,
-0.024322321638464928,
0.2754354476928711,
1.103594422340393,
0.12506863474845886,
0.5460348725318909,
0.39315086603164673,
-0.13904140889644623,
-0.09410890191793442,
0.46769019961357117,
-0.5076461434364319,
0.5330016613006592,
0.02748669683933258,
0.6002115607261658,
0.09718333184719086,
0.6504303812980652,
-0.38877588510513306,
0.5505189299583435,
-0.990726113319397,
-0.7253467440605164,
0.6078677773475647,
-0.07416193932294846,
-0.2262282818555832,
0.09842637926340103,
-0.607882022857666,
0.1887209564447403,
-0.6734084486961365,
-0.16338194906711578,
0.6269709467887878,
-0.5395519137382507,
-0.02291983552277088,
0.7961728572845459,
-0.2081393599510193,
0.8154231905937195,
0.467970609664917,
0.4635644555091858,
0.20557378232479095,
-0.5339092016220093,
0.3916725814342499,
-0.032426368445158005,
0.1108635887503624,
-0.5385301113128662,
0.8446846008300781,
0.25227198004722595,
-0.27035456895828247,
0.5931158065795898,
0.04806707799434662,
-0.10918097198009491,
-0.20784969627857208,
0.25965678691864014,
-0.7460373044013977,
0.25870680809020996,
-0.20554067194461823,
0.39647048711776733,
-0.9552226662635803,
-0.2901066839694977,
-1.3414818048477173,
0.5332738757133484,
-0.9427862167358398,
0.07184115797281265,
0.23500800132751465,
0.522566556930542,
-1.4784016609191895,
0.3832484185695648,
-1.1290615797042847,
-0.13320882618427277,
0.6917328834533691,
-0.03961583599448204,
-0.3561740517616272,
-0.60743248462677,
0.5665817856788635,
-0.2494230568408966,
0.4108966588973999,
-0.7728628516197205,
0.21427471935749054,
-0.06998305022716522,
-0.18335556983947754,
0.35986900329589844,
0.9765245318412781,
0.14613042771816254,
0.8117611408233643,
0.4932050108909607,
-0.37487614154815674,
1.2549508810043335,
-0.4806203246116638,
-0.39484846591949463,
0.21811354160308838,
0.2684163749217987,
-0.07138372957706451,
0.047613948583602905,
0.37050721049308777,
0.48957905173301697,
-0.03146062046289444,
0.23994402587413788,
1.3345097303390503,
0.4361329674720764,
0.6379774212837219,
0.37171852588653564,
0.09843595325946808,
0.20682790875434875,
-0.27076661586761475,
0.5885900855064392,
0.18420416116714478,
0.41986745595932007,
-0.5275765657424927,
0.3138507604598999,
-0.8240782618522644,
0.40480151772499084,
-0.6438213586807251,
0.49724987149238586,
-0.5459436178207397,
0.5623524785041809,
-0.14333070814609528,
0.511755108833313,
-1.459179162979126,
0.31706833839416504,
-0.4078696072101593,
0.041122887283563614,
-0.1488664597272873,
-0.5051141977310181,
0.3492058515548706,
-0.30327102541923523,
-0.3015820384025574,
-0.6077815890312195,
-0.24072463810443878,
0.8857120871543884,
0.1606162041425705,
0.42982494831085205,
0.690589427947998,
-0.015310307964682579,
-1.562275767326355,
0.25168105959892273,
-1.4094555377960205,
0.06893924623727798,
-0.45745331048965454,
0.3717750608921051,
0.5835771560668945,
-0.7594847679138184,
0.3796416223049164,
-0.2514392137527466,
-0.41922527551651,
0.4257553219795227,
-0.41260308027267456,
0.5021670460700989,
-0.1746504306793213,
0.009974327869713306,
-1.1910864114761353,
0.520881175994873,
-1.2722783088684082,
-0.2478538602590561,
-0.2138643115758896,
0.3960524797439575,
0.880861759185791,
-0.3208557069301605,
0.34001025557518005,
0.14590954780578613,
-0.40741923451423645,
-0.1719525307416916,
-0.039808306843042374,
-0.7256518006324768,
-0.17088991403579712,
-0.12034396827220917,
-0.6259874701499939,
-0.816047728061676,
-1.1351393461227417,
0.9671126008033752,
0.11617550998926163,
-0.10245151072740555,
0.4301467537879944,
0.2522353231906891,
-0.29915928840637207,
0.21830084919929504,
0.6042931079864502,
-0.1727541983127594,
-0.027782518416643143,
1.025371789932251,
0.6226791739463806,
0.32190147042274475,
0.10625788569450378,
-0.8743061423301697,
-0.14461363852024078,
0.5524890422821045,
0.03710717335343361,
-0.5034958720207214,
0.14630697667598724,
1.4234126806259155,
0.1760355830192566,
-0.7065207958221436,
0.15773923695087433,
-0.9469805359840393,
-0.7448388934135437,
-0.1287778913974762,
-0.946216881275177,
0.4899081289768219,
0.1418425440788269,
0.43812164664268494,
-1.192491888999939,
-0.48711416125297546,
-0.4026464819908142,
0.38679686188697815,
0.3910709023475647,
-0.41077977418899536,
0.27567359805107117,
0.6191383004188538,
0.2643047273159027,
-0.563886821269989,
0.18107864260673523,
-0.17429131269454956,
-0.11594346165657043,
0.5723636746406555,
-0.5876164436340332,
0.34134089946746826,
0.37061789631843567,
0.19152429699897766,
0.01625903509557247,
0.3232974410057068,
-0.8064324855804443,
-0.3768925666809082,
-0.6011163592338562,
-0.3532973825931549,
-0.1136888936161995,
0.4489390254020691,
-0.2685317099094391,
-0.06310999393463135,
-1.1155718564987183,
-0.5839238166809082,
0.13974587619304657,
-0.2254682332277298,
0.9182540774345398,
-1.0580806732177734,
0.23939669132232666,
0.14774270355701447,
-0.17949749529361725,
0.5747379064559937,
-0.3400806784629822,
0.19706712663173676,
0.07056564092636108,
-0.32022568583488464,
0.7988306283950806,
-0.3547000288963318,
-0.6643330454826355,
-0.28205469250679016,
1.107456088066101,
0.7760143280029297,
0.6065708994865417,
0.12478188425302505,
-0.44208621978759766,
-0.5481377243995667,
-0.330276757478714,
-0.49478694796562195,
-0.2936423420906067,
-0.5436847805976868,
-0.6474868655204773,
0.02787591889500618,
-0.2122567743062973,
0.08793268352746964,
0.3102889657020569,
0.9044455289840698,
0.5550605654716492,
0.22805175185203552,
0.47286170721054077,
0.4682079553604126,
0.5149904489517212,
0.44842690229415894,
0.11064973473548889,
0.04743369668722153,
-0.9028570652008057,
0.460831880569458,
0.6159795522689819,
-0.020914550870656967,
-0.18209116160869598,
-0.3895057737827301,
-0.12040763348340988,
-0.4840577244758606,
0.43581488728523254,
-0.05388599634170532,
-0.5897446274757385,
0.5938528180122375,
-0.3487386107444763,
0.4567176401615143,
-0.3361127972602844,
-0.5268025398254395,
0.6939893364906311,
0.5672343373298645,
0.18595896661281586,
-0.8661187887191772,
0.3861219882965088,
-0.20239363610744476,
0.43686723709106445,
0.5929825901985168,
-0.8187241554260254,
-1.1993588209152222,
-0.4096943736076355,
-0.31450551748275757,
-0.24522556364536285,
0.07833682745695114,
1.1518752574920654,
-0.12042804807424545,
0.4205700755119324,
-0.9075520634651184,
-0.17398227751255035,
0.8190708160400391,
-0.7072840332984924,
-0.11086840182542801,
0.18673795461654663,
0.1503968983888626,
0.0864306390285492,
0.7644660472869873,
-0.264128178358078,
-0.6744014024734497,
-0.7419707775115967,
-0.5189944505691528,
-0.1805698573589325,
-0.06931199133396149,
-0.09334349632263184,
-0.0874137431383133,
-0.2223869413137436,
-0.033197320997714996,
0.6417672634124756,
0.22780823707580566,
0.0922057181596756,
-0.13140814006328583,
0.15104718506336212,
0.11306436359882355,
-0.2941330671310425,
0.10372520983219147,
0.4289357364177704,
0.5456094145774841,
1.026422381401062,
0.46933215856552124,
0.3662271797657013,
-0.4184347093105316,
0.24453234672546387,
-0.06130744144320488,
-0.21285445988178253,
0.025697730481624603,
-0.3171219527721405,
-0.263312429189682,
-0.08852427452802658,
-0.4031544625759125,
-0.949982225894928,
0.7468716502189636,
0.15878377854824066,
0.4959842264652252,
-0.025127079337835312,
-0.1442214399576187,
-0.9267774224281311,
-0.5077906847000122,
-0.6176972985267639,
0.9697193503379822,
-0.1639205515384674,
-0.007679760456085205,
1.1435219049453735,
-0.6775606870651245,
0.2018304318189621,
0.1403186321258545,
-0.20296896994113922,
-0.13606208562850952,
0.11437156051397324,
1.037217378616333,
0.5218844413757324,
0.8471639752388,
-0.35982203483581543,
0.4142776429653168,
0.07723306119441986,
0.06811767816543579,
-0.2504812777042389,
0.20998966693878174,
-0.26908811926841736,
-0.4766683876514435,
0.2922499477863312,
-0.8031141757965088,
-0.20370104908943176,
0.13869573175907135,
-0.08743605762720108,
0.09407880902290344,
-0.1675320863723755,
-0.20668844878673553,
-0.3368838429450989,
0.12862995266914368,
0.5269346833229065,
-0.6025959253311157,
0.5074306726455688,
1.4943046569824219,
0.3515826463699341,
0.5418967008590698,
-0.09881992638111115,
-0.1291220784187317,
0.18491116166114807,
-0.6835512518882751,
0.38558635115623474,
-1.1060734987258911,
-0.5464910268783569,
-0.054987046867609024,
-0.21131235361099243,
0.7005183100700378,
0.3746277987957001,
-0.4380791485309601,
-0.08600650727748871,
-0.03523300215601921,
-0.40094879269599915,
0.4578931927680969,
-0.9415087103843689,
-0.31520241498947144,
-0.10980340838432312,
-0.6370354294776917,
-0.8667610883712769,
0.981391966342926,
-0.1291894167661667,
0.4281668961048126,
0.49479153752326965,
-0.24784350395202637,
0.13850854337215424,
-0.07169191539287567,
-0.26601874828338623,
-0.3110157549381256,
-0.19755055010318756,
0.5346029996871948,
-0.05937224254012108,
0.21911652386188507,
-0.4326961040496826,
0.593083381652832,
-0.46964842081069946,
0.8548165559768677,
-0.19161470234394073,
-0.5553911924362183,
-0.11360897868871689,
0.3552798330783844,
1.0594228506088257,
-0.541145920753479,
0.731376051902771,
0.1704118400812149,
-0.3593675196170807,
0.6433362364768982,
-0.002269152784720063,
-0.4408293664455414,
-0.25280678272247314,
-0.3098468780517578,
-0.7580211758613586,
0.4317707121372223,
0.2591807544231415,
-0.45245715975761414,
-0.8151132464408875,
-0.5287424325942993,
-0.17552942037582397,
-0.40098005533218384,
-0.06037662550806999,
0.29119810461997986,
-0.37049949169158936,
0.5847569108009338,
0.10606986284255981,
0.1274002492427826,
-0.5508028864860535,
-0.4844065308570862,
-0.1082758679986,
-0.03326210752129555,
-0.03223824501037598,
0.41080012917518616,
-0.2637932598590851,
-1.2535237073898315,
-0.4148176610469818,
0.5507017970085144,
0.421629935503006,
-0.5572682619094849,
0.7044915556907654,
0.035723425447940826,
-0.42316120862960815,
-0.7304377555847168,
0.22981701791286469,
-0.20794929563999176,
0.04650044068694115,
0.5149326920509338,
0.142944797873497,
0.10454878211021423,
0.0875362977385521,
0.6797434687614441,
-0.15591686964035034,
-0.23172803223133087,
0.46603119373321533,
-0.5908737182617188,
-0.41407158970832825,
0.19359301030635834,
0.06420106440782547,
-0.35269251465797424,
-0.2956673800945282,
-1.3256042003631592,
-0.5106971263885498,
-0.31351956725120544,
-0.4157670736312866,
0.23357948660850525,
-0.1959265172481537,
-0.5065509676933289,
0.5622986555099487,
0.6466404795646667,
0.1798553168773651,
0.2383013367652893,
-0.058542147278785706,
-0.299964040517807,
-0.13249535858631134,
0.06709044426679611,
1.1779628992080688,
0.38577041029930115,
-0.4689163863658905,
0.15560513734817505,
-0.17713186144828796,
-0.6526373624801636,
0.22319138050079346,
0.44578447937965393,
-0.6156324148178101,
0.42161327600479126,
0.3082481026649475,
0.07402355223894119,
0.29235637187957764,
0.43015438318252563,
0.5004745721817017,
0.01712988317012787,
-0.13006165623664856,
-0.3641583323478699,
0.06966150552034378,
-0.5016714334487915,
-0.019197318702936172,
1.2374807596206665,
0.04275621846318245,
0.21846719086170197,
-0.2831658720970154,
-0.6658058762550354,
-0.8988586068153381,
-0.9971436262130737,
-0.03211614862084389,
-0.7830250263214111,
-0.3858190178871155,
-0.2469760626554489,
-0.5984495878219604,
0.3006851375102997,
0.16507601737976074,
-0.26267874240875244,
0.09128538519144058,
-0.7801432609558105,
0.3914225995540619,
0.37079307436943054,
0.1898878812789917,
-0.10274364054203033,
-0.5824617147445679,
-0.7407383918762207,
0.08420220762491226,
-0.6143752932548523,
-0.12023383378982544,
-0.4948979616165161,
-0.5467255115509033,
0.17066547274589539,
0.5660800337791443,
-0.1652897596359253,
0.9238383769989014,
-0.8400627374649048,
-0.9026071429252625,
-0.4199924170970917,
-0.4525996744632721,
-0.5296039581298828,
0.08019745349884033,
0.11950036138296127,
0.6347192525863647,
0.46724963188171387,
-0.04226228967308998,
-0.45470717549324036,
0.4658593237400055,
-0.8520915508270264,
0.2592284083366394,
0.35884106159210205,
0.11343983560800552,
-0.5296107530593872,
-0.1797124445438385,
-0.04345691576600075,
0.1490347981452942,
-0.8545969724655151,
0.5619306564331055,
-0.6683385372161865,
-0.3940333127975464,
-0.33460327982902527,
0.27983689308166504,
0.6039964556694031,
0.6813507676124573,
-0.7150315046310425,
0.2362326979637146,
-0.3996032774448395,
-0.10377618670463562,
0.3369770348072052,
0.016702696681022644,
-0.23400112986564636,
0.20796039700508118,
0.44438448548316956,
-0.5951518416404724,
-0.09725316613912582,
0.1754717379808426,
-0.7143218517303467,
0.22928129136562347,
-0.06631540507078171,
-0.26304200291633606,
-0.07843480259180069,
-0.1665055900812149,
-0.9412692785263062,
0.4280996024608612,
0.22635027766227722,
-0.31825384497642517,
-0.5965800881385803,
-0.4377071261405945,
-0.8462493419647217,
0.2525467276573181,
-0.75323486328125,
-0.3478931784629822,
0.0918484553694725,
-0.2647082805633545,
-0.45825180411338806,
-0.08355712890625,
-0.11653964221477509,
0.5134008526802063,
0.16495217382907867,
0.3720160722732544,
-0.12843002378940582,
0.16993403434753418,
-0.08883749693632126,
0.06931477040052414,
-0.7504628300666809,
-0.40918317437171936,
-0.19897377490997314,
0.6347250938415527,
-0.43936747312545776,
-0.6174262166023254,
-0.533968985080719,
0.45279547572135925,
-0.12293897569179535,
0.33834943175315857,
0.000006673528332612477,
0.022483959794044495,
0.047445062547922134,
0.047554194927215576,
-0.2309098243713379,
0.4142202138900757,
-0.4794861674308777,
0.8676570057868958,
0.23754341900348663,
-1.0243072509765625,
0.343889057636261,
-0.03168673813343048,
0.1084854006767273,
-0.5149073600769043,
-0.5722238421440125,
1.0187954902648926,
0.0038150628097355366,
-0.2108955681324005,
0.7113454937934875,
0.26433223485946655,
-0.30020713806152344,
-0.02668699249625206,
-0.3185364603996277,
0.4046201705932617,
-0.32550719380378723,
0.06704845279455185,
0.7943248152732849,
0.4244058430194855,
0.39510378241539,
0.7903846502304077,
0.4865797460079193,
-0.013682044111192226,
0.09223918616771698,
-0.17947565019130707,
0.49659714102745056,
0.4620051681995392,
-0.030300574377179146,
-0.0010968840215355158,
0.5796407461166382,
-0.015037224628031254,
-0.08932526409626007,
-0.17768727242946625,
-0.00016875941946636885,
0.10444087535142899,
0.05990568548440933,
0.2849547564983368,
-0.7581504583358765,
-0.5384592413902283,
-0.4926437735557556,
0.20392648875713348,
-0.2784188687801361,
0.047568801790475845,
-0.15537434816360474,
0.4937531352043152,
0.6971396803855896,
0.15559573471546173,
0.390388548374176,
0.6558212041854858,
0.6303553581237793,
1.1870982646942139,
0.5496545433998108,
0.03391551226377487,
0.36356544494628906,
0.08532020449638367,
0.510961651802063,
-0.915726363658905,
-0.17718808352947235,
0.8064358234405518,
-1.0099366903305054,
0.4408387839794159,
-0.10777952522039413,
-0.3250376880168915,
-0.14626255631446838,
-0.743368923664093,
0.3169921338558197,
-0.2823416292667389,
0.10699605196714401,
0.9107841849327087,
-0.36305826902389526,
0.20372293889522552,
1.3052908182144165,
-0.09414620697498322,
0.05642402544617653,
0.29633820056915283,
-0.06663456559181213,
0.4181322157382965,
1.0395889282226562,
1.5798465013504028,
0.045438189059495926,
0.06577549129724503,
0.3149149417877197,
-0.516737163066864,
0.25746288895606995,
0.4017997682094574,
-0.026171209290623665,
0.83444744348526,
-0.8143779039382935,
-0.3982517719268799,
0.5958704948425293,
0.6980569958686829,
-0.06642129272222519,
-0.008196821436285973,
-0.046437591314315796,
-0.12906603515148163,
-0.6869217753410339,
-0.7005399465560913,
1.3868261575698853,
0.35552990436553955,
0.03299222141504288,
-0.2921716272830963,
0.13618780672550201,
-0.4037467837333679,
-0.07144924998283386,
-0.6526322960853577,
-0.013605757616460323,
0.14997781813144684,
0.0512395054101944,
-0.026255110278725624,
-1.2111481428146362,
-0.1458948850631714,
-1.048840045928955,
0.09061703085899353,
-0.8695220947265625,
0.33177003264427185,
0.31066474318504333,
0.6807990074157715,
0.02262590453028679,
-0.549586832523346,
-0.12978513538837433,
-0.04589082673192024,
1.0852938890457153,
0.01847839169204235,
0.2568052113056183,
0.5329974293708801,
-0.04031182453036308,
-0.6916154623031616,
0.6896125078201294,
0.680912971496582,
-0.44242480397224426,
0.6788961887359619,
-0.5354976058006287,
0.5797681212425232,
0.2582089304924011,
-0.40674203634262085,
0.4047298729419708,
-0.2839961647987366,
0.7708863615989685,
-0.310693621635437,
-0.2871948778629303,
-0.5354160070419312,
-0.7523344159126282,
0.3329737186431885,
-0.7641413807868958,
-0.028570929542183876,
-0.19855110347270966,
0.20770081877708435,
0.017512530088424683,
-1.0272190570831299,
4.155331134796143,
0.5896403789520264,
0.5773491859436035,
-0.13898862898349762,
0.43292972445487976,
0.40751785039901733,
-0.1436292678117752,
0.25614678859710693,
0.27310043573379517,
-0.8154836893081665,
-0.6535788774490356,
0.28342342376708984,
0.3104642927646637,
-0.06848855316638947,
-0.301278680562973,
0.37110939621925354,
-0.2544787526130676,
0.06278453767299652,
0.11730463802814484,
-0.8710257411003113,
-0.6582410335540771,
0.039124518632888794,
0.4526822865009308,
-0.1377394199371338,
-0.1967715471982956,
-0.2638731896877289,
0.3660954236984253,
-0.7173862457275391,
-0.8727214336395264,
-0.7940887212753296,
-0.2732962369918823,
-1.3804348707199097,
0.12573014199733734,
-0.15594929456710815,
-0.633181095123291,
-0.04245074838399887,
0.4740441143512726,
-0.1568853259086609,
0.25863760709762573,
0.14723064005374908,
-0.14255684614181519,
0.10319317132234573,
0.3915548324584961,
-0.6394233107566833,
-0.5965918898582458,
0.7153828144073486,
0.000047830279072513804,
0.631619393825531,
0.03397421911358833,
-0.3486299514770508,
0.4065006375312805,
-0.31660735607147217,
0.6051694750785828,
-0.32919949293136597,
-0.9063843488693237,
0.18150876462459564,
-0.8251627087593079,
0.08438011258840561,
0.02806924469769001,
0.13859045505523682,
-0.07398917526006699,
-0.4558621346950531,
-0.05856545642018318,
-0.2846255600452423,
0.047359008342027664,
0.1814379245042801,
-0.03670087829232216,
-0.022662706673145294,
0.3253241777420044,
0.024675065651535988,
0.10608243942260742,
-0.8373091220855713,
-0.3786350190639496,
0.2041943222284317,
0.5586647391319275,
-0.16985511779785156,
-0.15315325558185577,
0.9055364727973938,
-0.15494279563426971,
0.30041325092315674,
-0.1726153939962387,
0.036346521228551865,
-0.5022116303443909,
0.44194984436035156,
-0.04267042130231857,
1.2370021343231201,
-0.5981579422950745,
-0.20241287350654602,
-0.06707100570201874,
0.5890256762504578,
0.3848739266395569,
1.6805393695831299,
-0.08470755070447922,
0.018628738820552826,
-1.1510428190231323
] |
Topological susceptibility and string tension in CP(N-1) models
|
We investigate the features of ${\rm CP}^{N-1}$ models concerning confinement and topology. In order to study the approach to the large-$N$ asymptotic regime, we determine the topological susceptibility and the string tension for a wide range of values of $N$, in particular $N=4,10,21,41$. Quantitative agreement with the large-$N$ predictions is found for the ${\rm CP}^{20}$ and the ${\rm CP}^{40}$ models. Problems related to the measure of the topological susceptibility and the string tension on the lattice are discussed.
|
Massimo Campostrini, Paolo Rossi, and Ettore Vicari (Dipartimento di Fisica dell'Universit\`a and Istituto Nazionale di Fi...
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210012
|
hep-lat/9210013
|
[
0.5421100854873657,
-0.6951325535774231,
0.18540263175964355,
-0.21714767813682556,
-0.7771458029747009,
-0.31379276514053345,
0.09707117825746536,
-0.17260149121284485,
0.16931799054145813,
0.703123152256012,
0.001769481459632516,
-0.2885375916957855,
0.195317804813385,
-0.2698613703250885,
-0.10492870211601257,
0.8101054430007935,
-0.23208963871002197,
-0.29186132550239563,
-1.1569173336029053,
0.7471723556518555,
0.5025686621665955,
-0.6976509094238281,
-0.9867121577262878,
-0.18330521881580353,
-0.6685445308685303,
0.7130215167999268,
0.6483028531074524,
-0.11154436320066452,
0.8976592421531677,
0.38449063897132874,
0.05166374519467354,
-0.5580728054046631,
0.3717310130596161,
-0.8468987345695496,
-0.059668656438589096,
0.09808974713087082,
0.05278173089027405,
-0.3187415599822998,
0.3662099242210388,
-0.4816184341907501,
0.8412194848060608,
-0.461353063583374,
-0.419120192527771,
-0.40204331278800964,
-0.8694316148757935,
-0.15336108207702637,
-0.38192594051361084,
-0.2636040151119232,
0.5409204363822937,
-1.2561252117156982,
0.24577338993549347,
0.5650710463523865,
0.9979850053787231,
-0.2389925867319107,
-0.7287542819976807,
-0.09179029613733292,
-0.2419424206018448,
-0.35975801944732666,
-0.5411063432693481,
-0.1559545397758484,
0.4051189124584198,
-0.018840499222278595,
0.15069635212421417,
-0.6171778440475464,
-0.08095768094062805,
0.7257195115089417,
-0.2590009868144989,
0.686149537563324,
0.18296565115451813,
-0.26480987668037415,
0.6640434265136719,
0.09551263600587845,
-1.2780200242996216,
0.26459401845932007,
-0.7950059175491333,
0.271927148103714,
0.05913972482085228,
-0.2171160727739334,
-0.7351475954055786,
-0.017307179048657417,
-0.09484164416790009,
-0.5338064432144165,
-0.3804541826248169,
0.5184677243232727,
-0.425231397151947,
0.39497506618499756,
-0.18495574593544006,
-0.49567723274230957,
0.2281017005443573,
-0.16809873282909393,
0.6267418265342712,
0.9821193814277649,
-0.4203750789165497,
-0.5711176991462708,
0.4521213173866272,
0.05261777713894844,
-0.12513798475265503,
0.18585996329784393,
0.47759371995925903,
0.7436466217041016,
0.06253769248723984,
-0.001825295272283256,
-0.7969550490379333,
0.3632982671260834,
0.01859501376748085,
0.6838976740837097,
-0.4207959771156311,
0.30720144510269165,
-0.13349884748458862,
-0.4680142104625702,
0.46437379717826843,
-0.8285853862762451,
0.26874133944511414,
-0.009923080913722515,
-0.2913639545440674,
0.6942899227142334,
-0.17078985273838043,
0.3286373019218445,
-0.07514465600252151,
-0.27312758564949036,
0.2025986611843109,
0.12443316727876663,
0.26532143354415894,
0.1067429631948471,
-0.414791077375412,
0.3640371561050415,
-0.39348334074020386,
0.3283063471317291,
-0.8801605701446533,
-0.14019624888896942,
0.04751206934452057,
-0.6608990430831909,
-0.3450024724006653,
0.20673801004886627,
-0.8393926620483398,
-0.06883485615253448,
0.010352203622460365,
0.10855025053024292,
-0.604823648929596,
-0.6197894215583801,
0.24457120895385742,
0.2152886688709259,
0.020058192312717438,
1.449190616607666,
0.23472988605499268,
0.6193922162055969,
0.009035264141857624,
0.39016810059547424,
-0.8015378713607788,
0.6423134207725525,
-0.7503136992454529,
-0.2877446711063385,
-0.49979367852211,
0.788673460483551,
-0.39189067482948303,
0.01892780140042305,
-0.04775899648666382,
0.12277799099683762,
-0.2597961127758026,
-0.3447631001472473,
-0.27770304679870605,
0.04346572980284691,
0.1209428533911705,
0.4271765649318695,
-0.4203994572162628,
-0.11516030877828598,
-1.117847204208374,
-0.5810613632202148,
0.30407989025115967,
-0.6667535901069641,
-0.27876603603363037,
-0.043295472860336304,
-0.262470006942749,
0.8940768241882324,
0.8485168218612671,
0.10106632113456726,
0.6696129441261292,
-0.0006553825223818421,
-0.35717278718948364,
0.7274110317230225,
0.09863133728504181,
-0.3672735095024109,
0.23666805028915405,
0.3743641674518585,
-0.047310423105955124,
-0.14471709728240967,
-0.05574386566877365,
-0.5328192114830017,
0.018668845295906067,
0.17062439024448395,
0.06730400770902634,
0.43434807658195496,
-0.30777832865715027,
0.485759437084198,
-1.0212628841400146,
-0.16044791042804718,
-0.425291508436203,
0.4705570638179779,
-0.995403528213501,
-0.4841768741607666,
0.41255977749824524,
-0.11771543323993683,
-0.8994013667106628,
0.026608485728502274,
-1.1422868967056274,
-0.2023342251777649,
0.7997943758964539,
0.6178876757621765,
-0.5894483327865601,
0.16134636104106903,
0.0455898679792881,
0.18326082825660706,
0.13246184587478638,
-0.15096966922283173,
0.33541494607925415,
0.25177788734436035,
0.39648139476776123,
0.8100298047065735,
-0.46325552463531494,
-0.22537989914417267,
0.25622400641441345,
0.16854970157146454,
0.01287016086280346,
0.2987767457962036,
-0.14258253574371338,
-0.4108114242553711,
-0.24485279619693756,
0.7058138251304626,
0.14615406095981598,
-0.8553445339202881,
-0.7997192144393921,
0.6194506287574768,
-0.085112065076828,
0.6921612620353699,
-0.7108176946640015,
0.4621508717536926,
0.7885802388191223,
-0.14843575656414032,
0.7089990377426147,
0.03500636667013168,
-0.24694198369979858,
-0.9151709079742432,
0.3165985345840454,
0.022940266877412796,
-0.08950734883546829,
-0.392792284488678,
-0.10503717511892319,
-0.18667301535606384,
-0.7379485368728638,
0.6341221332550049,
-0.42864635586738586,
0.42652472853660583,
-0.02899489738047123,
0.5207894444465637,
-0.7709882855415344,
-0.40361759066581726,
0.1530773788690567,
0.500128984451294,
0.4493926167488098,
0.07572636753320694,
0.552421510219574,
0.7646488547325134,
-0.2117716670036316,
-0.8067829608917236,
0.10873644798994064,
1.5865503549575806,
0.14907300472259521,
0.7004365921020508,
0.6796889901161194,
-0.7164251208305359,
-1.0787044763565063,
-0.5950777530670166,
-0.9717810750007629,
0.1601286083459854,
-0.7719902396202087,
0.413046658039093,
0.747140645980835,
-0.8690800070762634,
1.1638193130493164,
0.34677305817604065,
-0.2886740565299988,
0.19299818575382233,
-0.28059297800064087,
0.25176501274108887,
0.4204133152961731,
0.13987883925437927,
-0.6324231028556824,
1.2085920572280884,
-0.5797513723373413,
-0.4840887188911438,
-0.669684648513794,
0.02011052332818508,
0.8135324716567993,
-0.5079219937324524,
-0.2837326228618622,
-0.502791166305542,
-0.1562352329492569,
0.6291851997375488,
-0.6067709922790527,
-0.6294639706611633,
0.08494838327169418,
1.0100070238113403,
-0.20710374414920807,
-0.8951601982116699,
-0.8254638910293579,
0.7855237126350403,
0.2152024805545807,
-0.83311927318573,
-0.5177063345909119,
-0.07718601822853088,
-0.5088334083557129,
1.0383787155151367,
0.2188018262386322,
-0.23722624778747559,
-0.3699890673160553,
0.7979585528373718,
0.4177640378475189,
0.2726896405220032,
0.04322344809770584,
-0.6104990839958191,
-1.1993240118026733,
0.2974280118942261,
-0.3665996193885803,
0.34734222292900085,
-0.5385141968727112,
0.8600485324859619,
0.20754285156726837,
-0.712386965751648,
0.8270539045333862,
-0.7668135762214661,
-0.722520112991333,
-0.07220674306154251,
-0.14763741195201874,
0.25221750140190125,
-0.6903260946273804,
0.10163545608520508,
-0.5573466420173645,
0.4474622905254364,
0.5380210876464844,
0.14671295881271362,
0.8258845210075378,
-0.570737898349762,
0.25100991129875183,
0.3927808701992035,
0.314321905374527,
0.2803867757320404,
-0.4650425910949707,
-0.6512353420257568,
-0.6143871545791626,
-0.3287932276725769,
-1.181117057800293,
0.008631405420601368,
-0.5630269050598145,
0.6070460081100464,
0.2562040388584137,
1.2213174104690552,
-0.6102352142333984,
-0.5831843018531799,
-0.377468079328537,
-0.13981617987155914,
-0.028144460171461105,
1.0004113912582397,
0.49235308170318604,
-0.37917447090148926,
-0.12031584978103638,
0.2938438355922699,
0.275269478559494,
-0.318298876285553,
0.34928807616233826,
-0.7829087972640991,
0.5284196734428406,
-0.7174639701843262,
-0.6660348176956177,
-0.1121368557214737,
-0.12239807844161987,
0.07723028212785721,
0.5472372770309448,
0.7558004856109619,
1.5873587131500244,
-0.19183464348316193,
-0.6502686142921448,
-0.5464364886283875,
-0.016916373744606972,
0.27261465787887573,
0.3078055679798126,
0.21638739109039307,
0.19420960545539856,
0.0712231770157814,
-0.37392351031303406,
-1.1403402090072632,
-0.4657042920589447,
0.09408672153949738,
-0.3817182183265686,
0.20212358236312866,
-0.30926984548568726,
0.18359217047691345,
0.590650737285614,
-0.2991354167461395,
0.8960898518562317,
-0.3004814684391022,
0.7187959551811218,
0.029597647488117218,
1.0425246953964233,
0.6077715754508972,
-0.05945601314306259,
0.2598353326320648,
-0.3010250926017761,
0.026357196271419525,
0.2559733986854553,
0.0489882193505764,
-0.6736440658569336,
-0.16260722279548645,
0.13028572499752045,
0.07097931951284409,
0.5333738327026367,
-0.40614935755729675,
-0.3835304379463196,
0.41101574897766113,
-0.13935352861881256,
0.7248114943504333,
0.14735622704029083,
0.1909850686788559,
0.611085832118988,
-0.056480396538972855,
0.62965327501297,
-0.8643743395805359,
1.000105381011963,
-0.5671376585960388,
0.24329844117164612,
0.9148303866386414,
-0.7578744888305664,
-0.8670581579208374,
-1.307204246520996,
-0.20655770599842072,
-0.16364319622516632,
0.30925607681274414,
0.8126316070556641,
0.6911760568618774,
0.7950574159622192,
-0.3843740224838257,
0.01037412416189909,
0.8357685208320618,
-0.10003243386745453,
0.5787542462348938,
0.5048576593399048,
0.04752198979258537,
-0.5521427392959595,
0.19403977692127228,
-0.3043946325778961,
-0.18980038166046143,
0.5218064188957214,
-1.1563606262207031,
0.9233126640319824,
-0.4963490962982178,
0.10843075811862946,
-0.23306190967559814,
0.30238479375839233,
-0.23091161251068115,
0.048744622617959976,
0.8615198731422424,
-0.4701940715312958,
-0.3958594799041748,
0.4508800804615021,
-0.15347285568714142,
-0.13515450060367584,
0.6299515962600708,
0.04475010558962822,
0.824394166469574,
0.45914211869239807,
-0.16552241146564484,
0.017730386927723885,
0.4454823136329651,
-0.32252180576324463,
0.00854727253317833,
0.4943249523639679,
-0.39654451608657837,
-0.6583216190338135,
-0.19952628016471863,
-0.7204052805900574,
-0.25776389241218567,
-0.48768314719200134,
-0.219448521733284,
-0.5741838216781616,
0.27779415249824524,
0.6788118481636047,
-0.6274990439414978,
-0.003930851351469755,
-0.4249390959739685,
-0.501672089099884,
0.10438168793916702,
0.2863095998764038,
-0.20902198553085327,
0.751361072063446,
-0.17078959941864014,
1.0044950246810913,
-0.592922568321228,
-0.7725604176521301,
-0.09080886095762253,
1.038123369216919,
0.3867771029472351,
-0.10762948542833328,
0.403217077255249,
-0.9111896753311157,
0.519770085811615,
-0.5215949416160583,
0.20212998986244202,
-0.45029550790786743,
-0.4879768192768097,
-0.4601745307445526,
-0.1889263391494751,
0.06815154105424881,
0.34879112243652344,
0.09997264295816422,
0.06611991673707962,
0.033154916018247604,
0.05594446137547493,
0.5477022528648376,
-0.8949097990989685,
-0.7908125519752502,
0.5774991512298584,
0.3483993113040924,
-0.3181975185871124,
-0.3011021912097931,
0.527572751045227,
-0.3269757926464081,
0.9178180694580078,
0.14720125496387482,
-0.854363739490509,
0.6354333162307739,
-0.1156899705529213,
0.523903489112854,
-0.8108452558517456,
0.020719153806567192,
-0.7720844149589539,
-0.9392425417900085,
0.45758798718452454,
0.36251410841941833,
0.9958842396736145,
-0.8134795427322388,
-1.288935661315918,
-0.5117868781089783,
0.04352058097720146,
0.1484040766954422,
0.09442184865474701,
-0.38851532340049744,
-0.11920369416475296,
-0.2292303591966629,
0.35960936546325684,
-0.6315334439277649,
0.23701946437358856,
0.21763373911380768,
-0.04315446689724922,
0.6359238624572754,
0.5485540628433228,
0.44274887442588806,
0.021426228806376457,
0.20907437801361084,
0.20604762434959412,
-0.09403997659683228,
0.21000204980373383,
0.1075802892446518,
-0.015469894744455814,
-0.8514173626899719,
0.4462619125843048,
-0.3703939616680145,
-0.31016266345977783,
0.5284374356269836,
0.20897254347801208,
0.9644099473953247,
-0.8763699531555176,
-0.37504100799560547,
-0.24654246866703033,
0.7560181021690369,
0.5109184384346008,
0.12910474836826324,
-0.012320047244429588,
-1.0015612840652466,
-0.8777146935462952,
-0.5406237840652466,
0.1210503876209259,
0.20665541291236877,
-0.38322800397872925,
-0.33338239789009094,
-0.3132864534854889,
-0.14288032054901123,
-0.4763377904891968,
1.098508596420288,
0.6460668444633484,
-0.027257656678557396,
0.09761992841959,
0.16706521809101105,
-0.15973913669586182,
-0.5685830116271973,
0.5120115876197815,
-0.16769807040691376,
0.015357162803411484,
0.5484097003936768,
0.6164239645004272,
-0.9243122339248657,
-0.18978577852249146,
-0.4005696177482605,
0.3604333698749542,
-0.10590305924415588,
0.11873059719800949,
1.3306143283843994,
0.8918207883834839,
0.2286527007818222,
-0.10129348933696747,
0.31139934062957764,
0.3888435959815979,
0.22527581453323364,
0.34966060519218445,
0.23730157315731049,
0.6854285001754761,
-0.030986174941062927,
0.16557328402996063,
-0.9082422852516174,
-0.08087356388568878,
1.4408646821975708,
-0.863267183303833,
-0.2108023315668106,
0.06310652941465378,
0.6706081032752991,
-0.9489843249320984,
-0.34831371903419495,
-0.07063080370426178,
0.3917359709739685,
-0.9400905966758728,
-0.2963203489780426,
-0.3709801137447357,
-0.24828103184700012,
-0.5581364035606384,
-0.01505329180508852,
0.023683901876211166,
-0.2253285050392151,
0.5264528393745422,
0.1792764514684677,
0.1049806997179985,
-0.19077670574188232,
-0.2708285450935364,
1.462215542793274,
-0.041194748133420944,
-0.6170963048934937,
-0.157601997256279,
0.038413915783166885,
-0.5448678731918335,
-0.02707650512456894,
0.7424722909927368,
0.16963493824005127,
-0.35493719577789307,
0.8707273602485657,
0.7254400253295898,
-0.16826291382312775,
1.0032938718795776,
0.004849912133067846,
0.404857873916626,
0.19286923110485077,
-0.7435369491577148,
-0.6298999190330505,
-0.19855409860610962,
0.7758053541183472,
0.9366509914398193,
0.1830153465270996,
0.080696240067482,
0.047932375222444534,
-0.3140702545642853,
0.254101037979126,
-1.0128891468048096,
-0.1371644139289856,
-0.8819950819015503,
-0.7428719401359558,
-0.21472769975662231,
-0.5395585894584656,
0.47522327303886414,
0.6558771729469299,
-0.908514142036438,
0.39865225553512573,
-0.567754864692688,
0.2963942289352417,
-0.38911524415016174,
0.35433346033096313,
-0.291166216135025,
-0.15565447509288788,
0.00845006201416254,
-0.20362098515033722,
-0.7208670377731323,
0.08265484124422073,
-0.7181355953216553,
-0.162457674741745,
-0.06417299062013626,
0.15190188586711884,
0.2032860964536667,
0.7416605353355408,
-0.939022421836853,
-0.5570549964904785,
0.38235971331596375,
-0.32831335067749023,
-0.8593675494194031,
0.4722667634487152,
-0.2509320080280304,
0.3613181412220001,
0.5968218445777893,
0.2927752435207367,
-0.4041144847869873,
0.2602088153362274,
-0.29778268933296204,
-0.45413073897361755,
-0.4133252203464508,
1.0013586282730103,
-0.19118940830230713,
0.3549732565879822,
-0.023313166573643684,
-0.041674960404634476,
-1.0293267965316772,
0.4629201591014862,
0.08764702826738358,
0.34869515895843506,
0.19575010240077972,
0.49989834427833557,
-0.07485898584127426,
-0.028880948200821877,
0.8425309062004089,
0.15010306239128113,
0.17298024892807007,
-0.6606093645095825,
-0.22354532778263092,
0.263353168964386,
-0.026859013363718987,
0.292914479970932,
-0.29010048508644104,
-0.31310129165649414,
-0.6857213973999023,
0.344596266746521,
-0.3924766182899475,
0.3145331144332886,
-0.1642795205116272,
-0.2719966769218445,
-0.6577878594398499,
-0.012878358364105225,
-0.7748070955276489,
0.2960474491119385,
0.0908016636967659,
-0.8921826481819153,
0.33525311946868896,
-0.321033775806427,
-0.5390533208847046,
0.5741088390350342,
-0.8929641842842102,
-0.7549861073493958,
-0.12982966005802155,
-0.7068551778793335,
0.11768815666437149,
0.32460492849349976,
-0.2500641345977783,
0.1714950054883957,
0.22728370130062103,
0.4185943901538849,
-0.676430344581604,
-0.23022595047950745,
-0.8143007755279541,
0.346770703792572,
-0.892406165599823,
-0.11153128743171692,
-0.5525925159454346,
0.24362342059612274,
-1.16213858127594,
-0.6331644654273987,
0.505047619342804,
1.0765730142593384,
-0.10897411406040192,
-0.34066835045814514,
-0.11954299360513687,
-0.4200619161128998,
-0.4372762441635132,
0.8424906730651855,
-1.1586660146713257,
-0.3218124210834503,
-0.775479257106781,
0.06643063575029373,
-0.1335824579000473,
0.11996765434741974,
0.2148706018924713,
1.0970615148544312,
0.8535922169685364,
-0.016016636043787003,
0.40270930528640747,
0.8474379777908325,
0.5000656843185425,
-0.14874881505966187,
0.48227012157440186,
0.438926100730896,
0.5565395951271057,
0.07982111722230911,
-1.1993147134780884,
0.23089800775051117,
0.7912856340408325,
0.2931651473045349,
0.7986767292022705,
-0.27088943123817444,
0.33635860681533813,
0.14405490458011627,
0.09376164525747299,
0.0547591932117939,
-0.19562987983226776,
0.5312070250511169,
0.897805392742157,
0.3571145832538605,
0.18115775287151337,
-0.12355494499206543,
0.1865406334400177,
-0.1759440153837204,
0.17813841998577118,
-0.4663974344730377,
-0.9305035471916199,
-0.6860944032669067,
-0.12953424453735352,
0.2263304442167282,
-0.13306468725204468,
-0.36457276344299316,
-0.29981908202171326,
0.2140769213438034,
0.40603315830230713,
0.6374645233154297,
-0.13911527395248413,
0.04232954978942871,
1.2142307758331299,
0.04240631312131882,
-0.22073572874069214,
0.6349103450775146,
-0.41967615485191345,
1.2685385942459106,
0.36755606532096863,
1.0313752889633179,
0.05524316430091858,
1.0480924844741821,
0.2746305763721466,
-0.4784471094608307,
-0.39456260204315186,
0.524501383304596,
-0.07936649769544601,
0.09368661046028137,
-0.8460702896118164,
0.022182205691933632,
-0.2058783322572708,
0.09571216255426407,
0.9829026460647583,
-0.7216220498085022,
0.1315668672323227,
1.1411972045898438,
-0.4790749251842499,
-0.6817148327827454,
0.35364800691604614,
-0.7913608551025391,
-0.17612823843955994,
0.809715747833252,
0.1091325581073761,
0.17443512380123138,
1.0599435567855835,
1.1292972564697266,
-0.3935804069042206,
0.07468646764755249,
-0.03443222865462303,
0.3039110004901886,
0.1413925737142563,
0.19551974534988403,
-0.8773749470710754,
0.11660180985927582,
-0.3383506238460541,
-0.5974355340003967,
-0.1017976626753807,
0.48902228474617004,
-0.3006281554698944,
-0.6337727308273315,
1.247262954711914,
0.2042931765317917,
-0.9418565630912781,
-0.1461220383644104,
1.0624699592590332,
0.35548198223114014,
0.33078718185424805,
-0.809998095035553,
-0.2647550702095032,
-0.15989762544631958,
-0.3911271393299103,
-0.6031813621520996,
0.25014248490333557,
-0.7124310731887817,
-0.24910062551498413,
-0.13185687363147736,
0.34454262256622314,
-0.7204950451850891,
-0.47240403294563293,
-0.45491570234298706,
-0.451026976108551,
0.12259161472320557,
0.23880106210708618,
0.4316146671772003,
-0.21027924120426178,
-0.6438966989517212,
-0.3366599380970001,
0.20688101649284363,
0.6537277102470398,
-0.05940656736493111,
0.5756068229675293,
1.2892392873764038,
0.23074325919151306,
0.07596390694379807,
0.13582593202590942,
0.5876012444496155,
-0.540950357913971,
0.42629989981651306,
-0.3102877736091614,
0.7961729168891907,
0.4820496439933777,
-0.6180766820907593,
-0.049014847725629807,
-0.19881901144981384,
-0.12677055597305298,
-0.07984833419322968,
0.37135758996009827,
0.12441431730985641,
-0.2436133325099945,
-0.13207833468914032,
-0.5099065899848938,
0.8651871681213379,
-0.28654173016548157,
0.1725734919309616,
-0.05167844519019127,
-0.5203676223754883,
4.01049280166626,
0.6786305904388428,
1.3847119808197021,
0.5008926391601562,
0.3192703127861023,
0.769622266292572,
-0.30977368354797363,
-0.7457877993583679,
-0.45303836464881897,
-0.41556990146636963,
-0.8872758746147156,
0.04184156656265259,
0.5499554872512817,
0.2800696790218353,
0.09691056609153748,
1.1272393465042114,
-0.4720463752746582,
-0.3690827786922455,
0.30427008867263794,
-1.0326675176620483,
-0.7158995866775513,
-0.15461000800132751,
0.18534474074840546,
-0.060893796384334564,
0.10417471826076508,
0.1559184193611145,
-0.34984686970710754,
-0.395636647939682,
-0.290790855884552,
0.04233541339635849,
-0.7132688760757446,
-0.7045502662658691,
0.5691231489181519,
0.07724637538194656,
-0.47893425822257996,
-0.3172265887260437,
-0.45836785435676575,
-0.23997238278388977,
-0.3037295639514923,
0.19336546957492828,
-0.006756423972547054,
-0.5616732239723206,
0.6604663133621216,
-0.38965097069740295,
-0.01893490180373192,
1.6871192455291748,
-0.565483570098877,
0.8686812520027161,
0.7169203758239746,
-0.7716992497444153,
1.0625135898590088,
-1.125662088394165,
-0.031327150762081146,
-0.7714023590087891,
-0.8292206525802612,
0.48816972970962524,
-0.049321118742227554,
-0.17700402438640594,
0.1609644889831543,
0.38851478695869446,
0.3244762718677521,
-0.04604899883270264,
-0.31349173188209534,
-0.26614147424697876,
-0.1378106027841568,
0.5123904943466187,
0.6135156154632568,
0.11341355741024017,
-0.4135323166847229,
0.07692667841911316,
-0.2335115671157837,
-0.19485239684581757,
0.027326231822371483,
0.053643230348825455,
0.31308332085609436,
-0.40512219071388245,
-0.6584692001342773,
0.08737660944461823,
0.016263756901025772,
-0.3967231214046478,
0.5750744938850403,
0.14623533189296722,
-0.6943525671958923,
0.28832802176475525,
0.5610553622245789,
0.8626825213432312,
-1.1084728240966797,
-0.02109500952064991,
0.10361841320991516,
0.5854476094245911,
0.6445232033729553,
0.7842137813568115,
0.34492847323417664,
0.17045585811138153,
-0.64045649766922
] |
Wave functions and their use in spectroscopy and phenomenology
|
We describe the calculation of Coulomb gauge wave functions for light quark systems, and their use as interpolating fields for excited state spectroscopy.
|
T. DeGrand and M. Hecht
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210013
|
hep-lat/9210014
|
[
0.10735400021076202,
-0.30733275413513184,
-0.0790533721446991,
-0.001002008793875575,
-0.32168376445770264,
0.09732292592525482,
-0.060870882123708725,
-0.7278728485107422,
-0.5184321999549866,
1.4226127862930298,
0.48715442419052124,
0.0505397766828537,
0.32176998257637024,
-0.8083323836326599,
-0.13737495243549347,
0.6796097755432129,
-0.06289329379796982,
-1.0517394542694092,
-1.6641292572021484,
0.3291768431663513,
-0.057520024478435516,
-0.6609324216842651,
-1.0493704080581665,
-0.6939560770988464,
-0.26363405585289,
0.7149013876914978,
-0.36025190353393555,
0.07145562022924423,
1.0233830213546753,
0.47828397154808044,
0.5542150139808655,
-0.47595563530921936,
-0.42679792642593384,
-0.7989308834075928,
-0.28813254833221436,
-0.36810103058815,
0.01603255420923233,
-0.039828017354011536,
0.8872963786125183,
-0.33488568663597107,
0.699304461479187,
-0.36919111013412476,
0.41277074813842773,
-0.22500284016132355,
-0.5123459696769714,
0.20390139520168304,
0.1333959549665451,
0.10910041630268097,
0.14062564074993134,
-1.1420800685882568,
0.05006421357393265,
0.902707040309906,
0.5772653818130493,
-0.5337236523628235,
-0.4119744300842285,
0.05740195885300636,
0.042050156742334366,
0.14873553812503815,
-0.9066795706748962,
-0.6009907126426697,
0.48993077874183655,
-0.021643787622451782,
0.8821353912353516,
-0.7408806085586548,
-0.16666269302368164,
0.8175486922264099,
-0.08355072885751724,
0.10990750789642334,
0.18896590173244476,
-0.59804767370224,
-0.4979184567928314,
-0.4285450875759125,
-0.003922081086784601,
-0.12779201567173004,
-0.7624781727790833,
0.5858766436576843,
-0.22932805120944977,
-0.37752947211265564,
-0.9833217859268188,
-0.13761569559574127,
-0.20533381402492523,
0.4980549216270447,
-0.3114545941352844,
0.3906978964805603,
-0.41804641485214233,
-0.2215748280286789,
0.15176726877689362,
-0.26543092727661133,
0.19864493608474731,
0.5916880965232849,
0.4192434549331665,
0.9083689451217651,
-0.043785903602838516,
0.7787636518478394,
0.41396304965019226,
0.818027913570404,
-0.3409356474876404,
0.6803022027015686,
0.38328906893730164,
0.5954485535621643,
-0.35793882608413696,
0.7609267234802246,
-0.7834166288375854,
-0.05378969758749008,
-0.8439275026321411,
0.34960320591926575,
-0.004307042341679335,
0.23728081583976746,
-0.2853984236717224,
-0.6609229445457458,
-0.15713965892791748,
0.3862457871437073,
0.4125075042247772,
0.2844131886959076,
0.3508262038230896,
0.631440281867981,
-0.567510187625885,
-0.3345879912376404,
-0.9016708135604858,
0.0009248658316209912,
-0.24112752079963684,
0.336895614862442,
-0.38254621624946594,
0.46822333335876465,
-0.006350180134177208,
-0.15988975763320923,
0.6656219363212585,
0.4033524692058563,
-0.2640625834465027,
0.16881702840328217,
-0.1571919023990631,
-0.09784605354070663,
-0.38012680411338806,
1.1550158262252808,
-0.3385777473449707,
-0.059182144701480865,
-0.3255426585674286,
0.5121573209762573,
0.5976195335388184,
-0.1546158641576767,
0.47767966985702515,
-0.2935273349285126,
0.0460740327835083,
0.9566566944122314,
0.04618295654654503,
-0.28627607226371765,
0.09957797080278397,
0.14952272176742554,
-0.28881484270095825,
0.40009304881095886,
-0.6922752261161804,
0.13766998052597046,
0.1254536658525467,
0.2095714956521988,
0.16694577038288116,
0.5667346715927124,
-1.177025318145752,
0.4109271764755249,
-0.5506033897399902,
-0.623222291469574,
0.09696255624294281,
-0.03137282282114029,
-0.5663304924964905,
0.12872952222824097,
-0.6825544238090515,
-0.40673893690109253,
-0.39142924547195435,
0.20701804757118225,
-0.058928731828927994,
-1.148677945137024,
-0.14746323227882385,
0.7134408354759216,
-0.5419607162475586,
0.2088107466697693,
0.44816529750823975,
-0.0612109899520874,
0.4078419804573059,
-0.3082961142063141,
0.33466529846191406,
-0.03553501516580582,
0.13028240203857422,
-0.35899046063423157,
0.5025991201400757,
0.032162994146347046,
-0.3840407729148865,
-0.11952515691518784,
0.0946270078420639,
-0.3271537125110626,
0.2787339389324188,
0.04129943251609802,
-0.6049347519874573,
0.5057586431503296,
-0.5636405944824219,
0.3961693048477173,
-0.3100248873233795,
-0.45865508913993835,
-1.01945161819458,
0.507074773311615,
-0.6940383911132812,
0.16324637830257416,
-0.3820783495903015,
0.5503578186035156,
-0.8634212017059326,
0.6628056764602661,
-1.443941593170166,
-0.23412418365478516,
0.47768667340278625,
-0.6716617941856384,
-0.5432220101356506,
-0.18613013625144958,
0.9010284543037415,
-0.45703834295272827,
0.01722440868616104,
-0.3391334116458893,
-0.12584978342056274,
0.2777983248233795,
-0.6816220879554749,
-0.05645017698407173,
0.5179483890533447,
0.17194318771362305,
0.6994367837905884,
-0.4281962811946869,
-0.36436939239501953,
0.6915283799171448,
-0.3956824541091919,
-0.36730101704597473,
0.001486232620663941,
0.6565585732460022,
-0.060032445937395096,
-0.40726882219314575,
0.1615818589925766,
0.47601306438446045,
0.16871437430381775,
0.2419101893901825,
0.6973431706428528,
0.5652018189430237,
0.16196763515472412,
0.5269507169723511,
0.30514100193977356,
-0.037407323718070984,
0.15487344563007355,
-0.43360424041748047,
0.4864802658557892,
0.3584817945957184,
-0.06500954180955887,
-0.1505555808544159,
-0.5278095006942749,
0.2866966724395752,
-0.38504356145858765,
0.10548464953899384,
-0.4319910705089569,
0.6137136816978455,
-0.03487428277730942,
0.6862810254096985,
-1.0303467512130737,
-0.35599449276924133,
-0.6496672630310059,
-0.06600311398506165,
-0.11575400084257126,
-0.17253749072551727,
0.038299404084682465,
0.057318802922964096,
-0.05871289595961571,
-0.5301011204719543,
-0.36321771144866943,
0.9404855966567993,
-0.00005528992915060371,
0.23330216109752655,
0.8022266030311584,
-0.49348390102386475,
-0.5991258025169373,
0.1390760838985443,
-0.8605139851570129,
0.10671520978212357,
-0.2516828179359436,
0.5711908340454102,
0.6174068450927734,
-1.030967354774475,
0.25040754675865173,
0.2917635440826416,
-0.33906200528144836,
0.615946352481842,
-0.3659500479698181,
0.242455393075943,
0.3748447000980377,
0.14326803386211395,
-0.8816612958908081,
0.49358120560646057,
-0.6940728425979614,
0.0205294881016016,
-0.22449453175067902,
0.0146305151283741,
0.8440873622894287,
-0.5891203880310059,
0.09598826617002487,
0.05994483456015587,
-0.6350229382514954,
-0.014810224063694477,
-0.3701011836528778,
-0.6261215806007385,
0.3828717768192291,
0.14140932261943817,
-0.05691969394683838,
0.05614449456334114,
-0.9681916236877441,
0.7658369541168213,
0.19655919075012207,
-0.17183223366737366,
0.5471310615539551,
0.3349139988422394,
0.05978453904390335,
0.4300755262374878,
-0.6464613080024719,
0.01610960252583027,
-0.2327263057231903,
1.4842954874038696,
0.44787365198135376,
0.3178204894065857,
-0.12240594625473022,
-0.044923085719347,
-0.5564265251159668,
0.5796639919281006,
-0.33731281757354736,
-0.5138225555419922,
0.08995223045349121,
0.8707991242408752,
0.1351199448108673,
-0.7356088757514954,
0.5744903683662415,
-0.5423862338066101,
-0.5850874185562134,
0.44630739092826843,
-0.3657989799976349,
0.6939408183097839,
-0.17045891284942627,
0.31386682391166687,
-0.5617385506629944,
0.41455286741256714,
0.011776375584304333,
0.15838082134723663,
0.6738518476486206,
-0.32533156871795654,
0.36454764008522034,
0.4516698122024536,
0.13355866074562073,
0.28412166237831116,
0.37760844826698303,
-0.1715310961008072,
-0.24253375828266144,
-0.169883593916893,
-0.7393296360969543,
0.041414517909288406,
0.1033836379647255,
0.04291209578514099,
0.04700302332639694,
-0.008489841595292091,
-0.5022788047790527,
-0.7219026684761047,
-0.4012638330459595,
-0.7505040168762207,
0.490323543548584,
0.37321364879608154,
-0.5197188854217529,
-0.08811717480421066,
-0.6256049871444702,
-0.460296094417572,
0.45831963419914246,
-0.018779488280415535,
0.33001208305358887,
-0.6944594979286194,
0.09849434345960617,
-0.08003085851669312,
-0.4694802165031433,
-0.11008055508136749,
-0.06412697583436966,
0.22186356782913208,
0.48056352138519287,
0.2471441775560379,
0.15205523371696472,
-0.6998003125190735,
-0.4084625542163849,
0.2927837371826172,
0.8492771983146667,
0.9313510060310364,
1.009049415588379,
1.0319788455963135,
-0.1666378527879715,
0.5379388928413391,
-0.6735031604766846,
-0.4382023811340332,
-0.3394298255443573,
-0.22046341001987457,
0.34495317935943604,
-0.7818683981895447,
0.03035707212984562,
-0.14433729648590088,
0.5122806429862976,
0.8860160112380981,
0.34566953778266907,
0.4031824767589569,
0.9809335470199585,
-0.008904330432415009,
0.08293896168470383,
0.8360932469367981,
0.04979846999049187,
0.18746423721313477,
-0.7517195343971252,
0.5122320055961609,
-0.07830045372247696,
-0.12482507526874542,
-0.1540025770664215,
-0.8126302361488342,
-0.4858332574367523,
-1.0264769792556763,
0.8804291486740112,
0.19434989988803864,
-0.2833729684352875,
0.3906250596046448,
-0.06478794664144516,
0.7938101291656494,
-0.6018674373626709,
-0.3167194426059723,
0.417074590921402,
0.615948498249054,
-0.022609036415815353,
-0.37095028162002563,
0.24334032833576202,
-0.4368208050727844,
0.6970230340957642,
0.5617268085479736,
-0.8116590976715088,
-0.9079557657241821,
-0.46267005801200867,
0.23262721300125122,
-0.349446177482605,
-0.18767540156841278,
1.211014747619629,
-0.1280166059732437,
0.46893322467803955,
-0.5703363418579102,
-0.6455363035202026,
0.8236038088798523,
-0.723929762840271,
-0.8435546159744263,
0.206735759973526,
-0.1534339189529419,
0.047388430684804916,
0.8839196562767029,
-0.16165943443775177,
-0.6759533882141113,
-0.2199375480413437,
-0.4548126757144928,
0.339159220457077,
-0.5394836664199829,
-0.4485110938549042,
-0.11681004613637924,
-0.31120264530181885,
-0.3480452597141266,
0.6396002173423767,
0.10956360399723053,
-0.3799864649772644,
0.16325818002223969,
-0.1322399526834488,
-0.3472515344619751,
-0.10099286586046219,
0.15735478699207306,
0.3043440580368042,
0.7012477517127991,
0.8478820323944092,
0.37229645252227783,
-0.07116459310054779,
0.39656537771224976,
0.7802639007568359,
0.12427382171154022,
-0.0704578161239624,
-0.21964994072914124,
-0.35217222571372986,
-0.24491016566753387,
-0.32276472449302673,
-0.7470487356185913,
-0.5453017354011536,
0.14942701160907745,
-0.5081183314323425,
1.2292273044586182,
0.09074952453374863,
-0.6211668848991394,
0.08222956955432892,
-0.27030056715011597,
-0.5566788911819458,
0.36734047532081604,
-0.40897810459136963,
0.14905233681201935,
0.8352077007293701,
-0.19683629274368286,
0.11860158294439316,
-0.11850312352180481,
-0.2580503523349762,
-0.3190423250198364,
-0.11495605111122131,
0.5463723540306091,
0.07440143078565598,
0.8812906742095947,
-0.9248571991920471,
0.3453315198421478,
-0.4165300130844116,
0.4830999970436096,
-0.29534971714019775,
-0.41451504826545715,
-0.14560554921627045,
-0.5054607391357422,
0.6207616925239563,
-0.031212104484438896,
-0.026915451511740685,
-0.32829350233078003,
-0.27231937646865845,
-0.42788034677505493,
0.5962733030319214,
0.00024836251395754516,
-0.19925062358379364,
0.45438912510871887,
-0.034787267446517944,
-0.6915130019187927,
0.3743276298046112,
0.44375646114349365,
0.30829402804374695,
0.19415375590324402,
0.2795434594154358,
-0.22294187545776367,
0.30012038350105286,
-0.3072625696659088,
0.5237302184104919,
-0.3474765419960022,
-0.06093893200159073,
-0.26399022340774536,
0.08354348689317703,
-0.07363064587116241,
0.5626286864280701,
-0.012677397578954697,
0.09621365368366241,
-0.37747320532798767,
-0.5053501129150391,
0.3617214560508728,
-0.2062820941209793,
-0.37252581119537354,
-0.5249722003936768,
-0.10649504512548447,
-0.7236170768737793,
0.38243043422698975,
-0.5954060554504395,
0.18429632484912872,
0.4912821650505066,
0.026835301890969276,
0.16315023601055145,
0.5838153958320618,
0.19147524237632751,
0.29308807849884033,
0.2604909837245941,
0.7957180142402649,
-0.34493309259414673,
0.4992493987083435,
0.022858820855617523,
0.27556875348091125,
-0.7057985067367554,
0.9784215092658997,
-0.9561302661895752,
-0.16883036494255066,
0.12397037446498871,
0.1664379984140396,
0.6998331546783447,
-0.4053122103214264,
0.7625839710235596,
0.7234927415847778,
-0.06602726876735687,
0.48166361451148987,
0.14247609674930573,
-0.47618550062179565,
-0.4033672511577606,
-0.23914700746536255,
-0.958632230758667,
0.595005989074707,
0.07676350325345993,
-0.22613151371479034,
-0.6598361134529114,
-0.9737445712089539,
-0.276068776845932,
0.16213417053222656,
-0.1723550260066986,
0.3879026472568512,
-0.29523563385009766,
0.08921591937541962,
0.2170380800962448,
0.6147047877311707,
-0.22098879516124725,
-0.32656198740005493,
-0.2234106957912445,
-0.19460834562778473,
-0.3680168688297272,
0.09961658716201782,
-0.43695467710494995,
-0.7721899747848511,
-0.2668887972831726,
0.4514332711696625,
0.13610289990901947,
0.12310373038053513,
0.9178634881973267,
-0.7339529991149902,
-0.6799532771110535,
-0.433479368686676,
-0.09963171929121017,
0.11900923401117325,
-0.08366931974887848,
0.23407860100269318,
0.2808530032634735,
0.2608645260334015,
0.2300282120704651,
0.9818146824836731,
-0.131771057844162,
-0.12085428833961487,
0.24018195271492004,
-0.3632352352142334,
-0.4267254173755646,
0.7468132376670837,
0.05313799902796745,
-0.6185942888259888,
-0.22536252439022064,
-1.255266547203064,
0.1210494339466095,
-0.08230003714561462,
0.0738757848739624,
0.02481064945459366,
-0.2689158022403717,
-0.3824303448200226,
0.49914050102233887,
0.4280206561088562,
-0.28218305110931396,
-0.22567376494407654,
0.31664079427719116,
-0.4800402820110321,
-0.601833164691925,
-0.09196575731039047,
1.1094883680343628,
-0.05416279286146164,
-0.8534566760063171,
-0.3033931255340576,
-0.07982237637042999,
-0.07416528463363647,
0.11764706671237946,
0.33106347918510437,
-0.21098771691322327,
0.5298610329627991,
0.43809774518013,
0.40300866961479187,
0.2576286792755127,
0.1791633814573288,
0.5590835213661194,
0.38379576802253723,
0.3442763388156891,
-0.7759976387023926,
-0.2768841087818146,
-0.38616228103637695,
-0.06550934165716171,
1.0109187364578247,
0.25198546051979065,
0.6902220845222473,
-0.32517310976982117,
-0.5553306937217712,
-0.6366618275642395,
-0.7207144498825073,
0.20601533353328705,
-0.832603394985199,
-0.24411888420581818,
-0.3123440444469452,
0.11210420727729797,
-0.3056834638118744,
0.4605061411857605,
0.0919162780046463,
-0.2524770498275757,
-0.16641341149806976,
-0.19996699690818787,
0.6755619049072266,
0.6284217834472656,
0.16002418100833893,
-1.28407883644104,
-0.45887869596481323,
-0.4303440451622009,
-0.4716664254665375,
-0.3503011465072632,
0.21908757090568542,
-0.08833767473697662,
-0.34857574105262756,
0.8210045099258423,
-0.40992942452430725,
0.8636791706085205,
-0.6540855765342712,
-0.6998180150985718,
-0.16893857717514038,
-0.0006374209187924862,
-0.24451173841953278,
0.28490880131721497,
0.1733584851026535,
0.676948606967926,
0.21766908466815948,
0.0680396631360054,
-0.16071060299873352,
0.39070743322372437,
-0.884689211845398,
-0.18904608488082886,
-0.02126779593527317,
0.8722143173217773,
-0.09777134656906128,
-0.5561158657073975,
-0.026677921414375305,
0.6247424483299255,
-1.0633422136306763,
0.30005061626434326,
-0.5952650904655457,
-0.18365544080734253,
-0.2589276134967804,
0.38593044877052307,
0.31865406036376953,
0.4984875023365021,
0.07045358419418335,
0.8643230199813843,
-0.619891345500946,
-0.42153459787368774,
0.056451357901096344,
0.49879583716392517,
-0.20004677772521973,
0.3038472533226013,
-0.18055559694766998,
-0.6938092112541199,
-0.3211101293563843,
0.8543795943260193,
-0.008523048833012581,
-0.24791942536830902,
0.14563852548599243,
-0.5898259282112122,
0.18946146965026855,
-0.15628276765346527,
-0.4590456783771515,
0.5803516507148743,
0.27021217346191406,
-0.6400327682495117,
-0.47247177362442017,
-0.7080758810043335,
-0.6816244721412659,
-0.04444906860589981,
-0.5876173973083496,
-0.47838759422302246,
-0.12876443564891815,
0.22415581345558167,
-0.4443837106227875,
0.005739735439419746,
-0.2743558883666992,
0.5419517755508423,
0.14245542883872986,
0.11100562661886215,
-0.13096709549427032,
-0.3837778568267822,
-0.11055154353380203,
-0.025432566180825233,
-1.0023704767227173,
-0.4574931263923645,
-0.4259054660797119,
0.8858920931816101,
-0.5595213174819946,
-0.5422937870025635,
-0.5410260558128357,
0.21720856428146362,
0.13399697840213776,
0.1161760687828064,
0.07295341044664383,
-0.39940762519836426,
-0.15052677690982819,
0.148795485496521,
-0.6159414052963257,
-0.20867054164409637,
-0.6579546332359314,
0.2801816463470459,
-0.41360151767730713,
-1.1299880743026733,
0.07264450937509537,
0.04109560325741768,
-0.05223071202635765,
0.07648968696594238,
0.30395546555519104,
0.9991279244422913,
0.6950793266296387,
-0.41208839416503906,
1.092706561088562,
0.04599793255329132,
0.6070634722709656,
0.13295847177505493,
-0.5094203352928162,
0.06095222383737564,
0.599012553691864,
0.4616055488586426,
0.5344364643096924,
0.7199382781982422,
-0.03590061515569687,
0.5868152379989624,
0.07100459188222885,
0.007908928208053112,
0.1332695633172989,
0.14000825583934784,
0.13515962660312653,
0.6109557151794434,
-0.3720230758190155,
0.02998102456331253,
-0.09781499952077866,
0.2641306519508362,
0.19035576283931732,
0.08902955055236816,
-0.03278823569417,
0.013089031912386417,
-0.1978180706501007,
0.4156862497329712,
-0.8737238645553589,
0.1991529017686844,
-0.2969204783439636,
0.0036122945602983236,
0.2974046468734741,
-0.03995749354362488,
-0.3674211800098419,
0.26922231912612915,
0.4549173414707184,
0.15511742234230042,
-0.34052613377571106,
0.20066477358341217,
0.16805191338062286,
0.8856053352355957,
0.6160675287246704,
0.8513007760047913,
0.25426924228668213,
0.11268995702266693,
0.09736314415931702,
-1.3097714185714722,
0.7492108941078186,
0.8754079341888428,
-1.1149600744247437,
0.16787737607955933,
-0.32176902890205383,
0.1314389705657959,
-0.5321922898292542,
-0.6557294130325317,
0.29054224491119385,
-0.5531466007232666,
0.2719346880912781,
0.6239508986473083,
-0.3836804926395416,
0.5180854797363281,
0.7252326607704163,
0.308247834444046,
0.2954033315181732,
0.43240705132484436,
0.15337800979614258,
0.3783910870552063,
1.190972089767456,
1.3767366409301758,
-0.023747676983475685,
0.07285701483488083,
0.21586371958255768,
-0.8915399312973022,
0.38746634125709534,
0.4000305235385895,
-0.5604543089866638,
0.7450317740440369,
-0.39781296253204346,
-0.7212545275688171,
0.20561327040195465,
0.057828135788440704,
-0.33807313442230225,
-0.5371677875518799,
0.2900800406932831,
-0.010594026185572147,
-0.32704997062683105,
-1.1275285482406616,
1.0266720056533813,
0.5626736879348755,
-0.35891762375831604,
-0.5415555834770203,
0.05266240984201431,
0.40103140473365784,
-0.01821773499250412,
-0.7231956720352173,
0.09126929938793182,
0.032995328307151794,
0.0011591499205678701,
-0.3400920033454895,
-0.40424421429634094,
-0.7303733229637146,
-1.0853203535079956,
0.32648125290870667,
-0.48131346702575684,
0.24235229194164276,
0.09104742854833603,
0.5419847369194031,
0.06593970954418182,
-0.9421636462211609,
0.6465102434158325,
-0.0221390537917614,
1.195974588394165,
0.3703235685825348,
0.09378448873758316,
0.9329109787940979,
0.4837075471878052,
-1.0898600816726685,
0.21447701752185822,
1.0190175771713257,
-0.7531363368034363,
0.6418472528457642,
-0.12399870157241821,
-0.11883989721536636,
0.6462209224700928,
-0.07457233965396881,
0.22829735279083252,
0.03505997359752655,
0.4041885733604431,
-0.2821379601955414,
-0.02665039896965027,
-0.5760570168495178,
-0.7445878982543945,
0.37588703632354736,
-0.42333006858825684,
0.27813535928726196,
0.29286113381385803,
-0.16212916374206543,
0.7740415930747986,
-0.6549174189567566,
4.3302321434021,
0.8217111825942993,
0.44995102286338806,
0.10190722346305847,
0.7159335613250732,
0.3896803557872772,
-0.24726492166519165,
0.13285715878009796,
0.3019307255744934,
-0.30319082736968994,
-0.11444036662578583,
0.1519598662853241,
0.11791926622390747,
-0.11067555099725723,
-0.3184538185596466,
0.3898179829120636,
-0.2125938981771469,
0.10332314670085907,
-0.011239806190133095,
-1.0910488367080688,
-0.5894218683242798,
0.3342597484588623,
0.6624937057495117,
0.09785299748182297,
0.1608535498380661,
0.13024333119392395,
0.3239608108997345,
-0.8235725164413452,
-0.27400586009025574,
-0.7322493195533752,
-0.8794196248054504,
-1.3067377805709839,
-0.5312944054603577,
0.3226739764213562,
-0.8767799139022827,
0.20130281150341034,
0.32417479157447815,
0.1111229881644249,
0.18295449018478394,
-0.1275935024023056,
-0.12441706657409668,
-0.4832848906517029,
0.20869942009449005,
-0.40170833468437195,
-0.7035717964172363,
0.7675389647483826,
0.014826422557234764,
0.6901007294654846,
0.4547562003135681,
-0.4404603838920593,
0.5544824004173279,
-0.2647249698638916,
0.4459417462348938,
-0.1532086580991745,
-1.1002790927886963,
-0.12387461215257645,
-0.7169537544250488,
-0.4680997133255005,
-0.004511516075581312,
-0.02926073595881462,
0.35706421732902527,
-0.3029738962650299,
-0.002950957976281643,
0.2411961555480957,
-0.8470016121864319,
0.4310254156589508,
-0.3794125020503998,
0.4379768371582031,
-0.32865026593208313,
0.41670408844947815,
-0.3172895014286041,
-0.4446907937526703,
-0.32061541080474854,
-0.0226597897708416,
0.05217398330569267,
-0.17996810376644135,
-0.6433565020561218,
0.8159530758857727,
0.19981680810451508,
0.32567745447158813,
0.4515036642551422,
-0.060404229909181595,
0.07522953301668167,
0.8388152122497559,
0.38839608430862427,
0.6959289312362671,
-0.389373242855072,
-0.6824018955230713,
0.17309226095676422,
0.5518758893013,
0.5009574890136719,
0.9244012832641602,
0.4153200387954712,
0.8152365684509277,
-0.7538325786590576
] |
The U(1)-Higgs Model: Critical Behaviour in the Confinig-Higgs region
|
We study numerically the critical properties of the U(1)-Higgs lattice model, with fixed Higgs modulus, in the region of small gauge coupling where the Higgs and Confining phases merge. We find evidence of a first order transition line that ends in a second order point. By means of a rotation in parameter space we introduce thermodynamic magnitudes and critical exponents in close resemblance with simple models that show analogous critical behaviour. The measured data allow us to fit the critical exponents finding values in agreement with the mean field prediction. The location of the critical point and the slope of the first order line are accurately given.
|
Alonso, Azcoiti, Campos, Ciria, Cruz, Iniguez, lesmes, Piedrafita, Rivero, Tarancon, Badoni, Fernandez, Munoz Sudupe, Ruiz...
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210014
|
hep-lat/9210015
|
[
-0.11381067335605621,
-0.9716994166374207,
0.245122030377388,
0.7737850546836853,
-0.1259472370147705,
-0.4125698506832123,
-0.40622836351394653,
-0.5520443320274353,
-1.2108910083770752,
1.5320396423339844,
-0.3818691670894623,
-0.7156347036361694,
0.6185005307197571,
-0.7617884874343872,
0.1581864356994629,
0.2147781401872635,
-0.1338873952627182,
-0.35908618569374084,
-1.2006862163543701,
0.5734268426895142,
-0.4374488294124603,
-0.08108676970005035,
-1.3379387855529785,
-0.23704418540000916,
-0.2697862982749939,
0.9858443737030029,
-0.021708816289901733,
0.2269725352525711,
0.7280471920967102,
0.4231455624103546,
0.16611936688423157,
-0.24898222088813782,
-0.551622211933136,
-0.16626764833927155,
-0.43025320768356323,
-0.09127560257911682,
-0.2601674497127533,
-0.12666957080364227,
0.17594222724437714,
-0.3061460852622986,
0.6669781804084778,
-0.5101343393325806,
-0.272824764251709,
-0.2345106303691864,
-0.6659266352653503,
-0.0540715828537941,
-0.09171798825263977,
0.16318266093730927,
0.06525580585002899,
-1.401045322418213,
-0.1631755530834198,
0.3087320923805237,
0.15637409687042236,
-0.4198524057865143,
-0.13052061200141907,
-0.4181579053401947,
0.015484669245779514,
0.48334217071533203,
-0.8013089895248413,
-0.4307381212711334,
0.5108019709587097,
0.2815219461917877,
0.43929392099380493,
-0.6530267596244812,
-0.29847103357315063,
1.1295102834701538,
-0.6084464192390442,
1.130550742149353,
-0.3060685694217682,
-0.5956316590309143,
-0.4333570897579193,
-0.26189637184143066,
-1.1401798725128174,
0.8166309595108032,
-0.5120983719825745,
-0.1923557072877884,
0.05014470964670181,
-0.33114442229270935,
-0.5953230857849121,
-0.37458035349845886,
-0.07031883299350739,
-0.2785192131996155,
-0.49417296051979065,
0.03159846365451813,
0.09037451446056366,
-0.18659615516662598,
-0.14947861433029175,
-0.2147819846868515,
0.07691654562950134,
0.37670254707336426,
-0.0013955824542790651,
0.6887747049331665,
-0.17827162146568298,
-0.2660878896713257,
0.6240742206573486,
0.785568356513977,
-0.4414178133010864,
-0.021664902567863464,
0.5445048213005066,
0.3458283841609955,
-0.02478155680000782,
0.35424917936325073,
-0.24449406564235687,
0.24876531958580017,
-0.8896751999855042,
0.7582048773765564,
-0.3294149339199066,
-0.27315908670425415,
-0.13490253686904907,
-0.9036734700202942,
-0.002864415291696787,
-0.1259995698928833,
0.29567092657089233,
0.3205541670322418,
0.046177640557289124,
0.6154298782348633,
-0.5539611577987671,
-0.45700401067733765,
-0.5841543078422546,
-0.4507853388786316,
0.45020464062690735,
0.05811028182506561,
0.387798547744751,
0.30757543444633484,
-0.11725614219903946,
-0.4725746512413025,
0.13712354004383087,
0.6622931957244873,
-0.4212847948074341,
0.1495804488658905,
0.4213128685951233,
-0.10692983120679855,
-0.4038589596748352,
0.542741060256958,
-0.3110356330871582,
0.5274717807769775,
-0.26688748598098755,
-0.09102816879749298,
-0.25224027037620544,
-0.19187350571155548,
0.5804355144500732,
-0.35553446412086487,
0.4450552761554718,
1.0308432579040527,
0.14846280217170715,
0.28944316506385803,
0.4343402683734894,
0.5171563029289246,
-0.39845767617225647,
0.3136851191520691,
-0.3654627501964569,
-0.08200319111347198,
-0.2660236358642578,
0.13486206531524658,
-0.055937349796295166,
0.7564893364906311,
-0.5258074998855591,
-0.23303471505641937,
-0.17914918065071106,
-0.8570928573608398,
0.19619908928871155,
-0.21495108306407928,
-0.5426377058029175,
0.39586594700813293,
-0.7099934816360474,
-0.19276003539562225,
-0.8832655549049377,
-0.43104222416877747,
0.5826155543327332,
-0.1556057631969452,
-0.31376758217811584,
0.23778800666332245,
-0.24591971933841705,
1.1488854885101318,
0.672363817691803,
0.13217654824256897,
0.903523862361908,
0.4335445761680603,
-0.23321837186813354,
0.32954108715057373,
-0.20132359862327576,
-0.6254377365112305,
0.3775808811187744,
-0.26064157485961914,
-0.49027639627456665,
0.2125859558582306,
-0.72309809923172,
-0.12918280065059662,
0.3319735527038574,
0.6934471130371094,
-0.2647823691368103,
0.5448979139328003,
-0.7062313556671143,
0.7303415536880493,
-0.6043233871459961,
0.050392765551805496,
-0.9497154355049133,
-0.016725776717066765,
-0.4478416442871094,
-0.6359188556671143,
0.2288808375597,
0.062317777425050735,
-1.0352070331573486,
0.8877689242362976,
-1.0863780975341797,
0.2664692997932434,
0.6790186762809753,
-0.0457553006708622,
-0.5204675197601318,
-0.06600861996412277,
0.42892396450042725,
-0.2718839943408966,
-0.3190188705921173,
-0.6738799810409546,
0.5921664237976074,
0.16753867268562317,
0.0443999245762825,
0.4340240955352783,
0.6415716409683228,
-0.014850366860628128,
0.1651780903339386,
0.03321182727813721,
0.19045068323612213,
1.2824870347976685,
-0.2969769239425659,
-0.1595875769853592,
0.5465855002403259,
0.1424381136894226,
0.4567709267139435,
-0.2254907637834549,
0.2135012298822403,
0.4721866846084595,
0.06357850134372711,
0.3783442974090576,
0.39900121092796326,
0.4595375955104828,
0.3605489134788513,
0.28504475951194763,
-0.1838987022638321,
-0.2066481113433838,
-0.10269127786159515,
-0.34610119462013245,
-0.031089698895812035,
-0.09510910511016846,
-0.20916205644607544,
0.0355643592774868,
-0.500076413154602,
0.15148025751113892,
-0.7326368093490601,
0.9499366879463196,
-0.34055429697036743,
0.25914475321769714,
0.3920114040374756,
-0.12004407495260239,
-1.245956540107727,
0.35777217149734497,
-0.157586932182312,
0.7033725380897522,
-0.0307546928524971,
-0.11640115082263947,
0.3961294889450073,
0.27794235944747925,
-0.3386684060096741,
-0.4785195291042328,
-0.9990798830986023,
0.8422390818595886,
-0.05388662591576576,
0.13477997481822968,
0.8249573707580566,
-0.2605654299259186,
-1.0445740222930908,
-0.2931302785873413,
-0.9229821562767029,
0.3680378794670105,
-0.08620046824216843,
0.5719269514083862,
0.6682726740837097,
-0.6777666211128235,
0.5481492280960083,
0.40364453196525574,
-0.16426625847816467,
0.7524772882461548,
0.3211502730846405,
0.1300560086965561,
0.3523630201816559,
-0.052604030817747116,
-0.4198899269104004,
0.5515516996383667,
-0.32559317350387573,
-0.16448667645454407,
-0.3009466826915741,
0.048718612641096115,
0.7726492881774902,
-0.5312142968177795,
0.6317528486251831,
-0.3458806872367859,
-0.7452560663223267,
0.2679622769355774,
-0.0217446256428957,
-0.8252596259117126,
0.405497282743454,
0.3110978603363037,
0.0008403206011280417,
-0.3604532480239868,
-0.7712789177894592,
1.0671223402023315,
-0.06917347013950348,
-0.4413967430591583,
0.4727364480495453,
-0.12011586874723434,
-0.22073182463645935,
0.37433677911758423,
0.23070339858531952,
-0.1041049212217331,
0.23753216862678528,
1.0869582891464233,
0.9886000752449036,
-0.12620891630649567,
-0.12036898732185364,
-0.8504807353019714,
-0.5580312013626099,
-0.48972588777542114,
0.3658655881881714,
-0.7066256403923035,
0.14624635875225067,
0.3948896825313568,
-0.22028081119060516,
-0.3551124036312103,
0.5796498656272888,
-0.7851112484931946,
-0.6190330982208252,
0.4705294072628021,
-0.37431100010871887,
0.17391182482242584,
-0.3374137580394745,
0.13985522091388702,
-0.8829173445701599,
0.15973347425460815,
0.19622264802455902,
0.41744861006736755,
0.41690316796302795,
-0.3567069172859192,
0.32478395104408264,
0.30714720487594604,
0.5047445297241211,
-0.44800448417663574,
0.22525213658809662,
-0.2767643928527832,
-0.2987443506717682,
-0.2607288956642151,
-0.9835264086723328,
-0.00409794133156538,
-0.39402180910110474,
-0.07464413344860077,
0.04536960646510124,
-0.11575796455144882,
-0.4784691035747528,
-0.6552171111106873,
-0.7142517566680908,
-0.6723451018333435,
-0.2878169119358063,
0.16296038031578064,
-0.193473219871521,
-0.21574164927005768,
-0.87553471326828,
0.158644899725914,
-0.13262028992176056,
-0.03940099850296974,
0.5600676536560059,
-0.6670499444007874,
0.3728131353855133,
0.33610105514526367,
-0.5479655265808105,
0.05766219273209572,
-0.1044013500213623,
0.4662707448005676,
0.3075920641422272,
-0.006713179871439934,
0.5548966526985168,
-0.3869542181491852,
-1.3506748676300049,
-0.5355660915374756,
1.0037163496017456,
1.1957337856292725,
0.6810889840126038,
0.11765051633119583,
0.230912446975708,
0.06091555580496788,
-0.5462357401847839,
-0.44884106516838074,
-0.21619167923927307,
0.10762659460306168,
0.1691981703042984,
-0.03017137572169304,
0.09479543566703796,
0.4477814733982086,
0.554645299911499,
0.3080021142959595,
0.450810045003891,
0.07940593361854553,
0.25695502758026123,
0.11232765763998032,
0.7936111688613892,
0.19209808111190796,
-0.1937076300382614,
0.02506108209490776,
-0.7275223135948181,
0.5649755001068115,
0.4310511648654938,
0.4560798108577728,
-0.04109977185726166,
-0.47321388125419617,
0.1366828829050064,
-0.6997316479682922,
0.29219943284988403,
0.09539017826318741,
-0.37751007080078125,
0.1357441544532776,
0.0606364831328392,
0.08486168086528778,
0.002981986617669463,
0.23446142673492432,
0.43396690487861633,
0.659631609916687,
0.2271583378314972,
-0.8783569931983948,
-0.1329970359802246,
0.048336632549762726,
0.301090270280838,
0.6303895115852356,
-0.8788959383964539,
-0.6502792239189148,
-1.1208337545394897,
0.4290069043636322,
0.07144156098365784,
0.16542959213256836,
1.143701434135437,
0.17886359989643097,
-0.1244579330086708,
-0.7902626395225525,
-0.6838669776916504,
1.4207649230957031,
-0.24918769299983978,
-0.0272549819201231,
-0.13833995163440704,
-0.22635620832443237,
-0.061586737632751465,
0.9729414582252502,
-0.17923511564731598,
-0.5639722943305969,
0.08315835893154144,
-0.9306250214576721,
0.19442451000213623,
-0.5019345283508301,
-0.23066768050193787,
-0.04745936766266823,
-0.44673866033554077,
-0.5413920879364014,
0.2844420075416565,
0.533143937587738,
-0.10981912910938263,
-0.028858620673418045,
0.26708081364631653,
-0.23015984892845154,
0.28638193011283875,
0.055637359619140625,
-0.017677053809165955,
0.8154590129852295,
0.408849835395813,
0.38140663504600525,
0.7045298218727112,
0.542270302772522,
-0.5064072608947754,
0.22417396306991577,
0.41967737674713135,
0.1915532648563385,
-0.6758010387420654,
-0.37695276737213135,
0.2604725956916809,
-0.920283317565918,
-0.4992375075817108,
-0.14215002954006195,
-0.45506030321121216,
0.5882552266120911,
0.6584560871124268,
-0.888451874256134,
-0.5460148453712463,
-0.4222518801689148,
-0.4506223499774933,
0.33689308166503906,
-0.09307830780744553,
-0.20881347358226776,
0.8433552384376526,
-0.11730615049600601,
-0.24181190133094788,
-0.24417145550251007,
0.2696550488471985,
-0.6845299601554871,
0.15712979435920715,
0.7061198949813843,
-0.4293892979621887,
0.14038792252540588,
-1.0777641534805298,
0.5992569327354431,
-0.050416890531778336,
0.25043633580207825,
-0.38817736506462097,
-0.08899103850126266,
-0.4421708583831787,
0.07930000126361847,
0.5319249629974365,
0.10047972202301025,
0.1805533617734909,
0.30531731247901917,
0.11039257049560547,
0.11944948881864548,
-0.603187084197998,
-0.8459688425064087,
-0.48847097158432007,
0.6847791075706482,
0.632814347743988,
-0.35411903262138367,
0.15992096066474915,
1.086337924003601,
-0.4394180476665497,
0.9854369163513184,
-0.002777500543743372,
-0.4749175012111664,
0.39076122641563416,
-0.46350428462028503,
0.1651524305343628,
-0.9264942407608032,
-0.6244699954986572,
-0.10085777938365936,
-0.12380125373601913,
0.1959366500377655,
0.49647918343544006,
-0.07878589630126953,
-0.5099251866340637,
-0.7871142029762268,
-0.3008277118206024,
0.7373343110084534,
-0.14584806561470032,
-0.2488601952791214,
-0.49552804231643677,
-0.18676383793354034,
-0.33057302236557007,
0.5765705108642578,
-0.20919592678546906,
0.2569199204444885,
-0.24646835029125214,
0.050449781119823456,
0.027781231328845024,
0.7579387426376343,
0.2962140440940857,
-0.022749584168195724,
0.2226092666387558,
0.32576489448547363,
0.31282997131347656,
0.7167363166809082,
-0.882173478603363,
-0.22374007105827332,
-1.194321632385254,
0.6124218106269836,
-0.12489937245845795,
-0.25914105772972107,
0.023297786712646484,
0.6755009889602661,
0.6043606400489807,
-0.7755337357521057,
0.4860450327396393,
0.36545997858047485,
-0.24525602161884308,
0.6290073394775391,
0.7526079416275024,
-0.6044806241989136,
-0.08302829414606094,
-0.49982598423957825,
-1.0456218719482422,
0.4679640531539917,
0.5896735787391663,
-0.26787519454956055,
-0.023061778396368027,
-0.26982682943344116,
-0.2289559692144394,
0.21301637589931488,
0.5101644992828369,
0.5004974603652954,
0.04063747823238373,
0.45803579688072205,
0.4278389513492584,
-0.18624760210514069,
-0.7093130946159363,
-0.3250824809074402,
-0.3322828412055969,
-0.09273701161146164,
-0.2538047730922699,
0.041124869138002396,
-0.44213923811912537,
-0.16323266923427582,
-0.3731221854686737,
1.0107696056365967,
0.16875720024108887,
-0.12593205273151398,
0.718443751335144,
0.5747374296188354,
-0.4181033670902252,
-0.688025176525116,
-0.9183490872383118,
0.2493855357170105,
-0.4027674198150635,
0.5375692248344421,
0.10054712742567062,
0.6067827939987183,
-0.30744990706443787,
0.15906967222690582,
-0.5645972490310669,
-0.3156556189060211,
0.3403241038322449,
-0.7559390664100647,
0.007170045282691717,
0.4867403209209442,
-0.21002168953418732,
-0.6666556596755981,
-0.1458214521408081,
-0.9211827516555786,
-0.13394571840763092,
-0.4616667330265045,
-0.4981418251991272,
-0.22462816536426544,
0.34574660658836365,
-0.06821471452713013,
0.40767407417297363,
0.6790564656257629,
0.1308492124080658,
0.24910327792167664,
0.07073171436786652,
-0.3670485019683838,
-0.06659108400344849,
0.27332913875579834,
1.262465238571167,
0.06772196292877197,
-0.7886505126953125,
-0.3509407043457031,
0.16655367612838745,
-0.14884105324745178,
-0.22187170386314392,
0.6451992988586426,
-0.44529756903648376,
0.30662479996681213,
-0.3525386452674866,
0.12341002374887466,
0.0021332032047212124,
0.9702104926109314,
-0.3793973922729492,
-0.07967684417963028,
-0.19870714843273163,
-0.5686026811599731,
-0.4258098900318146,
-0.20075763761997223,
0.31236013770103455,
1.058923602104187,
-0.12230503559112549,
-0.0504513718187809,
-0.23347687721252441,
-1.06889009475708,
0.0783814862370491,
-0.5772866606712341,
-0.06590154767036438,
-1.0737218856811523,
-0.3768363296985626,
-0.869352400302887,
-0.43740028142929077,
0.090563103556633,
0.6818832755088806,
-0.49359115958213806,
0.11727328598499298,
-0.9231147766113281,
-0.09366371482610703,
-0.17898227274417877,
0.079543836414814,
0.21976874768733978,
-0.44164854288101196,
-0.18650928139686584,
-0.12730088829994202,
0.5358118414878845,
-0.4845256805419922,
-0.32370349764823914,
0.3399166464805603,
-0.2801740765571594,
0.5096011757850647,
-0.5151563882827759,
0.6882286071777344,
-1.4959725141525269,
-0.8385666608810425,
-0.42385178804397583,
0.23033222556114197,
-1.1625638008117676,
0.735755980014801,
0.27726680040359497,
0.5090479254722595,
0.35239940881729126,
-0.1346272975206375,
-0.3949476480484009,
-0.054730769246816635,
-0.9257363080978394,
0.1976976990699768,
0.01435584481805563,
-0.08454922586679459,
-0.198513001203537,
-0.8924816846847534,
-0.42029544711112976,
0.31317490339279175,
-0.6814533472061157,
0.7138557434082031,
-0.626027524471283,
0.6916075944900513,
-0.3455761671066284,
0.21608620882034302,
0.45841535925865173,
0.16611261665821075,
-0.09961364418268204,
1.192239761352539,
-0.17172600328922272,
-0.6468504071235657,
0.22646352648735046,
0.08910302072763443,
-0.20034830272197723,
-0.17592290043830872,
0.1649063676595688,
-0.3802618086338043,
-0.23891021311283112,
0.4303451180458069,
0.13153202831745148,
0.036847926676273346,
0.3460361361503601,
-0.24013325572013855,
-0.13761961460113525,
-0.10036035627126694,
-1.0566554069519043,
0.6417742967605591,
0.49637240171432495,
-0.6230576038360596,
-0.34395936131477356,
-0.5721588730812073,
-1.2926316261291504,
0.5345348119735718,
-0.020658964291214943,
-0.6492257714271545,
-0.05609654635190964,
-0.23018868267536163,
0.08916427195072174,
0.3358832001686096,
-0.005584001075476408,
0.176910400390625,
-0.08591824024915695,
0.4860409200191498,
0.16685248911380768,
0.3453325033187866,
-0.8872191905975342,
-0.1804249882698059,
-0.7424307465553284,
-0.29345834255218506,
-0.7752214074134827,
0.17381881177425385,
-0.510003924369812,
-0.7130370736122131,
-0.3558309078216553,
0.42041081190109253,
0.8126586079597473,
0.13547804951667786,
-0.32779639959335327,
-0.1410495489835739,
-0.37952667474746704,
-0.1076371967792511,
0.09681642055511475,
0.21597738564014435,
-0.17728643119335175,
0.44132205843925476,
-0.04521525278687477,
-0.2961333394050598,
0.5725762248039246,
0.11547736078500748,
0.5459458827972412,
-0.335662841796875,
0.21157193183898926,
1.452093243598938,
0.52068030834198,
-0.4870430529117584,
0.06875695288181305,
-0.13798615336418152,
-0.03291434422135353,
0.4764472544193268,
-0.7964972257614136,
0.543251097202301,
0.7052881717681885,
-0.03394735977053642,
1.095218539237976,
0.7887959480285645,
0.45664769411087036,
0.7586284279823303,
0.5542570352554321,
0.347467303276062,
-0.13218006491661072,
0.7199222445487976,
0.32885634899139404,
0.6538387537002563,
-0.10273588448762894,
0.2410414069890976,
-0.1238507553935051,
0.26339277625083923,
0.6303601264953613,
-0.2867351174354553,
-0.4015519917011261,
-0.2063329517841339,
0.12860606610774994,
0.4336080551147461,
-0.5721070766448975,
-0.4812166690826416,
-0.5436076521873474,
0.3622044324874878,
0.04922713711857796,
0.2946445643901825,
0.03133191540837288,
0.6719381213188171,
0.48960912227630615,
0.1566314846277237,
0.5709693431854248,
0.8203264474868774,
-0.06554815173149109,
0.7019511461257935,
1.082411289215088,
0.37081655859947205,
0.7000108957290649,
0.4418700337409973,
0.39701035618782043,
-0.7524475455284119,
-0.14146117866039276,
0.29380080103874207,
-1.1315701007843018,
-0.1928270012140274,
-0.3649275302886963,
-0.23975662887096405,
-0.3336304724216461,
-0.3755543828010559,
0.10906162858009338,
-0.8003557324409485,
0.16352857649326324,
0.9029656648635864,
-0.3356311321258545,
0.5075333118438721,
0.05625799670815468,
-0.11729845404624939,
-0.06007228046655655,
0.6962595582008362,
-0.613164484500885,
-0.6861358284950256,
1.3799272775650024,
1.2582720518112183,
0.01666455902159214,
0.3934657871723175,
-0.046934351325035095,
-0.29584890604019165,
0.3479310870170593,
0.5476478934288025,
0.19380109012126923,
0.8038896322250366,
-1.2457677125930786,
-0.4860875606536865,
0.04317359998822212,
0.3250032961368561,
-0.18236437439918518,
-0.015007900074124336,
-0.21868593990802765,
0.16202519834041595,
-0.1782113015651703,
-0.662749707698822,
1.3807125091552734,
0.2881104350090027,
-0.7734335660934448,
-0.8335927724838257,
-0.08653906732797623,
-0.39639315009117126,
-0.7328612208366394,
-0.6197957992553711,
0.7367067337036133,
0.07018915563821793,
0.1736944615840912,
0.2019505649805069,
-0.20401015877723694,
-1.080356240272522,
-1.23662531375885,
0.2381325662136078,
-0.3264315724372864,
0.4245343804359436,
0.28936031460762024,
0.056221384555101395,
0.26807838678359985,
-0.06524865329265594,
0.11146863549947739,
0.13755308091640472,
1.0823065042495728,
-0.4747934639453888,
-0.04614168033003807,
0.9228495359420776,
0.5085682272911072,
-0.5879198908805847,
0.8280011415481567,
0.519702672958374,
-0.5959672927856445,
0.5578956604003906,
-0.4694264829158783,
0.1995777189731598,
0.41896384954452515,
0.42430824041366577,
0.2774268090724945,
0.10693191736936569,
0.17719626426696777,
-0.19848018884658813,
-0.36792099475860596,
0.7075358629226685,
-0.33890438079833984,
-0.5572003722190857,
-0.27593281865119934,
0.2859955430030823,
-0.023864977061748505,
0.6161332726478577,
-0.05459936708211899,
-0.5059610605239868,
4.202661991119385,
0.4898824989795685,
0.6091707348823547,
0.7952685356140137,
0.6559808850288391,
1.2798019647598267,
0.3048524260520935,
-0.43491318821907043,
0.1362905353307724,
-0.9811903238296509,
-0.3236713111400604,
0.47449809312820435,
0.19353939592838287,
-0.34134355187416077,
-0.5720275044441223,
0.7141431570053101,
-0.09394741803407669,
-0.5799803733825684,
0.37729769945144653,
-0.7081266045570374,
-0.12673035264015198,
-0.15163491666316986,
0.8022799491882324,
0.2895354628562927,
-0.108265221118927,
-0.02314899116754532,
0.7307198643684387,
-0.43795812129974365,
-0.3057136535644531,
-0.8335667252540588,
-1.3767459392547607,
-0.7421832084655762,
0.37373659014701843,
-0.6043689250946045,
-0.6543335318565369,
0.6370507478713989,
0.1673002690076828,
-0.2992248833179474,
0.6515324711799622,
0.3569302558898926,
-0.00954550039023161,
-0.6266990303993225,
0.37290728092193604,
-0.3581700325012207,
-0.6948636174201965,
1.2082958221435547,
0.4527098536491394,
0.8203669190406799,
0.2493421882390976,
-0.2911825478076935,
0.47335681319236755,
-0.40211305022239685,
0.2565532624721527,
-0.4530075788497925,
-0.43495461344718933,
0.20363953709602356,
-0.6056938171386719,
-0.4125627875328064,
0.5571179986000061,
0.18867848813533783,
0.4339561462402344,
-0.5489842295646667,
-0.24891626834869385,
0.17242290079593658,
0.5490552186965942,
0.6281920671463013,
0.29653623700141907,
0.1340201199054718,
0.13207748532295227,
-0.5660051107406616,
0.04722779989242554,
-0.07212816178798676,
-0.22736407816410065,
0.09919428825378418,
0.0808074027299881,
-0.2682080566883087,
0.5642732381820679,
0.5531437993049622,
-0.01730959303677082,
0.42322489619255066,
-0.04937624931335449,
-0.18067525327205658,
-0.3961118161678314,
0.5372737050056458,
0.2268640547990799,
0.2787106931209564,
-0.29592666029930115,
0.11535012722015381,
0.058264706283807755,
0.4938536286354065,
-0.10882976651191711,
0.734587550163269,
0.43099433183670044,
0.38258373737335205,
-1.2491731643676758
] |
The nature of the continuum limit in strongly coupled quenched QED
|
We review the results of large scale simulations of noncompact quenched $QED$ which use spectrum and Equation of State calculations to determine the theory's phase diagram, critical indices, and continuum limit. The resulting anomalous dimensions are in good agreement with Schwinger-Dyson solutions of the ladder graphs of conventional $QED$ and they satisfy the hyperscaling relations expected of a relativistic renormalizable field theory. The spectroscopy results satisfy the constraints of the Goldstone mechanism and PCAC, and may be indicative of Technicolor versions of the Standard Model which are strongly coupled at short distances.
|
Mp Lombardo, J.B. Kogut, A. Kocic and K.C. Wang
|
hep-lat hep-ph
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210015
|
hep-lat/9210016
|
[
0.2851654887199402,
0.5730834007263184,
0.6113928556442261,
-0.19873344898223877,
-0.024561908096075058,
-0.41608017683029175,
-0.24271132051944733,
-0.18301726877689362,
-0.9929453730583191,
0.916617214679718,
0.7114495635032654,
-0.5647692680358887,
0.3922383189201355,
-0.9290274381637573,
-0.42973628640174866,
-0.16258588433265686,
0.2759664058685303,
-0.6570715308189392,
-0.4616728723049164,
-0.7409852147102356,
-0.013564608991146088,
-0.22363106906414032,
-1.1318976879119873,
-0.485487163066864,
0.022904783487319946,
-0.07317439466714859,
0.7632082104682922,
-0.15513162314891815,
1.5946691036224365,
0.02964746206998825,
0.6297675371170044,
-0.3992786407470703,
0.03336711972951889,
-0.9574219584465027,
0.20844817161560059,
-0.6522539258003235,
0.734814465045929,
0.2884017527103424,
0.04185003787279129,
-0.24844832718372345,
0.7025110721588135,
-0.0018879958661273122,
-0.2196091115474701,
-0.35007596015930176,
-0.6801860928535461,
-0.18591539561748505,
0.056372664868831635,
0.3502693474292755,
0.4658185541629791,
-0.8415403962135315,
0.3590965270996094,
0.2574456036090851,
0.21544575691223145,
-0.6954806447029114,
0.10587834566831589,
-0.5071396231651306,
0.11006371676921844,
0.10470593720674515,
-0.18925318121910095,
-0.06663479655981064,
0.6909045577049255,
0.31557321548461914,
0.32038187980651855,
-0.9187535643577576,
0.3617590665817261,
0.5253203511238098,
-0.40729454159736633,
0.9726675748825073,
-0.036016181111335754,
0.10994196683168411,
-0.028490889817476273,
-0.6859927773475647,
-0.7735623717308044,
-0.12364792078733444,
-0.5456026196479797,
0.7219129204750061,
0.3533839285373688,
0.3399199843406677,
-0.5881728529930115,
0.19379746913909912,
0.08109846711158752,
-0.22893266379833221,
-0.012515303678810596,
0.6144962310791016,
-0.6734552979469299,
-0.44335147738456726,
1.2063671350479126,
0.14871977269649506,
-0.12003345787525177,
0.3055952191352844,
0.028199782595038414,
0.26061198115348816,
0.3370092511177063,
-0.06631703674793243,
0.244450643658638,
0.20807689428329468,
0.20846936106681824,
0.8674913048744202,
0.062112562358379364,
0.06182613968849182,
0.044870525598526,
1.2687790393829346,
-0.22894187271595,
0.6911531686782837,
-0.20626063644886017,
0.6807224750518799,
0.15397877991199493,
0.2172519564628601,
-0.7759298086166382,
-0.07837966084480286,
0.37832731008529663,
-0.09875555336475372,
0.3111492693424225,
0.7990278005599976,
-0.4167773127555847,
0.8582816123962402,
0.32661041617393494,
0.07539155334234238,
-0.7797276377677917,
-0.19206297397613525,
-0.15653949975967407,
-0.04219929128885269,
0.7520016431808472,
0.4045078754425049,
-0.015045871026813984,
-0.7534974813461304,
-0.1868770569562912,
0.5148255825042725,
-0.8280929923057556,
0.18927180767059326,
-0.26155009865760803,
0.1985958218574524,
-0.7845008969306946,
0.7712636590003967,
-0.1780918687582016,
-0.008991235867142677,
-0.3610105812549591,
0.6437683701515198,
0.12991663813591003,
-0.7464205622673035,
0.21241872012615204,
-0.16044041514396667,
-0.33050233125686646,
1.3295894861221313,
-0.9548521041870117,
-0.2822948098182678,
0.5724053382873535,
-0.7519670128822327,
-0.7749103307723999,
0.6021329164505005,
-0.41427287459373474,
-0.3042866587638855,
-0.32766950130462646,
0.9486170411109924,
0.5713262557983398,
0.44902536273002625,
0.36091169714927673,
0.25937598943710327,
-0.7746982574462891,
-0.20489612221717834,
0.2949846684932709,
-0.17493663728237152,
-0.6887050271034241,
0.4427807331085205,
-0.052910659462213516,
0.10164990276098251,
-0.4251977205276489,
0.13039639592170715,
-1.0269120931625366,
-1.3670148849487305,
0.3047238886356354,
-0.2610054612159729,
0.22017011046409607,
0.5960320830345154,
0.15532773733139038,
0.3855338394641876,
0.48604264855384827,
-0.3440539538860321,
0.33484452962875366,
0.026898136362433434,
-0.2292662113904953,
-0.30482086539268494,
0.5775832533836365,
0.5458131432533264,
0.32381564378738403,
-0.3232455253601074,
-0.3040054738521576,
-0.23368389904499054,
-0.09563114494085312,
0.7446672916412354,
0.22479577362537384,
0.42584434151649475,
0.22356247901916504,
0.811820387840271,
-0.8366992473602295,
-0.08999045938253403,
0.21929869055747986,
-0.16402873396873474,
-0.7066726684570312,
-0.6351015567779541,
-0.07216958701610565,
0.32217931747436523,
-0.5948324203491211,
0.06993826478719711,
-0.7107512950897217,
0.4153563380241394,
-0.08787474781274796,
0.3062315285205841,
-0.5689419507980347,
0.04817437753081322,
-0.11195623129606247,
0.32694071531295776,
0.03706034645438194,
-0.34662163257598877,
0.027299506589770317,
0.29949209094047546,
-0.15942439436912537,
-0.05520053952932358,
-0.15608972311019897,
-0.046752508729696274,
0.21698744595050812,
-0.33848345279693604,
0.006022494751960039,
0.35484960675239563,
0.41203004121780396,
-0.48272231221199036,
0.011888929642736912,
1.0487593412399292,
0.5842253565788269,
0.17053677141666412,
0.4007769227027893,
0.4435262084007263,
-0.26446616649627686,
0.768152117729187,
0.5473095178604126,
0.37697234749794006,
0.6852251291275024,
-0.07370280474424362,
0.33606210350990295,
0.7179090976715088,
-0.3819314241409302,
0.09771241247653961,
0.6979222297668457,
0.5151808857917786,
-0.008796137757599354,
0.8449069857597351,
-0.41714000701904297,
0.2731611728668213,
-0.4103880226612091,
-0.3195064663887024,
-0.0527823343873024,
0.3601563274860382,
0.2779425084590912,
0.7664662003517151,
-1.001081943511963,
-0.34403035044670105,
-0.36482641100883484,
0.5582131147384644,
0.030618799850344658,
-0.5144150853157043,
-0.687850832939148,
0.2534412741661072,
0.08328647911548615,
-0.5225368738174438,
-0.49107152223587036,
1.2151445150375366,
0.02352161519229412,
0.13171029090881348,
0.11801654100418091,
-0.5662210583686829,
-1.113207221031189,
-0.4066362679004669,
-1.0307139158248901,
-0.5326173305511475,
0.018173953518271446,
-0.7155558466911316,
0.5459418296813965,
-0.825168788433075,
0.12970316410064697,
-0.4549025595188141,
-0.5060061812400818,
0.626494288444519,
0.1258547455072403,
0.17304006218910217,
0.4794904291629791,
-0.5121666789054871,
-0.6388609409332275,
0.7801793813705444,
-0.9520838260650635,
0.3659846782684326,
-0.000479002483189106,
0.056964367628097534,
-0.2536543607711792,
-0.2571203112602234,
-0.4168524742126465,
-0.4557192325592041,
-0.3730241358280182,
0.427046000957489,
-0.12163609266281128,
-0.8014401793479919,
0.2539404630661011,
0.3542165160179138,
-0.08899056166410446,
-0.6347048878669739,
-0.8852741122245789,
-0.18030475080013275,
0.7863516807556152,
-0.6654089093208313,
0.0023103177081793547,
0.8074836134910583,
-1.2928526401519775,
0.5022276639938354,
-0.2988523840904236,
-0.08676475286483765,
-0.0057271067053079605,
0.444263219833374,
1.0196514129638672,
0.1729700118303299,
0.05533682927489281,
-0.8771649599075317,
-0.27202874422073364,
0.006575992330908775,
-0.01354697160422802,
-0.3386685848236084,
0.40869140625,
1.1778020858764648,
-0.08431126922369003,
-0.4346978962421417,
0.20333190262317657,
-0.3090130388736725,
-1.31782066822052,
-0.05448741093277931,
-0.5744895339012146,
0.2915131449699402,
0.8778034448623657,
-0.18984834849834442,
-0.6242371201515198,
0.06387057900428772,
0.4787891209125519,
0.5190224647521973,
0.3635541498661041,
-0.7406893372535706,
0.3723328411579132,
0.7672135233879089,
0.5469108819961548,
0.5300388336181641,
1.2420092821121216,
-0.6004287600517273,
0.20312148332595825,
-0.175044447183609,
0.4342455565929413,
-0.020723676308989525,
0.2878040671348572,
-0.3560236096382141,
-0.6040866374969482,
0.319406658411026,
-0.38101881742477417,
0.690338134765625,
0.6069024801254272,
-0.4907720983028412,
0.5160945653915405,
0.6030772924423218,
-0.0711577981710434,
0.46659520268440247,
0.5732645392417908,
-0.4524300694465637,
0.24709109961986542,
-0.2605442404747009,
0.4111141860485077,
-1.9465028047561646,
0.4546450078487396,
-0.4237709641456604,
-0.23255692422389984,
-0.3101431131362915,
0.5105756521224976,
-0.24509386718273163,
0.17756229639053345,
0.39698654413223267,
1.0762380361557007,
-1.231603741645813,
-0.40360844135284424,
0.15692272782325745,
0.6753581762313843,
0.5418050289154053,
1.2378226518630981,
0.5269784331321716,
0.5983478426933289,
-0.5661933422088623,
-0.0384247712790966,
-0.3502853214740753,
-0.401246041059494,
-0.3389807939529419,
-0.29744020104408264,
-0.3973538875579834,
-0.953551173210144,
-0.6665650606155396,
0.4326537549495697,
-0.3347894847393036,
0.19061467051506042,
0.39756932854652405,
0.9588958024978638,
-0.6996085047721863,
0.5288386940956116,
0.5638801455497742,
0.43096083402633667,
-0.35169580578804016,
-0.642333984375,
0.7128625512123108,
-0.3518826365470886,
-0.25226402282714844,
-0.23176972568035126,
0.20400284230709076,
0.0712813213467598,
0.019718270748853683,
0.5450662970542908,
0.37083899974823,
0.011088200844824314,
0.33395689725875854,
-0.1657894104719162,
0.5055055022239685,
0.4118081033229828,
-0.13649208843708038,
0.13571757078170776,
0.686927855014801,
0.08038529008626938,
-1.3821735382080078,
-0.36364322900772095,
-0.36213311553001404,
0.6194850206375122,
0.21657827496528625,
-0.06536828726530075,
-0.4796876013278961,
-0.6748762130737305,
-0.3384472131729126,
-0.1357574462890625,
0.05403856933116913,
1.2275540828704834,
-0.5355504751205444,
0.09968330711126328,
-0.7350320816040039,
-0.42558786273002625,
-0.1267794370651245,
-0.42659062147140503,
-0.5483957529067993,
0.44349411129951477,
0.11697155982255936,
0.02209514193236828,
0.48924294114112854,
-0.25116127729415894,
-0.7431638836860657,
-0.14887119829654694,
-0.7185933589935303,
0.4205890893936157,
-0.7403695583343506,
-0.04014946147799492,
-0.48881497979164124,
0.18602988123893738,
-0.6734194755554199,
0.46765875816345215,
-0.012783695012331009,
-0.22049172222614288,
-0.426557719707489,
0.2918074429035187,
-0.7499591708183289,
-0.5901201367378235,
-0.027806349098682404,
0.05034460499882698,
0.5097653865814209,
0.8632156252861023,
-0.0010768288047984242,
0.18505413830280304,
0.2631774842739105,
-0.07567581534385681,
-0.4467359781265259,
0.1480260044336319,
-0.2643515467643738,
0.3158106505870819,
-0.17873430252075195,
-0.1117272600531578,
-0.3585379123687744,
-0.43772366642951965,
0.11095773428678513,
-0.3563207685947418,
-0.18223363161087036,
0.7017018795013428,
-0.9564010500907898,
-0.25719529390335083,
0.22096554934978485,
-1.0246833562850952,
-0.3623180389404297,
-0.034900449216365814,
-0.740212619304657,
0.009375851601362228,
-0.4551556706428528,
-0.2928270697593689,
0.7059636116027832,
-0.8163792490959167,
-0.07154951244592667,
0.5502268671989441,
0.6247426271438599,
0.38993021845817566,
-0.4130227565765381,
-0.3276447355747223,
0.730441689491272,
-0.5345463156700134,
0.21845601499080658,
-1.0461329221725464,
-0.21722252666950226,
0.1940750628709793,
-0.5033785700798035,
-0.7335914373397827,
0.1788792610168457,
0.06810640543699265,
-0.1507503241300583,
-0.09081607311964035,
-0.04151427373290062,
-0.7206408977508545,
-0.5320613980293274,
-0.13368503749370575,
0.9110648036003113,
-0.7020751237869263,
-1.2028589248657227,
-0.4448573887348175,
-0.08385124057531357,
-0.29616278409957886,
-0.08974236994981766,
0.8281177878379822,
-1.2078617811203003,
0.07065402716398239,
-0.5277327299118042,
-0.15010099112987518,
-1.2160924673080444,
0.4219246506690979,
-0.9707502722740173,
-1.0739455223083496,
-0.60140460729599,
0.3312302529811859,
0.6420314311981201,
-0.4858000874519348,
-0.22511880099773407,
-0.1795920729637146,
0.19627688825130463,
-0.8102166652679443,
-0.432630717754364,
0.0008193239336833358,
0.6283394694328308,
-0.5961256623268127,
0.8836429715156555,
-0.5923596024513245,
-0.48577553033828735,
0.1580602079629898,
0.20768818259239197,
0.3815017640590668,
0.7646445035934448,
-0.4338423013687134,
-0.20619110763072968,
-0.28456616401672363,
-0.17618364095687866,
0.3238319158554077,
0.836811900138855,
-0.47590333223342896,
0.6016733646392822,
-0.7850260138511658,
0.25778862833976746,
-0.8658921122550964,
-0.6919682621955872,
0.21328799426555634,
0.23519739508628845,
0.45924147963523865,
-0.9105122685432434,
0.8211559653282166,
0.4580950140953064,
0.15417836606502533,
0.4407968819141388,
0.20952987670898438,
-0.3547651767730713,
-0.08965937793254852,
-1.1954002380371094,
-1.0049664974212646,
0.8923520445823669,
-0.30111098289489746,
-0.15634985268115997,
-0.17917750775814056,
-0.2521938681602478,
0.3575037717819214,
-0.5503823161125183,
0.952537477016449,
0.5303582549095154,
0.12468138337135315,
0.3151484727859497,
0.1010284349322319,
-0.9351395964622498,
-0.33458036184310913,
-0.3436143696308136,
0.6252453327178955,
-0.2710559666156769,
-0.830357551574707,
0.01966673508286476,
-0.5058128237724304,
-1.1062413454055786,
-0.4013661742210388,
0.3319934904575348,
0.03620150685310364,
-0.007764337584376335,
0.7339243292808533,
-0.7604799270629883,
0.022950157523155212,
-0.6743936538696289,
0.04546639323234558,
0.5205802917480469,
0.025605103000998497,
0.43172046542167664,
0.3501147925853729,
0.9308539628982544,
0.4904854893684387,
-0.2651140093803406,
-0.4837194085121155,
-1.0082318782806396,
1.1059281826019287,
-0.23847252130508423,
-0.6828666925430298,
0.6499524116516113,
0.3753592073917389,
-0.398147314786911,
-0.3113560080528259,
-0.1214563250541687,
-0.030494870617985725,
-0.776785135269165,
-0.6449328660964966,
-0.21829165518283844,
-0.07090575993061066,
-0.4176895320415497,
0.0634918063879013,
0.2736869752407074,
-0.6970136165618896,
0.0027813760098069906,
0.6461050510406494,
0.2823236584663391,
-1.5159982442855835,
0.6226800680160522,
1.015038251876831,
-0.263370543718338,
0.20821575820446014,
-0.3173553943634033,
-0.690822422504425,
0.00038027315167710185,
-0.0029993755742907524,
0.3176962435245514,
-0.3038199841976166,
-0.20258666574954987,
0.6011276245117188,
0.13154110312461853,
0.6894534230232239,
0.5835367441177368,
0.47724130749702454,
-0.09963976591825485,
-0.27897071838378906,
-0.6088030338287354,
-0.5726325511932373,
0.3658007085323334,
-0.4629898965358734,
0.47708678245544434,
0.3413654565811157,
0.25561922788619995,
0.5750119686126709,
0.40197548270225525,
-0.11950421333312988,
-1.249280333518982,
0.4205070436000824,
-0.8645080924034119,
-0.4399344325065613,
-0.775038480758667,
-0.2179567515850067,
-0.18116448819637299,
0.49997809529304504,
0.10871889442205429,
-0.2667972445487976,
-0.09030161052942276,
0.4537261426448822,
0.10107816010713577,
0.11581724137067795,
-0.6570926308631897,
-0.24846430122852325,
-0.1818234622478485,
-0.347270131111145,
-0.280413955450058,
-0.22655652463436127,
0.06765315681695938,
0.40365147590637207,
0.0033536062110215425,
0.6910892128944397,
-0.36682865023612976,
0.16018003225326538,
0.00859835185110569,
-0.19151239097118378,
0.015935679897665977,
-0.6073490381240845,
-1.4394474029541016,
0.259651243686676,
-0.030539577826857567,
0.02322368323802948,
0.45614859461784363,
-0.5202221870422363,
0.3599732518196106,
-0.01607207953929901,
0.37184491753578186,
-0.22276541590690613,
-0.11459783464670181,
1.307784914970398,
0.05862122029066086,
-0.18967974185943604,
-0.021389517933130264,
0.5286852121353149,
-1.3386298418045044,
-0.20633603632450104,
-0.14426332712173462,
-0.16051998734474182,
-0.3311711847782135,
0.6427288055419922,
0.5203317999839783,
0.6553723812103271,
0.07050248235464096,
0.45377299189567566,
0.03334106504917145,
-0.09773759543895721,
0.020006204023957253,
-0.2977238595485687,
-0.7027156949043274,
0.03582986816763878,
-0.15764018893241882,
-1.3003745079040527,
0.12206602096557617,
0.7288775444030762,
-0.14498065412044525,
-0.2742078900337219,
-0.2716318964958191,
-0.10493963956832886,
-0.5824828743934631,
-0.1951150745153427,
0.025869805365800858,
1.115488886833191,
0.0210549458861351,
-0.533470094203949,
-0.24728813767433167,
-0.3924000561237335,
-0.5000718832015991,
0.023084254935383797,
-0.9993802309036255,
-0.06753921508789062,
0.3224032521247864,
-0.7694588899612427,
0.5479338765144348,
-0.48964110016822815,
-0.3755031228065491,
0.16738110780715942,
0.394968718290329,
0.6519428491592407,
-0.34698915481567383,
0.05167718231678009,
-0.04524652287364006,
0.6712252497673035,
-1.0638724565505981,
-0.1709265410900116,
-0.15536309778690338,
0.3120151460170746,
-0.4396931231021881,
-0.8038331270217896,
0.09187191724777222,
0.7272128462791443,
-0.26467886567115784,
-0.5823398232460022,
-0.39516547322273254,
0.6969629526138306,
-0.0465872697532177,
-0.46507179737091064,
-0.4538567066192627,
0.07163175195455551,
0.17676931619644165,
0.2535230219364166,
-0.328744500875473,
-0.29298368096351624,
0.15562979876995087,
0.61910080909729,
0.29277247190475464,
-0.25383368134498596,
-0.4510713219642639,
0.23597486317157745,
-0.2379099428653717,
-0.922579824924469,
0.7635614275932312,
0.1829492300748825,
1.2120674848556519,
-0.1377437859773636,
0.43266385793685913,
0.17914611101150513,
0.35401585698127747,
0.44699472188949585,
0.5997281074523926,
-0.3876880705356598,
-0.16650700569152832,
0.4600302577018738,
0.1915067434310913,
-0.3856971859931946,
0.4339573085308075,
0.4846326410770416,
-0.5010989904403687,
0.3191741704940796,
-0.5325440168380737,
0.11906290799379349,
-0.3977718949317932,
0.05817241221666336,
-0.34660813212394714,
0.06603918224573135,
0.1420212686061859,
0.04073316603899002,
-0.21815618872642517,
0.1552732288837433,
-0.43069079518318176,
-1.1155023574829102,
-0.3754456043243408,
0.7060980796813965,
0.3672969937324524,
0.03629382327198982,
0.11819349974393845,
-0.34438419342041016,
0.5470122694969177,
0.31979385018348694,
0.14152269065380096,
0.800687313079834,
0.11143656820058823,
0.534633457660675,
-0.25947096943855286,
1.5274569988250732,
-0.1952500194311142,
0.3232699930667877,
0.07443344593048096,
-0.20056267082691193,
-0.18968461453914642,
0.32709744572639465,
-0.578881561756134,
-0.31779611110687256,
-0.21575601398944855,
-0.15129677951335907,
0.059178635478019714,
-0.8820977210998535,
0.3851831555366516,
-0.7467154264450073,
0.45851001143455505,
1.1303517818450928,
-0.21859271824359894,
-0.10632669180631638,
0.539158046245575,
0.2536751329898834,
0.5797034502029419,
1.3430184125900269,
0.18921023607254028,
0.1257113218307495,
1.9999173879623413,
0.9667574763298035,
0.07609402388334274,
0.8376675248146057,
0.5099245309829712,
-0.1499786227941513,
0.15667474269866943,
-0.06078942120075226,
-0.3581646978855133,
0.8805772662162781,
-0.1385652869939804,
0.09020613133907318,
0.11092604696750641,
0.36424946784973145,
-0.192925825715065,
-0.21593767404556274,
0.32979482412338257,
0.19289390742778778,
-0.48925691843032837,
-0.4525013864040375,
0.8955634236335754,
0.9573200941085815,
-0.19703148305416107,
0.23919297754764557,
0.19985714554786682,
-0.3181857466697693,
-0.3532051146030426,
-0.7088128328323364,
-0.055318500846624374,
0.14287453889846802,
-0.254547119140625,
-0.7610388994216919,
-0.6374940872192383,
0.0357523187994957,
-0.3410872519016266,
0.1721464842557907,
-0.11927642673254013,
0.794773280620575,
1.0468062162399292,
0.3149399757385254,
0.4816173017024994,
-0.36871856451034546,
-0.09380073845386505,
0.6334803700447083,
0.5553085803985596,
0.010526641272008419,
0.5919390320777893,
0.986742377281189,
0.7791029214859009,
0.2683826684951782,
0.047809138894081116,
0.3759284019470215,
-0.40906259417533875,
0.06412139534950256,
-0.151039257645607,
0.005219125654548407,
-0.35690078139305115,
-0.3897334635257721,
-0.5225755572319031,
0.8983018398284912,
-0.041413940489292145,
-0.7241543531417847,
-0.581923246383667,
0.6957425475120544,
-0.935348391532898,
0.6099393963813782,
-0.6693911552429199,
1.2009683847427368,
0.2350805550813675,
0.4093494415283203,
-0.6309765577316284,
-0.29868054389953613,
4.046751976013184,
1.1108837127685547,
0.9262569546699524,
0.0844307467341423,
1.2509770393371582,
0.8244988322257996,
0.23852479457855225,
-0.524906575679779,
-0.30543482303619385,
0.008515889756381512,
0.08956064283847809,
-0.14103588461875916,
0.09114371240139008,
0.16108006238937378,
-1.1412783861160278,
0.10033047199249268,
-0.8793647885322571,
-0.2546766698360443,
0.5665454864501953,
-0.5398108959197998,
-0.4124932587146759,
0.458359032869339,
-0.1775909960269928,
0.17287877202033997,
0.3128904402256012,
0.217445507645607,
0.3023102283477783,
-0.17190687358379364,
0.5085462927818298,
-0.5520287752151489,
-0.39896121621131897,
-0.7237473726272583,
-0.04269463196396828,
-0.0717337355017662,
-0.20085307955741882,
0.2505086362361908,
0.3152559995651245,
-0.11466845870018005,
0.01620103418827057,
-0.5958744883537292,
0.04168165847659111,
-0.25570905208587646,
0.06516598910093307,
-0.06261204183101654,
-1.2817258834838867,
0.7796880006790161,
-0.018405554816126823,
0.7337678670883179,
0.8301630020141602,
-1.010834813117981,
0.4316789209842682,
-0.4355509281158447,
0.8419477343559265,
-0.3982100486755371,
-1.2804539203643799,
0.13084298372268677,
-1.3599228858947754,
-0.32092246413230896,
-0.28925007581710815,
0.5789406299591064,
0.5959733128547668,
-0.2075508087873459,
-0.19566643238067627,
0.2687588036060333,
-0.4437297582626343,
0.20578493177890778,
0.09022385627031326,
0.04732409864664078,
-0.4560496509075165,
0.0887749120593071,
-0.03896181285381317,
-0.00781489908695221,
0.01190477516502142,
-0.5423046946525574,
0.02368011884391308,
0.3907991051673889,
-0.3056381046772003,
0.8880006670951843,
0.036726780235767365,
-0.15754064917564392,
0.36678701639175415,
-0.2166295349597931,
1.1399683952331543,
-0.15487070381641388,
-0.09917812049388885,
0.6070234179496765,
-0.3568361699581146,
0.5852420330047607,
-0.023650191724300385,
1.162972331047058,
0.517630934715271,
0.9722819328308105,
-0.12523460388183594,
0.21344125270843506,
-0.6093093752861023
] |
Improvement of efficiency in generating random $U(1)$ variables with Boltzmann distribution
|
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling parameters, which makes the present method especially suitable for parallel and pipeline vector processing machines. Results of computer runs are presented to illustrate the efficiency. An idea to find such algorithms is also presented, which may be applicable to other distributions of interest in Monte Carlo simulations.
|
Tetsuya Hattori and Hideo Nakajima
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210016
|
hep-lat/9210017
|
[
0.35492295026779175,
-0.32717153429985046,
0.33743786811828613,
0.46486571431159973,
0.6006689071655273,
-0.3745494782924652,
0.08146551251411438,
0.061769723892211914,
-1.0058482885360718,
1.3948793411254883,
1.3158645629882812,
0.05819891393184662,
0.8645321130752563,
-0.31422877311706543,
-0.22881273925304413,
0.5229686498641968,
0.20716696977615356,
-0.6662335991859436,
-1.0848455429077148,
0.7142584323883057,
0.3079542815685272,
-0.07432950288057327,
-1.2411274909973145,
-0.21909894049167633,
-0.845507025718689,
1.0142831802368164,
-0.42527535557746887,
0.2734266519546509,
1.3175480365753174,
0.4664646089076996,
0.3736895024776459,
-0.49457401037216187,
-0.14003118872642517,
-0.6677546501159668,
-0.8259080648422241,
-0.41630297899246216,
-0.08603213727474213,
-0.2889969050884247,
0.5934796333312988,
-0.3616529107093811,
0.9254785776138306,
-0.24511387944221497,
0.565497875213623,
-0.03496813401579857,
-0.5201715230941772,
0.6195849776268005,
-0.2555524408817291,
0.09043809771537781,
0.052602458745241165,
-1.3493893146514893,
-0.18797190487384796,
0.13690073788166046,
0.43263503909111023,
-0.2006261646747589,
-0.2109563648700714,
-0.185604989528656,
0.49505355954170227,
0.729293167591095,
-0.7209787964820862,
-0.672020673751831,
0.46644842624664307,
-0.29127147793769836,
0.20381763577461243,
-0.30095118284225464,
0.5678094625473022,
0.8540769815444946,
-0.11086878925561905,
0.5731227993965149,
0.47510358691215515,
-0.937143087387085,
-0.5673641562461853,
-0.5060248374938965,
-0.28787761926651,
0.4183228313922882,
-0.9699841141700745,
0.013482263311743736,
-0.018480084836483,
-0.5937366485595703,
-1.4182794094085693,
0.012807848863303661,
-0.165168896317482,
-0.3269365429878235,
-0.7926604151725769,
0.40295904874801636,
-0.4311826229095459,
-0.49028080701828003,
-0.38992902636528015,
-0.05143582448363304,
0.20897161960601807,
0.7789331674575806,
0.18748731911182404,
0.700027346611023,
0.3570161461830139,
-0.1139259934425354,
0.533307671546936,
0.5790814161300659,
0.6392233371734619,
0.26351678371429443,
-0.24947921931743622,
0.34337911009788513,
-0.056711532175540924,
0.5647972822189331,
-0.00517128873616457,
0.25808557868003845,
-1.2004120349884033,
0.15044349431991577,
0.2771211564540863,
-0.070212721824646,
-0.393572598695755,
-0.5328723192214966,
0.1021980345249176,
0.026998290792107582,
0.3496224284172058,
0.6495705842971802,
0.33369559049606323,
0.30505073070526123,
0.08480185270309448,
-0.4944162666797638,
-0.6082693338394165,
-0.3160652816295624,
0.35539132356643677,
0.27009835839271545,
0.10633835196495056,
0.6630374193191528,
-0.26814985275268555,
-0.5574015378952026,
0.6366186738014221,
0.5211511850357056,
-0.12954652309417725,
-0.20527499914169312,
0.17573979496955872,
-0.1261749118566513,
-0.3941282033920288,
0.31208592653274536,
-0.19451555609703064,
0.288185715675354,
-0.16249606013298035,
0.20280292630195618,
0.3064578175544739,
-0.3007790744304657,
1.0697718858718872,
-0.8241231441497803,
0.03424520790576935,
1.0052999258041382,
0.1990540623664856,
-0.06921151280403137,
0.007465559057891369,
-0.08829313516616821,
-0.11692596226930618,
-0.13287179172039032,
-0.8482514023780823,
-0.06934180110692978,
-0.06060345843434334,
-0.18888528645038605,
0.14849822223186493,
0.5446535348892212,
-0.6484090089797974,
0.915070116519928,
-0.5779610276222229,
-1.0725345611572266,
1.23930823802948,
0.0317007452249527,
-0.7491766214370728,
0.6558482646942139,
-0.6383491158485413,
0.36212262511253357,
-1.2497847080230713,
0.024255208671092987,
0.10497057437896729,
-0.8061692118644714,
0.465663343667984,
0.3170454204082489,
-0.828666627407074,
0.8211125731468201,
0.4324377775192261,
0.2097688466310501,
0.6918133497238159,
-0.9414827823638916,
0.16194425523281097,
0.4362362325191498,
-0.10849928855895996,
-0.48619672656059265,
0.5826587677001953,
0.6293506026268005,
-0.4828084111213684,
0.017130179330706596,
-0.2456020563840866,
-0.3062390685081482,
-0.14237262308597565,
-0.24550014734268188,
0.06993713229894638,
0.5469405651092529,
-0.8097270131111145,
0.5043853521347046,
-0.7329192757606506,
-0.2681964933872223,
-1.3603652715682983,
0.213944211602211,
-0.6320304274559021,
-0.7390459775924683,
-0.43651124835014343,
0.4629959762096405,
-0.8708011507987976,
0.18849606812000275,
-1.6392242908477783,
0.36308640241622925,
0.5600966811180115,
-0.09489215910434723,
-0.9620537757873535,
-0.12087082862854004,
0.3889138102531433,
-0.330351859331131,
0.4766586124897003,
-0.005252053029835224,
-0.46139824390411377,
0.5022558569908142,
-0.08004822582006454,
0.42804762721061707,
0.4312860071659088,
0.0653436928987503,
0.7467728853225708,
0.5216472744941711,
-0.5322142243385315,
0.6724514365196228,
0.21342475712299347,
-0.8212574124336243,
0.3195948898792267,
0.40639910101890564,
0.4584938585758209,
-0.510020911693573,
-0.20507922768592834,
0.19184060394763947,
-0.048674874007701874,
-0.1250489354133606,
0.30247896909713745,
1.1532524824142456,
1.2729324102401733,
0.7918402552604675,
0.02070864476263523,
0.17205193638801575,
-0.01231116708368063,
0.11946225166320801,
0.19187581539154053,
0.05647864565253258,
0.44954827427864075,
0.26916518807411194,
-0.5155754685401917,
0.4146054983139038,
-0.8616511821746826,
0.7383114695549011,
-0.003075470682233572,
0.9144733548164368,
0.7097545266151428,
0.24356651306152344,
-0.7697672247886658,
0.06352104991674423,
-0.045144665986299515,
0.2355901300907135,
-0.290124773979187,
0.3031673729419708,
0.15293721854686737,
-0.21418076753616333,
0.5353268384933472,
-0.47591814398765564,
-0.5711836814880371,
0.9367209076881409,
0.11701503396034241,
0.11440027505159378,
0.29731038212776184,
-0.28354158997535706,
-1.2264678478240967,
-0.3161078095436096,
-0.6128594875335693,
-0.1816810518503189,
-0.2108747363090515,
0.2282959222793579,
1.0359047651290894,
-0.882307767868042,
0.38199469447135925,
0.4926018714904785,
-0.10718880593776703,
0.6976186037063599,
-0.27097946405410767,
0.16572467982769012,
1.0348891019821167,
-0.5059089660644531,
-0.8375465273857117,
0.22926399111747742,
-0.7616981267929077,
0.05117105692625046,
-0.0808267742395401,
0.4291970729827881,
1.1246498823165894,
-0.4507865607738495,
-0.009243909269571304,
0.6126802563667297,
-0.4343399405479431,
0.11759337037801743,
-0.48084986209869385,
-0.8305608034133911,
0.15589530766010284,
0.4340926706790924,
-0.5496858954429626,
-0.5105722546577454,
-0.838142454624176,
1.041736125946045,
0.3213822841644287,
-0.3476187288761139,
0.5595648288726807,
0.5103152990341187,
0.0823550671339035,
0.27359217405319214,
-0.5789995789527893,
0.411324679851532,
0.05014025419950485,
0.9409415125846863,
0.221310093998909,
-0.15521766245365143,
-0.05780058354139328,
-1.2065768241882324,
-0.12730059027671814,
0.06726629287004471,
0.24045529961585999,
-0.626807689666748,
-0.14844073355197906,
1.0117549896240234,
0.20249101519584656,
-0.9801687002182007,
0.5497178435325623,
-0.9648017287254333,
-0.8504389524459839,
0.07580392807722092,
-0.5452848076820374,
0.31339481472969055,
0.11783028393983841,
0.17362703382968903,
-0.8066440224647522,
0.11776439100503922,
-0.27746906876564026,
0.43518754839897156,
0.5571337342262268,
-0.25650912523269653,
0.0855632871389389,
0.5008071660995483,
0.5619218945503235,
0.03139317035675049,
0.11506371945142746,
0.10160839557647705,
-0.6940546035766602,
0.48682883381843567,
-0.39959752559661865,
0.5396314263343811,
0.45148545503616333,
0.6001143455505371,
-0.1862437129020691,
0.37285116314888,
-0.43342018127441406,
-0.8001677393913269,
-0.4474833309650421,
-0.6818505525588989,
-0.06517869979143143,
0.10348238795995712,
-0.43687209486961365,
-0.024985741823911667,
-0.31279265880584717,
-0.2387910932302475,
0.20038340985774994,
-0.11674195528030396,
0.8198184370994568,
-0.8689097762107849,
0.2515890598297119,
-0.00919800903648138,
-0.1226096898317337,
0.3280012011528015,
-0.11529627442359924,
0.5079553723335266,
-0.20359277725219727,
0.24790732562541962,
1.189587950706482,
-0.7673478126525879,
-0.872473955154419,
-0.3967452645301819,
0.9481443166732788,
0.7750768661499023,
0.8488165736198425,
0.5983176231384277,
-0.6571642756462097,
-0.42296504974365234,
-0.3832610845565796,
-0.26401808857917786,
0.02602238766849041,
0.07027943432331085,
-0.4823630154132843,
-0.09436197578907013,
-0.11255867779254913,
-0.48575520515441895,
0.4074562191963196,
0.6231884956359863,
0.4787164032459259,
-0.2281770408153534,
0.5389125943183899,
0.531499981880188,
1.2128123044967651,
0.8104096055030823,
0.0968775823712349,
0.0024318438954651356,
-1.1909886598587036,
0.5524857640266418,
0.11274341493844986,
0.5231437683105469,
-0.2625710368156433,
-0.6680358052253723,
-0.43596377968788147,
-0.9080736637115479,
0.6969358921051025,
0.1932355910539627,
-0.3430880010128021,
0.3689229488372803,
-0.19524917006492615,
-0.031329140067100525,
0.29725056886672974,
-0.3946400284767151,
0.5718336701393127,
-0.11391978710889816,
0.34691810607910156,
-0.7527601718902588,
0.09242485463619232,
-0.1659926176071167,
0.2574288249015808,
0.5530940890312195,
-0.5839992761611938,
-1.2177239656448364,
-1.025179386138916,
-0.12763620913028717,
-0.7397279143333435,
-0.18748785555362701,
0.6219701766967773,
0.09006265550851822,
0.24153488874435425,
-0.5901500582695007,
-0.1746111512184143,
0.723047137260437,
-0.6953880786895752,
-0.5575013756752014,
0.5290266275405884,
0.09107762575149536,
0.04961805045604706,
0.7046965956687927,
-0.13984550535678864,
-0.750170111656189,
0.12790149450302124,
-0.31791365146636963,
-0.28829213976860046,
0.03580382093787193,
-0.5161677598953247,
-0.4898177981376648,
-0.6582629084587097,
-0.09915139526128769,
1.1196728944778442,
-0.14861179888248444,
-0.47850435972213745,
0.3466252088546753,
-0.2045893520116806,
-0.22969460487365723,
-0.2685607969760895,
0.6066495776176453,
0.7785791754722595,
0.33350667357444763,
0.6623790860176086,
0.40767455101013184,
0.02433641254901886,
0.21221376955509186,
0.22276093065738678,
-0.027269942685961723,
0.3508877456188202,
0.15720471739768982,
-0.4121975004673004,
-0.5598800778388977,
-0.07560713589191437,
-0.7194778323173523,
-0.6275044083595276,
0.4663623571395874,
-0.4076361060142517,
0.7237231135368347,
0.5257343053817749,
-0.9657109975814819,
0.0004895394085906446,
-0.5273869633674622,
-0.7792844176292419,
0.41110119223594666,
-0.1746646910905838,
-0.13904692232608795,
0.5651175379753113,
-0.7569044232368469,
-0.09590009599924088,
0.5466351509094238,
0.17114987969398499,
-0.35402002930641174,
0.17184434831142426,
0.7731893062591553,
-0.14263410866260529,
0.5565105676651001,
-0.806082546710968,
0.3317866027355194,
-0.3478737771511078,
0.3494546413421631,
-0.31690797209739685,
-0.25554803013801575,
-0.4366038143634796,
-0.15682201087474823,
0.4517006278038025,
-0.631498396396637,
0.5243221521377563,
-0.17503046989440918,
-0.013940630480647087,
-0.024150285869836807,
0.22382783889770508,
-0.24742692708969116,
-0.12369858473539352,
0.7585330605506897,
0.09708067774772644,
-0.7223637700080872,
0.1296137273311615,
0.9077597856521606,
-0.16213829815387726,
0.06931307911872864,
-0.6044191122055054,
-0.21222174167633057,
-0.22228536009788513,
-0.3122462332248688,
0.11971011012792587,
-1.1423410177230835,
-0.9596573114395142,
0.035882432013750076,
-0.4711458683013916,
0.008402780629694462,
0.4885864555835724,
-0.16013993322849274,
0.17993906140327454,
-0.4516764283180237,
-0.976548969745636,
-0.23376409709453583,
-0.1787189245223999,
-0.7529234290122986,
-0.4249490797519684,
-0.46939679980278015,
-0.7202821373939514,
0.8011746406555176,
-0.10125400125980377,
0.3702639043331146,
0.6506009101867676,
-0.023076049983501434,
0.3348727524280548,
0.4362809360027313,
-0.15584219992160797,
0.5387475490570068,
0.32129108905792236,
0.41978180408477783,
-0.25132298469543457,
0.537843644618988,
-0.728296160697937,
0.8306995034217834,
-1.394120693206787,
1.3136780261993408,
-0.4818480312824249,
0.14900535345077515,
-0.36496928334236145,
0.205311581492424,
0.2830604910850525,
-0.573053240776062,
0.21401962637901306,
0.011323072947561741,
-0.09640277922153473,
0.7534593939781189,
0.33582502603530884,
-0.6679447293281555,
-0.7835185527801514,
-0.30486083030700684,
-1.1161149740219116,
0.5098816752433777,
-0.06295937299728394,
0.132050022482872,
-0.7316858768463135,
-1.0116055011749268,
0.20381149649620056,
0.1671164482831955,
0.28059664368629456,
0.6851003766059875,
-0.13918562233448029,
0.20932866632938385,
0.08695904910564423,
0.42184433341026306,
-0.4033493995666504,
-0.22562353312969208,
0.18061815202236176,
-0.0023592307697981596,
0.1373094916343689,
-0.43547144532203674,
-0.4206599295139313,
-1.0558801889419556,
-0.21434737741947174,
0.02081834152340889,
0.39030542969703674,
-0.3165782690048218,
0.3255022168159485,
-0.33713552355766296,
-0.8442499041557312,
-0.36731287837028503,
-0.20729349553585052,
-0.24645276367664337,
0.15936841070652008,
0.2567616403102875,
0.06362051516771317,
0.5142459273338318,
0.30665990710258484,
0.5538754463195801,
-0.22587816417217255,
-0.18531975150108337,
0.4672355651855469,
-0.21156997978687286,
-0.678242564201355,
0.1709434688091278,
0.5109217166900635,
-0.3033957779407501,
-0.27911585569381714,
-1.0751289129257202,
-0.3575794994831085,
-0.05315294489264488,
-0.7195165753364563,
0.23237740993499756,
-0.22932709753513336,
-0.3370113968849182,
0.8048434257507324,
0.24890656769275665,
-0.36567550897598267,
-0.06997539848089218,
-0.18066300451755524,
-0.41659948229789734,
-0.9939852356910706,
-0.007942414842545986,
1.312697410583496,
-0.4454261362552643,
-0.8222838640213013,
-0.11940894275903702,
0.08303208649158478,
-0.3782021403312683,
0.2502608895301819,
-0.23288342356681824,
-0.322709321975708,
0.3795068562030792,
0.5933586359024048,
0.5042510628700256,
0.1599271148443222,
0.23495246469974518,
0.5722211599349976,
-0.16109155118465424,
0.023775409907102585,
-0.8143117427825928,
-0.6627212166786194,
-0.3512142300605774,
0.11205191165208817,
1.2242070436477661,
-0.13053183257579803,
0.5920442938804626,
-0.4557375907897949,
-0.7927058339118958,
-0.16416959464550018,
-0.9584070444107056,
0.14634999632835388,
-0.8329118490219116,
-0.4081478416919708,
-0.8360336422920227,
-0.6256207823753357,
0.30837103724479675,
-0.39621710777282715,
-0.04210366681218147,
-0.08705493062734604,
-1.2792179584503174,
-0.08493904769420624,
0.22379115223884583,
0.01042997743934393,
0.07494666427373886,
-0.4527204632759094,
-0.2289864867925644,
0.016873955726623535,
-0.5721657276153564,
-0.35669031739234924,
-0.015191758051514626,
0.3304018974304199,
-0.008935986086726189,
0.413128137588501,
-0.09454437345266342,
0.6573319435119629,
-0.8042805194854736,
-0.8649744987487793,
-0.01818213425576687,
-0.4233042299747467,
-0.09896542876958847,
0.23535001277923584,
0.09455156326293945,
0.4619687795639038,
-0.044002607464790344,
0.0223905760794878,
-0.39879414439201355,
-0.09434398263692856,
-0.6365779042243958,
-0.15664628148078918,
-0.2934769093990326,
0.24897512793540955,
-0.12949199974536896,
-0.4988899827003479,
0.04815354570746422,
0.30906692147254944,
-0.885703980922699,
0.7290861010551453,
-0.921684980392456,
0.15835829079151154,
-0.10218940675258636,
0.11829458922147751,
0.8582387566566467,
0.5692220330238342,
-0.5884751081466675,
0.7054510712623596,
-0.21499201655387878,
0.17418161034584045,
-0.2656821608543396,
0.30486229062080383,
-0.17575693130493164,
0.6710997819900513,
0.385855108499527,
-0.61994469165802,
0.33319854736328125,
0.31646957993507385,
0.13307134807109833,
0.2983907461166382,
-0.47764861583709717,
-0.5230088233947754,
-0.010628728196024895,
0.2395794838666916,
-0.602979838848114,
0.606723427772522,
-0.23267269134521484,
-0.5600591897964478,
-0.6595953702926636,
-0.3489619493484497,
-0.6246709823608398,
0.3073074519634247,
-1.0173280239105225,
-0.038100000470876694,
-0.3869996964931488,
0.07901962846517563,
-0.07081758230924606,
0.27642884850502014,
-0.1363031417131424,
0.19612666964530945,
0.10424382984638214,
0.3420027196407318,
-0.11146291345357895,
0.08503852784633636,
-0.07272792607545853,
0.2504994869232178,
-0.504305899143219,
-0.4207015931606293,
-0.26642629504203796,
1.1640188694000244,
-1.0090510845184326,
-0.37918391823768616,
-0.5465295910835266,
0.4499867260456085,
-0.07563477009534836,
0.2705090641975403,
-0.12341776490211487,
-0.23987744748592377,
0.3974777162075043,
-0.14063343405723572,
-0.2599504590034485,
-0.11511030793190002,
-0.3168710172176361,
0.825031042098999,
0.20951825380325317,
-0.8121518492698669,
0.14000004529953003,
-0.08045369386672974,
-0.3399447500705719,
-0.0013151495950296521,
0.05911608040332794,
0.3865613639354706,
0.2355714738368988,
-0.8794711232185364,
0.6873665452003479,
0.06813610345125198,
0.6635315418243408,
0.4755149781703949,
-0.3608447313308716,
0.16112874448299408,
0.1679844856262207,
0.08930192142724991,
0.5868589282035828,
0.06912586092948914,
0.009167495183646679,
0.6668695211410522,
0.0661315768957138,
0.5042282938957214,
0.03783109039068222,
0.49498268961906433,
0.4531628489494324,
0.22582921385765076,
-0.11511238664388657,
0.13891077041625977,
0.3205515742301941,
0.34752729535102844,
-0.275459349155426,
-0.07380181550979614,
-0.33145561814308167,
0.025638306513428688,
0.5994042754173279,
0.7796478867530823,
-0.8035412430763245,
-0.47942933440208435,
-0.05768375098705292,
0.25203338265419006,
0.6723568439483643,
0.23954996466636658,
-0.06875227391719818,
0.866694986820221,
0.7208318114280701,
0.12434107065200806,
-0.1422150433063507,
0.5815936923027039,
0.3071897625923157,
0.797122061252594,
0.450593501329422,
0.37503793835639954,
0.5655710697174072,
0.6067923307418823,
0.0805380567908287,
-0.8521714210510254,
0.316070020198822,
0.9867686629295349,
-1.7588955163955688,
0.6886506676673889,
-0.03349871188402176,
-0.007713753264397383,
-0.4735789895057678,
-0.8531175255775452,
0.6990833878517151,
-0.693444013595581,
0.2302185744047165,
0.5840498208999634,
-0.3144112229347229,
0.48833656311035156,
0.84713214635849,
-0.08357256650924683,
0.4333433210849762,
0.7487542629241943,
-0.066531240940094,
0.018853774294257164,
0.8544874787330627,
1.6485117673873901,
-0.41658052802085876,
-0.07036660611629486,
-0.28632161021232605,
-0.8818429708480835,
0.5549987554550171,
-0.11796379089355469,
-0.031839706003665924,
0.6647591590881348,
-0.6602951288223267,
-0.5951682329177856,
0.5275539755821228,
0.08866511285305023,
0.20477817952632904,
-0.27985596656799316,
0.12305032461881638,
-0.08327111601829529,
-0.028302699327468872,
-0.9425504207611084,
1.7569409608840942,
0.7161306738853455,
0.0562097430229187,
-0.2511811852455139,
0.3658183813095093,
-0.1374744027853012,
-0.1147489920258522,
-0.2509985864162445,
0.39259955286979675,
-0.1508660465478897,
-0.033358097076416016,
-0.28425341844558716,
-0.5932347774505615,
-0.538796067237854,
-0.9947242140769958,
0.039695754647254944,
-0.5905817747116089,
0.8464672565460205,
0.12239398062229156,
0.16621457040309906,
0.6006910800933838,
-0.88885897397995,
0.15545062720775604,
0.15138012170791626,
1.097875952720642,
-0.1888466328382492,
0.09228704124689102,
0.6138070821762085,
0.5040643215179443,
-0.9674072861671448,
0.6385005712509155,
0.6159494519233704,
-0.5636010766029358,
0.6384920477867126,
-0.8052905797958374,
-0.03952544555068016,
0.9869225025177002,
-0.4448375105857849,
0.837157666683197,
-0.2713790535926819,
0.6356006264686584,
-0.007772078737616539,
-0.48997414112091064,
-1.0260803699493408,
-1.200769066810608,
0.18564991652965546,
-0.9203177094459534,
0.5835097432136536,
-0.35460570454597473,
0.5125100612640381,
0.8117159605026245,
-0.3227546513080597,
4.013136386871338,
1.249748706817627,
0.24933886528015137,
0.23969575762748718,
0.6375207901000977,
0.3498031497001648,
-0.3714902400970459,
-0.44256076216697693,
0.35941824316978455,
-1.126208782196045,
-0.6340001821517944,
0.7964605093002319,
0.37152814865112305,
-0.03242027387022972,
0.27813324332237244,
0.8398805856704712,
-0.3070782423019409,
0.15424911677837372,
-0.18312467634677887,
-1.1305440664291382,
-0.4877606928348541,
0.35403308272361755,
0.7629813551902771,
-0.04790695011615753,
0.4458076059818268,
-0.4673127830028534,
-0.1253531575202942,
-0.6384758949279785,
-0.7852370142936707,
-0.44654107093811035,
-0.7080647945404053,
-0.9639058113098145,
0.08955568075180054,
-0.08441367745399475,
-0.7997931241989136,
0.6519646048545837,
-0.05770063400268555,
-0.6959782242774963,
0.38033509254455566,
0.20743276178836823,
-0.05211186036467552,
0.049106840044260025,
-0.4289010763168335,
-0.5291977524757385,
-0.8261839151382446,
1.3525117635726929,
0.1391635537147522,
0.44659289717674255,
0.08733291178941727,
-0.3756999969482422,
0.5710002183914185,
-0.3797878921031952,
0.3825177550315857,
0.012005242519080639,
-1.317551851272583,
0.17287558317184448,
-0.3853563368320465,
-0.20960430800914764,
-0.10533304512500763,
0.34340929985046387,
0.814832866191864,
0.22865471243858337,
-0.11561755836009979,
0.19900764524936676,
-0.18051788210868835,
1.2224323749542236,
-0.08121039718389511,
-0.05448751151561737,
-0.5311660170555115,
-0.17687679827213287,
-0.2583561837673187,
-0.31825733184814453,
-0.3012756109237671,
0.4687732458114624,
0.25915372371673584,
0.12491921335458755,
0.08507392555475235,
0.4644640386104584,
-0.075757697224617,
0.1584765762090683,
0.10054490715265274,
-0.44738417863845825,
-0.9049447178840637,
0.156369149684906,
0.19371217489242554,
0.6415996551513672,
-0.3681899905204773,
0.2644609212875366,
-0.0488702654838562,
0.6702449321746826,
0.9477289319038391,
1.4212464094161987,
0.19219520688056946,
0.10677970945835114,
-0.49265995621681213
] |
Lee-Yang Zeroes and Logarithmic Corrections in the $\Phi^4_4$ Theory
|
The leading mean-field critical behaviour of $\phi^4_4$-theory is modified by multiplicative logarithmic corrections. We analyse these corrections both analytically and numerically. In particular we present a finite-size scaling theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit logarithmic corrections. On lattices from size $8^4$ to $24^4$, Monte-Carlo cluster methods and multi-histogram techniques are used to determine the partition function zeroes closest to the critical point. Finite-size scaling behaviour is verified and the logarithmic corrections are found to be in good agreement with our analytical predictions.
|
R. Kenna and C.B. Lang
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210017
|
hep-lat/9210018
|
[
0.5505620241165161,
-0.5450917482376099,
-0.05845670774579048,
0.0968107134103775,
-0.5867769718170166,
-0.4662373661994934,
-0.18714958429336548,
-0.13820911943912506,
-1.0294852256774902,
1.2706292867660522,
-0.014337658882141113,
-0.13484881818294525,
0.18346378207206726,
-0.3830462396144867,
-0.0541592575609684,
0.6857320666313171,
-0.10903698951005936,
-0.8482342958450317,
-0.945738673210144,
0.5309714078903198,
0.4360661804676056,
-0.07887265086174011,
-1.372201681137085,
-0.5113295316696167,
-0.3861943185329437,
0.6693775057792664,
0.09519568085670471,
-0.14864905178546906,
0.8529056906700134,
0.2718350887298584,
0.6064736247062683,
-0.5261982679367065,
-0.5936927795410156,
-0.31975141167640686,
-0.3537502586841583,
0.2284001260995865,
0.008097954094409943,
-0.06441495567560196,
0.8151506185531616,
0.45557907223701477,
0.6397793889045715,
-0.6175667643547058,
-0.6234688758850098,
-0.2360394448041916,
-0.17680583894252777,
-0.11262303590774536,
-0.7039887309074402,
-0.14435388147830963,
0.2487650066614151,
-0.5818838477134705,
0.17605815827846527,
0.1806948035955429,
0.8956131339073181,
-0.7485062479972839,
-0.6276193857192993,
-0.27350324392318726,
0.5612903237342834,
0.18526631593704224,
-0.4776337146759033,
-0.5649030804634094,
0.14093582332134247,
-0.17330482602119446,
0.3009187877178192,
-0.7402875423431396,
0.3296758830547333,
0.15011823177337646,
-0.5114954710006714,
0.3464565873146057,
-0.012217307463288307,
-0.7764405608177185,
-0.021345775574445724,
-0.6314360499382019,
-1.0730644464492798,
0.32178249955177307,
-0.795207679271698,
0.4645666480064392,
0.01269166823476553,
-0.5619463324546814,
-1.1513166427612305,
-0.19524994492530823,
-0.5754268765449524,
-0.19204270839691162,
0.03371868282556534,
0.15429750084877014,
-0.3548405170440674,
-0.7236307263374329,
-0.01632801815867424,
-0.3233782649040222,
0.25361576676368713,
0.701416015625,
0.45797401666641235,
0.8855140209197998,
-0.6318526864051819,
-0.15412667393684387,
0.30089545249938965,
0.3527851402759552,
-0.017993777990341187,
0.6231256127357483,
-0.07616990059614182,
-0.04201413318514824,
0.17514875531196594,
0.3208620548248291,
-0.9543888568878174,
0.6013503074645996,
-0.21065904200077057,
0.5313065052032471,
-0.21202054619789124,
-0.14388275146484375,
0.3030654788017273,
-0.4792335033416748,
0.3759427070617676,
-0.49119189381599426,
0.052837830036878586,
0.8111703395843506,
0.038835231214761734,
0.2810027301311493,
0.027881892397999763,
0.46219882369041443,
-0.4120216369628906,
-0.7181295156478882,
0.9006946682929993,
-0.018055656924843788,
0.3387858271598816,
0.18703366816043854,
0.5012455582618713,
-0.33486950397491455,
0.031279269605875015,
0.5047961473464966,
-0.6275061368942261,
0.4129713773727417,
-0.05259096249938011,
-0.2660718560218811,
-0.671360433101654,
0.4507717788219452,
-0.7388789057731628,
-0.3278736174106598,
-0.5040674209594727,
-0.10985908657312393,
-0.1543295681476593,
-0.009410531260073185,
0.9321945905685425,
-0.5200972557067871,
-0.18015974760055542,
0.9586368799209595,
0.09805518388748169,
-0.12180981040000916,
-0.09093307703733444,
0.3591516315937042,
-0.28311672806739807,
0.6147745847702026,
-0.9374257922172546,
-0.21611535549163818,
-0.35931396484375,
0.5679933428764343,
0.13891930878162384,
0.7471749186515808,
-0.4854884743690491,
-0.00883631780743599,
-0.5444896221160889,
-0.4211789667606354,
-0.0038275427650660276,
-0.47189098596572876,
-0.5664960741996765,
0.2721703350543976,
-0.9595726728439331,
0.11972679197788239,
-0.6894752979278564,
-0.5019121170043945,
0.3467365503311157,
-0.8263075351715088,
-0.16770116984844208,
0.26287996768951416,
-0.3022923767566681,
0.3233327269554138,
0.06554344296455383,
0.5928604602813721,
0.3140204846858978,
-0.5640982389450073,
-0.024548064917325974,
0.6437966823577881,
-0.3213087022304535,
-0.0838015004992485,
0.5491092801094055,
-0.43839001655578613,
-0.2789328992366791,
-0.2707841992378235,
-0.1394890397787094,
-0.4329424500465393,
-0.13356055319309235,
0.4091363251209259,
0.27968326210975647,
0.07339605689048767,
-0.19406820833683014,
0.8128620982170105,
-0.7034195065498352,
-0.3514668047428131,
-0.5907659530639648,
-0.03900425136089325,
-0.29386597871780396,
-0.8363971710205078,
0.1502920687198639,
-0.3462849259376526,
-0.7457894086837769,
0.4052116572856903,
-1.5151894092559814,
0.14785879850387573,
1.0814188718795776,
0.092953622341156,
-0.5659146904945374,
0.2807953357696533,
-0.16027145087718964,
-0.19683773815631866,
0.3374682366847992,
-0.4587618112564087,
0.08541077375411987,
0.3200407922267914,
0.8125461339950562,
0.5484254360198975,
0.8374687433242798,
0.746021032333374,
0.5807831287384033,
0.16498583555221558,
0.15136870741844177,
0.8018509745597839,
-1.0090829133987427,
-0.8192909359931946,
-0.08106561750173569,
0.6160462498664856,
0.24363012611865997,
-0.05643647909164429,
-0.1439482420682907,
0.2690486013889313,
-0.38660261034965515,
0.5373876690864563,
0.32148826122283936,
0.43104496598243713,
0.4014071226119995,
-0.05371752381324768,
0.7888907790184021,
1.0025461912155151,
-0.14397455751895905,
-0.06788910180330276,
0.33370518684387207,
-0.21063216030597687,
-0.041220635175704956,
0.31457358598709106,
-0.5995839834213257,
0.27811190485954285,
-0.24929669499397278,
0.29227593541145325,
-0.17366057634353638,
0.7586430907249451,
-0.028351513668894768,
0.4330879747867584,
-0.7515912652015686,
-0.2524416744709015,
0.11331842839717865,
0.37641817331314087,
-0.2692262530326843,
0.03986920043826103,
0.35836061835289,
0.2539551258087158,
-0.30445876717567444,
-0.82369065284729,
-0.41001731157302856,
1.1949764490127563,
0.0396529957652092,
0.3868715465068817,
0.5464746952056885,
-0.05009831115603447,
-0.5129077434539795,
-0.05412696674466133,
-1.0524541139602661,
0.4531666338443756,
-0.6645570993423462,
-0.39322906732559204,
0.7938506603240967,
-0.8245729207992554,
0.544076681137085,
-0.02712235040962696,
-0.15861113369464874,
0.5691352486610413,
-0.26784810423851013,
0.4266175627708435,
0.3623485863208771,
0.4266149401664734,
-0.2885025441646576,
0.331260621547699,
-0.26674720644950867,
-0.39731255173683167,
-0.2855328917503357,
0.062155500054359436,
0.6972706913948059,
-0.5531320571899414,
0.3440279960632324,
-0.30801427364349365,
-0.30147212743759155,
-0.01389335934072733,
-0.10316519439220428,
-0.9145668148994446,
0.19492319226264954,
0.45962196588516235,
-0.21942688524723053,
-0.45910727977752686,
-1.2850275039672852,
-0.06424999982118607,
0.541691780090332,
-0.32808440923690796,
0.09135153144598007,
-0.05472014844417572,
-0.28010258078575134,
0.6333540081977844,
-0.057639360427856445,
-0.028565233573317528,
-0.1633635014295578,
0.8150783181190491,
0.817915678024292,
0.07904792577028275,
-0.3708971440792084,
-0.5310983657836914,
-0.5288258790969849,
0.14322520792484283,
0.042153649032115936,
-0.4270295798778534,
-0.1632004827260971,
0.5315091013908386,
0.41692277789115906,
-0.5349926352500916,
0.2989087700843811,
-0.6189436316490173,
-0.2831154465675354,
-0.07269332557916641,
-0.5705476403236389,
0.5014873147010803,
-0.33978310227394104,
-0.1644817739725113,
-0.8458313941955566,
0.0574989914894104,
0.9746904373168945,
-0.036889344453811646,
0.30844250321388245,
-0.12308824062347412,
0.17555831372737885,
0.03452857956290245,
0.526264488697052,
-0.0651865005493164,
-0.3772607445716858,
0.06969720870256424,
-0.5224902629852295,
0.48200520873069763,
-0.7702339887619019,
0.07011386752128601,
-0.41274797916412354,
0.7097377777099609,
0.3418324887752533,
0.2680005729198456,
-0.34407562017440796,
-0.07137830555438995,
-0.7322813272476196,
-1.0140819549560547,
0.3843424618244171,
0.6431818008422852,
-0.2098357230424881,
-1.0932585000991821,
-0.5161047577857971,
-0.36912211775779724,
0.06004532426595688,
-0.16116853058338165,
0.12923307716846466,
-0.709196150302887,
0.20506609976291656,
0.255178302526474,
-0.3468320667743683,
0.022029219195246696,
-0.19920383393764496,
0.5789498090744019,
0.16143475472927094,
0.6102591156959534,
1.0561120510101318,
-0.27339228987693787,
-0.08767631649971008,
0.4010067880153656,
1.0633535385131836,
0.7784114480018616,
0.9517374634742737,
0.24551215767860413,
0.13388800621032715,
-0.09813300520181656,
-0.1591176986694336,
-1.148456335067749,
-0.12930454313755035,
0.039230089634656906,
0.4711110293865204,
-0.07286013662815094,
0.38773056864738464,
-0.20253539085388184,
0.10882990062236786,
-0.19630101323127747,
0.13416612148284912,
0.18145917356014252,
0.12319209426641464,
0.4734746515750885,
0.5700444579124451,
0.5152475237846375,
0.2815555930137634,
0.33546170592308044,
-0.8029568791389465,
0.27308380603790283,
0.2435326725244522,
0.7855851650238037,
-0.36055082082748413,
0.12055430561304092,
0.29449135065078735,
-0.652578592300415,
-0.007165025919675827,
0.4390692114830017,
-1.02890944480896,
0.28204506635665894,
0.3465516269207001,
1.0197863578796387,
0.5853598117828369,
0.18532374501228333,
0.8618418574333191,
0.38045555353164673,
0.5429099798202515,
-0.8426600098609924,
0.3608802556991577,
-0.29282599687576294,
0.7181888222694397,
-0.15703259408473969,
-1.2072324752807617,
-0.09699776768684387,
-1.033790946006775,
-0.3140731453895569,
-0.25835496187210083,
0.5028214454650879,
0.8723561763763428,
-0.15398702025413513,
0.38462188839912415,
-0.4541918933391571,
-0.13236932456493378,
0.40531137585639954,
-0.5120028853416443,
-0.7222583293914795,
0.6001777648925781,
0.11196811497211456,
-0.2673141658306122,
0.3603198230266571,
-0.0034161664079874754,
-0.7012319564819336,
0.2923465073108673,
-0.7118720412254333,
-0.16789618134498596,
-0.4911683201789856,
-0.497568815946579,
-0.2697749435901642,
-0.11439695209264755,
-0.4139421582221985,
0.06715338677167892,
0.45021846890449524,
-0.281176894903183,
-0.18016000092029572,
-0.5989204049110413,
-0.2233390063047409,
0.0786333680152893,
-0.008532707579433918,
0.052912626415491104,
1.0192323923110962,
0.5249470472335815,
0.6000582575798035,
0.8409709334373474,
0.15876780450344086,
0.31582194566726685,
-0.4988044500350952,
-0.07234818488359451,
0.1901797503232956,
-0.20247796177864075,
-0.32565727829933167,
-0.008713611401617527,
-0.25239044427871704,
-0.9175124168395996,
0.07584870606660843,
-0.42282235622406006,
0.6137166619300842,
0.1262560486793518,
-0.7631857395172119,
-0.43929362297058105,
-0.404308557510376,
-1.1425318717956543,
0.4253857731819153,
0.5637533068656921,
-0.19481980800628662,
0.6742089986801147,
-0.30878928303718567,
-0.01817721500992775,
-0.3904058635234833,
-0.5831596255302429,
-0.5535538196563721,
0.4767455458641052,
0.22810675203800201,
0.4889172613620758,
-0.07320648431777954,
-1.0638395547866821,
0.13855639100074768,
-0.40416383743286133,
-0.07028154283761978,
-0.39128467440605164,
-0.18190784752368927,
-0.03352325037121773,
-0.4483550488948822,
0.029651233926415443,
0.13013309240341187,
-0.0074272193014621735,
0.17730578780174255,
-0.575590193271637,
-0.611565887928009,
0.0775931254029274,
-0.19434478878974915,
0.12934130430221558,
0.9493219256401062,
0.7562209367752075,
-0.5580288171768188,
-0.7736459970474243,
0.31488093733787537,
-0.07376453280448914,
0.24048413336277008,
0.1308126151561737,
-0.6160343289375305,
0.3089539408683777,
0.32292526960372925,
0.5276145339012146,
-0.6451420783996582,
-0.837958574295044,
0.25030872225761414,
-0.3922404646873474,
0.3035341501235962,
0.007969478145241737,
0.21414227783679962,
-0.20529577136039734,
-0.5675990581512451,
0.29836174845695496,
0.6802269816398621,
-0.07524522393941879,
-0.3100548982620239,
-0.6236853003501892,
-0.196456179022789,
0.02195993810892105,
0.6826556921005249,
-0.09314126521348953,
0.2618787884712219,
0.11347456276416779,
-0.5416548848152161,
0.12206637859344482,
0.5860903859138489,
0.20305897295475006,
-0.28368818759918213,
0.18362575769424438,
0.44450271129608154,
-0.2841062843799591,
0.5888070464134216,
-0.4156438708305359,
0.6716866493225098,
-0.764565110206604,
1.334394097328186,
-0.7283926010131836,
0.12233460694551468,
-0.47904250025749207,
0.01235111802816391,
0.12198513746261597,
-0.9531642198562622,
0.47536730766296387,
0.5158117413520813,
-0.2362370789051056,
0.1267591118812561,
0.2973322570323944,
-0.3808174133300781,
-0.10549712181091309,
-1.052310824394226,
-0.7678284645080566,
0.5960271954536438,
-0.0994376540184021,
-0.05438812077045441,
-0.10609183460474014,
-0.7286015152931213,
0.11349360644817352,
-0.11946980655193329,
0.2988860607147217,
0.4062785506248474,
0.30462563037872314,
0.33827483654022217,
-0.23268865048885345,
-0.3573787212371826,
-0.6627670526504517,
0.22803999483585358,
0.23126743733882904,
-0.00047755023115314543,
0.20630820095539093,
0.37064477801322937,
-0.13162823021411896,
-0.5428109765052795,
-0.04755310341715813,
0.4976532459259033,
-0.02786588855087757,
-0.2925589382648468,
0.9235378503799438,
-0.26465800404548645,
-0.8659383058547974,
-0.3339160978794098,
0.006577736232429743,
0.4898182153701782,
0.393898069858551,
0.19411161541938782,
0.10665351152420044,
0.5548449754714966,
0.1965438425540924,
0.22815124690532684,
0.004045465029776096,
-0.6245343089103699,
0.3507797420024872,
-0.44922399520874023,
-0.623701810836792,
0.16103927791118622,
-0.1596444696187973,
-0.5884086489677429,
-0.24353405833244324,
-0.3501847982406616,
0.06917862594127655,
-0.4567241668701172,
0.08514374494552612,
-0.8722556829452515,
-0.0340636670589447,
-0.40491825342178345,
0.30987098813056946,
0.331046998500824,
0.03030378557741642,
-0.402455598115921,
0.06295516341924667,
-0.31327110528945923,
-0.28467029333114624,
-0.4200045168399811,
1.456209421157837,
0.08506476879119873,
-0.35690179467201233,
0.09748409688472748,
-0.13805951178073883,
-0.30438944697380066,
0.13185825943946838,
0.7661082744598389,
-0.18369077146053314,
0.49082309007644653,
-0.08713512867689133,
0.0454326868057251,
0.7259151935577393,
1.012566089630127,
0.11264243721961975,
-0.2450527548789978,
-0.0632915124297142,
-0.4828912913799286,
-0.455653578042984,
-0.6735427379608154,
0.46002301573753357,
0.519375205039978,
-0.08524743467569351,
0.13253067433834076,
-0.07217858731746674,
-0.46689438819885254,
-0.21057534217834473,
-0.608184814453125,
0.0682634562253952,
-0.7877081632614136,
-0.29705819487571716,
-0.2487969994544983,
-0.6078380942344666,
0.30939510464668274,
0.9435023069381714,
-0.020644471049308777,
-0.3271792232990265,
-0.3101969063282013,
-0.14241543412208557,
0.34756433963775635,
0.4501837193965912,
-0.27844417095184326,
-0.8399877548217773,
0.14579497277736664,
-0.7355431914329529,
-0.4197414815425873,
-0.6483787298202515,
-0.224796324968338,
-0.2630089521408081,
-0.3591524660587311,
-0.06210567429661751,
-0.015522783622145653,
0.9312031865119934,
-0.9194509387016296,
-0.713563859462738,
-0.18350696563720703,
-0.42425504326820374,
-0.5453681945800781,
0.41690632700920105,
0.1619955450296402,
0.8709596395492554,
0.255584180355072,
0.5200302600860596,
-0.3792122006416321,
0.29034674167633057,
-0.5595728754997253,
0.16613520681858063,
0.5429838299751282,
0.5674618482589722,
0.22771510481834412,
-0.8729194402694702,
-0.30183330178260803,
0.11646515876054764,
-0.9491186141967773,
0.4715458154678345,
-0.6136842370033264,
0.24301539361476898,
-0.3257827162742615,
0.47624513506889343,
0.34767308831214905,
0.7816520929336548,
0.3041791319847107,
0.9327875375747681,
-0.13440561294555664,
-0.3433433175086975,
0.37406885623931885,
0.5152917504310608,
-0.6223713159561157,
0.2402467131614685,
0.002873815596103668,
-0.461468368768692,
-0.3657701015472412,
0.4722936451435089,
-0.10871553421020508,
-0.020423652604222298,
0.03651450574398041,
-0.13884887099266052,
-0.3045479655265808,
-0.8503090739250183,
-0.662854015827179,
0.27854618430137634,
0.5500313639640808,
-0.7994797825813293,
-0.4333387315273285,
-0.5711216330528259,
-0.4544632136821747,
0.6123284101486206,
-0.7034336924552917,
0.05530327558517456,
0.5531639456748962,
-0.7833370566368103,
0.14847826957702637,
0.33271312713623047,
-0.13722443580627441,
-0.20480181276798248,
0.5358455181121826,
0.45331820845603943,
-0.00872250460088253,
0.08222122490406036,
-0.20054826140403748,
-0.24361935257911682,
-0.5170555710792542,
0.0013652315828949213,
-0.6741227507591248,
0.27649086713790894,
-1.0849249362945557,
-0.7955325245857239,
-0.4087638258934021,
0.5459760427474976,
0.5267868041992188,
-0.2838480770587921,
-0.2879696190357208,
-0.622047483921051,
0.3890644609928131,
-0.35600781440734863,
-0.4933427572250366,
-0.38221168518066406,
-0.7527559995651245,
0.5263004302978516,
-0.5082997679710388,
-0.4582422375679016,
0.12843109667301178,
-0.1353992074728012,
-0.07640313357114792,
0.05008293315768242,
-0.007142051123082638,
0.9271151423454285,
0.5825937986373901,
-0.5900964140892029,
0.7651519179344177,
0.2702701687812805,
-0.18170849978923798,
0.009945901110768318,
-0.38909250497817993,
0.35273277759552,
0.1763424426317215,
0.4179079830646515,
0.6214990615844727,
0.2855120599269867,
0.6486951112747192,
0.09608392417430878,
0.2615792751312256,
0.2712157666683197,
-0.10155795514583588,
0.37778761982917786,
0.5549397468566895,
0.23456533253192902,
0.1382759064435959,
0.1704866737127304,
-0.16775934398174286,
0.11751466244459152,
0.12097885459661484,
-0.24277353286743164,
-0.19071699678897858,
-0.1494874805212021,
-0.11443998664617538,
0.13764381408691406,
-0.24301643669605255,
-0.3564533293247223,
-0.3747263550758362,
-0.34554392099380493,
0.8768019676208496,
0.048894740641117096,
0.179496169090271,
0.3024511933326721,
0.5661630630493164,
-0.08863716572523117,
-0.5198625922203064,
0.8645567893981934,
-0.4141887128353119,
0.7982749342918396,
1.0813578367233276,
0.5538095235824585,
0.963559091091156,
0.8459281921386719,
0.2541063129901886,
-0.6864249110221863,
-0.08903253078460693,
0.5047520399093628,
-0.6914870738983154,
-0.0482846274971962,
-0.4283534586429596,
0.2889588475227356,
-0.3490176200866699,
-0.37929248809814453,
0.12615430355072021,
-0.6287574768066406,
0.0020152197685092688,
0.3417834937572479,
-0.793340265750885,
-0.025302216410636902,
0.7363196015357971,
0.25445154309272766,
-0.12166692316532135,
0.6372687816619873,
0.18633557856082916,
-0.09956473857164383,
1.2148040533065796,
1.0790648460388184,
0.037199195474386215,
0.2982434928417206,
0.3031982481479645,
-0.37625521421432495,
-0.08885710686445236,
0.03631970286369324,
-0.4665590822696686,
0.42718932032585144,
-0.24908557534217834,
-0.33187776803970337,
0.27521076798439026,
0.2993849813938141,
0.04904070496559143,
0.18419663608074188,
0.9341751337051392,
-0.4336484372615814,
-0.13749870657920837,
-0.7029619812965393,
1.505774974822998,
0.5725796818733215,
-0.6589295864105225,
-0.38115984201431274,
0.614652693271637,
-0.1046685054898262,
-0.2759910225868225,
-0.4858470857143402,
0.3598184585571289,
-0.48215731978416443,
-0.811931312084198,
-0.21719394624233246,
-0.3441222906112671,
-0.799380362033844,
-0.012236219830811024,
0.34660542011260986,
-0.6118797063827515,
0.6790188550949097,
0.5271412134170532,
-0.17763786017894745,
0.2974030077457428,
-0.4152505695819855,
0.29182490706443787,
0.4929583668708801,
0.8255571722984314,
0.06145996227860451,
0.3909023404121399,
0.36627840995788574,
0.6647464036941528,
-0.284146249294281,
0.42057234048843384,
0.7808863520622253,
-0.5731497406959534,
0.5205771327018738,
-0.37379249930381775,
0.626754641532898,
0.33489522337913513,
0.32426661252975464,
-0.09304961562156677,
0.037576623260974884,
-0.24016237258911133,
0.31241869926452637,
-0.13531550765037537,
0.1765487641096115,
-0.7386792302131653,
0.44984760880470276,
-0.2959885001182556,
0.5344439744949341,
-0.47315579652786255,
0.013343054801225662,
0.1603804975748062,
-1.1355496644973755,
4.3892998695373535,
0.9605839252471924,
0.5265616178512573,
0.4716719686985016,
0.6590544581413269,
0.9727654457092285,
-0.3142578899860382,
-0.8080436587333679,
-0.24822673201560974,
-0.44419533014297485,
-0.46149781346321106,
-0.17413684725761414,
-0.2255038022994995,
-0.5267179012298584,
-0.6510627865791321,
1.3572944402694702,
-0.28044393658638,
-0.9236530065536499,
0.6487076282501221,
-0.7411742806434631,
-0.16714149713516235,
0.2703925669193268,
0.4195050597190857,
-0.06316456943750381,
0.2099216729402542,
0.3975506126880646,
0.0566684864461422,
-0.5845037698745728,
0.134683296084404,
0.37864720821380615,
-0.43650904297828674,
-0.6157982349395752,
0.6769100427627563,
0.1905922144651413,
-0.4927206337451935,
0.6840031743049622,
0.3380301892757416,
-0.26106584072113037,
-0.19494833052158356,
-0.02360151894390583,
-0.24664132297039032,
-0.3579547703266144,
-0.12463390827178955,
-0.39948466420173645,
-0.22201743721961975,
0.49611902236938477,
-0.40204116702079773,
0.7066444754600525,
0.5722752809524536,
-0.8609213829040527,
0.9171115159988403,
0.22508768737316132,
0.547452449798584,
-0.4178938567638397,
-0.5008663535118103,
0.23049859702587128,
-0.3158113360404968,
0.46468380093574524,
0.5343619585037231,
0.08070053160190582,
0.12352177500724792,
-0.5881333947181702,
0.1341865062713623,
0.3436235189437866,
0.17912323772907257,
0.35686880350112915,
0.04501759260892868,
0.5985998511314392,
-0.5174529552459717,
-0.2519499361515045,
-0.12478422373533249,
-0.6816623210906982,
-0.16854828596115112,
0.8302254676818848,
0.6475262641906738,
-0.05395539477467537,
-0.06443098187446594,
0.1176995038986206,
-0.015647409483790398,
-0.4007229804992676,
0.5575906038284302,
-0.7178393602371216,
-0.27437013387680054,
-0.07250728458166122,
0.14404326677322388,
0.43786147236824036,
0.12079819291830063,
0.16973090171813965,
-0.0929294154047966,
0.2749692499637604,
0.20416946709156036,
1.0952883958816528,
0.24133697152137756,
-0.6880401372909546,
-0.02634342946112156
] |
The Kaon $B$-parameter with Wilson Fermions
|
We calculate the kaon $B$-parameter in quenched lattice QCD at $\beta=6.0$ using Wilson fermions at $\kappa=0.154$ and $0.155$. We use two kinds of non-local (``smeared'') sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for $\vec p =(0,0,0)$ and $\vec p =(0,0,1)$, we show that one can carry out the non-perturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral symmetry breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for $B$-parameters of the $\Delta I = 3/2$ part of the electromagnetic penguin operators, and preliminary results for \bk\ in the presence of two flavors of dynamical quarks.
|
Gupta, Daniel, Kilcup, Patel and Sharpe
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210018
|
hep-lat/9210019
|
[
0.0928969755768776,
-0.8791844844818115,
-0.04645540565252304,
-0.22209319472312927,
0.41679850220680237,
-1.1534430980682373,
0.2921282947063446,
-0.5074059963226318,
-1.5514322519302368,
1.5762791633605957,
1.075751781463623,
0.021066797897219658,
0.49763059616088867,
-1.0225721597671509,
-0.28977230191230774,
0.6312342286109924,
-0.2559877038002014,
-0.4879133701324463,
-1.330179214477539,
-0.10313268005847931,
-0.00589087326079607,
0.207173690199852,
-1.2574927806854248,
-0.5448347330093384,
-0.3441714644432068,
0.9804113507270813,
0.45844876766204834,
0.5477208495140076,
0.6428382396697998,
0.2827284336090088,
0.6607924103736877,
-0.45021265745162964,
-0.32607147097587585,
-0.2863633334636688,
-0.42615169286727905,
0.332179456949234,
0.19616033136844635,
-0.32487162947654724,
0.3125949501991272,
0.24924325942993164,
0.5889106392860413,
-0.19858203828334808,
0.13854847848415375,
-0.3811337649822235,
-0.27497926354408264,
-0.539267361164093,
-0.5931710004806519,
-0.013895382173359394,
0.4731782078742981,
-1.411752462387085,
-0.2177838534116745,
-0.11539068818092346,
0.9604077339172363,
-0.6061151623725891,
-0.10691272467374802,
-0.9802713394165039,
0.3228236734867096,
0.5008360147476196,
-0.04318059980869293,
-0.28020772337913513,
0.6077689528465271,
0.07040287554264069,
0.460002064704895,
-1.0701754093170166,
-0.17829212546348572,
0.3112167418003082,
-0.15214508771896362,
1.201477289199829,
0.2743920385837555,
-0.804051399230957,
-0.1728733628988266,
-1.0892611742019653,
-1.0310395956039429,
-0.0660528838634491,
-0.6685956120491028,
0.004311784636229277,
-0.3726193904876709,
-0.5549755692481995,
-1.1253055334091187,
-0.8405541777610779,
0.20863860845565796,
-0.6649578213691711,
-0.8468976020812988,
-0.2701493501663208,
-0.5358386039733887,
-0.5495994091033936,
0.07197227329015732,
-0.24344490468502045,
-0.20864024758338928,
0.29648277163505554,
0.39976581931114197,
0.8442474007606506,
0.3854755461215973,
-0.6012852787971497,
0.1854337602853775,
1.2184966802597046,
0.1873113512992859,
0.5613991618156433,
-0.2682740092277527,
0.2576347589492798,
-0.1365787386894226,
0.6325231790542603,
-0.5804337859153748,
0.5888057351112366,
-0.42297205328941345,
0.5210662484169006,
-0.09691993147134781,
-0.3580489158630371,
-0.2938794493675232,
-0.7917782664299011,
-0.16895318031311035,
-0.8053026795387268,
0.37579745054244995,
1.0217722654342651,
-0.10258997976779938,
0.8088988661766052,
0.13124756515026093,
0.3731939494609833,
-0.8966218829154968,
-0.10927334427833557,
0.5727779269218445,
0.13889241218566895,
0.8597069978713989,
0.28698238730430603,
0.007930249907076359,
-0.12113305926322937,
0.29633569717407227,
0.4187628924846649,
-0.300590842962265,
0.6085571050643921,
0.26479580998420715,
-0.1763727366924286,
-0.40245798230171204,
0.5416441559791565,
-1.375823974609375,
0.848601758480072,
-0.07236611098051071,
-0.15106691420078278,
0.47560644149780273,
0.030308062210679054,
0.667915940284729,
-0.972144603729248,
0.0033591873943805695,
0.8839792609214783,
-0.17321568727493286,
0.10934905707836151,
0.2993609309196472,
0.5155019164085388,
-0.27225399017333984,
0.3904664218425751,
-0.67593914270401,
0.6241628527641296,
0.06908555328845978,
0.6146479249000549,
-0.25579893589019775,
0.7975018620491028,
-0.09844834357500076,
0.4191238582134247,
-1.1563997268676758,
-0.7701214551925659,
0.11127118021249771,
-0.4868243932723999,
-0.7126447558403015,
0.22226963937282562,
-0.40577638149261475,
-0.08713794499635696,
-0.4239739179611206,
0.007455029990524054,
0.1737513393163681,
-0.3331545889377594,
0.0903240218758583,
0.23963741958141327,
-0.3641926646232605,
0.9173914194107056,
-0.3599798381328583,
0.3379364311695099,
0.6301860809326172,
-0.24742445349693298,
-0.11646272242069244,
0.07342148572206497,
-0.5560697913169861,
-0.3229832947254181,
0.27776217460632324,
-0.3276098966598511,
-0.05778633803129196,
-0.25417932868003845,
-0.3084471523761749,
-0.4768914580345154,
-0.04703463613986969,
0.5782874822616577,
0.18162474036216736,
0.7631505727767944,
-0.4121316075325012,
0.7018932104110718,
-0.41744619607925415,
0.27071988582611084,
-0.5431081056594849,
-0.14431238174438477,
-0.6826543807983398,
-0.7301385402679443,
-0.42522525787353516,
-0.3144436180591583,
-0.6349243521690369,
-0.036490585654973984,
-1.502563238143921,
0.34933871030807495,
0.4567442238330841,
0.08694279938936234,
0.07651054114103317,
-0.16942235827445984,
-0.6460347175598145,
-0.3622816801071167,
0.3674055337905884,
-0.7978035807609558,
0.3455455005168915,
-0.24214494228363037,
0.6109238862991333,
0.7044848799705505,
0.8872382640838623,
-0.11308025568723679,
0.6766576766967773,
0.4949757754802704,
0.008744762279093266,
0.9305080771446228,
-0.8117302656173706,
-0.6596792340278625,
0.4152428209781647,
0.7236953973770142,
0.5644335150718689,
-0.29170262813568115,
-0.3152244985103607,
0.3446286916732788,
-0.3832736611366272,
0.6629966497421265,
0.008005128242075443,
0.5775325894355774,
0.5904216766357422,
0.36508190631866455,
-0.25342628359794617,
0.4630032181739807,
0.06381012499332428,
0.2707095146179199,
0.7642927765846252,
0.19117075204849243,
-0.014620637521147728,
-0.1710323989391327,
-1.1173633337020874,
0.6575985550880432,
-0.3358014225959778,
0.3355444669723511,
-0.4002406597137451,
0.8313654661178589,
0.08923277258872986,
0.36533549427986145,
-0.7330261468887329,
-0.33170443773269653,
0.36325952410697937,
0.3304824233055115,
-0.6269423961639404,
-0.6402649283409119,
-0.49379536509513855,
0.07471708953380585,
-0.017764635384082794,
-0.7047077417373657,
-0.5294446349143982,
0.7178031802177429,
0.5120536088943481,
-0.04170570150017738,
0.04006773605942726,
0.053830597549676895,
-0.9990810751914978,
0.14402611553668976,
-0.8307456374168396,
0.5253084897994995,
-0.9440823793411255,
-0.3417065441608429,
0.4623418152332306,
-0.8560227751731873,
0.43830305337905884,
-0.3772972822189331,
-0.4976308047771454,
0.8864068984985352,
0.28374481201171875,
0.9700011014938354,
0.6847114562988281,
-0.0024547746870666742,
0.01534904632717371,
-0.13929390907287598,
-0.6143364906311035,
-0.04620153456926346,
-0.048542656004428864,
0.10665307193994522,
0.9721460342407227,
-0.28454676270484924,
0.3398030400276184,
-0.3866199553012848,
-0.5380554795265198,
0.24389290809631348,
0.10531378537416458,
-0.43644535541534424,
-0.49444580078125,
0.7438993453979492,
-0.3646799623966217,
-0.12784205377101898,
-1.3838956356048584,
0.5200153589248657,
0.4739237129688263,
-0.929571807384491,
0.40644654631614685,
-0.02685783989727497,
-0.5890716910362244,
0.8448725938796997,
-0.2510453462600708,
-0.3486889600753784,
0.01713300123810768,
1.2019002437591553,
0.8765265345573425,
0.019320420920848846,
-0.2796153426170349,
-0.3679511249065399,
-0.5641040205955505,
0.4941766858100891,
-0.0226391963660717,
-0.17115196585655212,
0.18656350672245026,
0.37044546008110046,
-0.08981301635503769,
-0.7278910279273987,
0.2271745651960373,
-0.8468331098556519,
-0.25576111674308777,
-0.3763728439807892,
-0.8762912154197693,
0.6154997944831848,
0.00806648563593626,
0.11652538180351257,
-0.8103213906288147,
-0.3738137483596802,
0.7421149015426636,
1.0850121974945068,
0.6892270445823669,
-0.239243283867836,
0.7270117402076721,
0.2944234609603882,
1.0362319946289062,
-0.5198944211006165,
0.003215136006474495,
-0.015463118441402912,
-0.4140501320362091,
0.24202023446559906,
-0.3003285229206085,
0.25849518179893494,
-0.13661012053489685,
0.11329606175422668,
-0.49347808957099915,
0.39108705520629883,
-0.48065224289894104,
-0.11732637137174606,
-0.6181213855743408,
-0.5106968283653259,
1.1281088590621948,
0.8185750842094421,
-0.43200334906578064,
-0.21348461508750916,
-0.785834014415741,
-0.31090378761291504,
0.22450648248195648,
-0.11562476307153702,
1.2003636360168457,
-1.3849695920944214,
0.434383362531662,
-0.0013448781101033092,
-0.5101065635681152,
0.3608924448490143,
-0.4555234909057617,
0.04816325753927231,
0.3143936097621918,
0.3729099929332733,
1.1009808778762817,
-0.24059264361858368,
-0.6675364375114441,
-0.18134993314743042,
1.1834373474121094,
0.7135185599327087,
0.9665415287017822,
0.812166154384613,
-0.7259613275527954,
0.10381153225898743,
-0.30467936396598816,
-0.5520379543304443,
-0.24784062802791595,
-0.3828217387199402,
-0.32121384143829346,
-0.3827635645866394,
0.251790314912796,
-0.05879650264978409,
0.9869818091392517,
-0.13120509684085846,
0.18070901930332184,
0.21298356354236603,
0.5082135200500488,
0.47525450587272644,
0.7824825048446655,
0.8756722211837769,
0.07242470234632492,
0.41652193665504456,
-0.6971237659454346,
0.19610978662967682,
0.25604918599128723,
0.8979058265686035,
-0.3514815866947174,
-0.4930879473686218,
-0.3489069938659668,
-0.8460533618927002,
0.592930257320404,
0.08233064413070679,
-0.5848736763000488,
0.7307950854301453,
0.19310913980007172,
0.6526747345924377,
0.3004482090473175,
0.6507197618484497,
0.7286719083786011,
0.6799871921539307,
-0.08235606551170349,
-1.0760425329208374,
-0.24117502570152283,
-0.011344832368195057,
0.6254509687423706,
0.4542009234428406,
-0.6915298700332642,
-0.7202663421630859,
-1.039815068244934,
0.16703803837299347,
-0.43113094568252563,
0.10277397930622101,
0.7652534246444702,
0.24613294005393982,
0.6043855547904968,
-0.788538932800293,
-0.34747689962387085,
0.17910906672477722,
-0.753191351890564,
-0.7830810546875,
-0.47934690117836,
-0.23809656500816345,
-0.6314753293991089,
0.5530502200126648,
-0.21664942800998688,
-0.7736781239509583,
0.04601040482521057,
0.0317397378385067,
-0.3447454571723938,
-0.12032998353242874,
-0.415989488363266,
-0.09119553118944168,
-0.25641220808029175,
-0.44922587275505066,
0.59780353307724,
0.27379411458969116,
0.09530387818813324,
-0.4741967022418976,
0.07190680503845215,
0.028628140687942505,
0.1651017963886261,
0.0977901816368103,
0.08957544714212418,
0.8574655055999756,
0.6657481789588928,
0.476552814245224,
0.42766013741493225,
0.17492125928401947,
-0.2166743278503418,
-0.24616791307926178,
0.567270815372467,
0.062288548797369,
-0.6036508083343506,
-0.8787308931350708,
0.09539922326803207,
-0.2553008496761322,
-0.5897104740142822,
-0.4659162163734436,
-0.42703476548194885,
1.3459889888763428,
0.43267253041267395,
-0.8822977542877197,
-0.08802597224712372,
-0.43508854508399963,
-0.9358944296836853,
0.25042861700057983,
-0.06655041128396988,
-0.7186103463172913,
0.5488311052322388,
-0.7480412721633911,
0.5244206786155701,
0.17970919609069824,
-0.6962541937828064,
-0.3896612823009491,
0.30476534366607666,
0.5923111438751221,
0.046739377081394196,
0.8134645223617554,
-0.6436948180198669,
0.1433713585138321,
-0.15343189239501953,
0.5426213145256042,
-0.26004093885421753,
0.019162587821483612,
0.3001076579093933,
-0.6262282729148865,
-0.23276139795780182,
-0.775242805480957,
-0.3387947976589203,
-0.13235174119472504,
-0.3023747503757477,
-0.25074076652526855,
-0.40263354778289795,
-0.2659691274166107,
-0.5343987345695496,
0.9545444846153259,
-0.24234168231487274,
-0.8181124329566956,
0.20766055583953857,
0.9325554966926575,
-0.50388103723526,
-0.22411800920963287,
0.6566159725189209,
-0.5681478977203369,
0.6062232255935669,
-0.12764966487884521,
0.4624367952346802,
-0.667830765247345,
-0.21981041133403778,
0.2083016335964203,
-0.6261925101280212,
0.6045793890953064,
0.5687427520751953,
0.16582748293876648,
0.1319614201784134,
-0.5331230759620667,
0.19131264090538025,
0.13732127845287323,
-0.06695496290922165,
-0.35307613015174866,
-0.3187338411808014,
-0.23324477672576904,
0.06795065850019455,
0.3739231824874878,
0.07384654879570007,
0.34258538484573364,
0.25652748346328735,
-0.2640751600265503,
-0.16031217575073242,
0.39322182536125183,
0.08089268207550049,
0.20584005117416382,
0.2400296926498413,
0.1365482211112976,
0.5441824197769165,
0.2706260681152344,
-0.6217254400253296,
0.7646969556808472,
-1.3731329441070557,
0.6892480850219727,
-0.6696386933326721,
-0.8029804229736328,
-0.03341405466198921,
0.36024126410484314,
0.4109557569026947,
-0.9893045425415039,
0.1813928186893463,
0.05323873460292816,
-0.04624183848500252,
0.42526233196258545,
0.18983113765716553,
-0.05657943710684776,
-0.8283053040504456,
-0.7284547090530396,
-0.8714753985404968,
0.5140402913093567,
0.09290225058794022,
-0.5265271663665771,
-0.2158036231994629,
-0.7049677968025208,
0.11376197636127472,
-0.02569652535021305,
0.08783894777297974,
0.5522634983062744,
0.5543904900550842,
-0.03856004402041435,
0.030286841094493866,
0.09005238860845566,
-0.7788547277450562,
-0.021225562319159508,
0.41799357533454895,
-0.11012028902769089,
-0.34604766964912415,
0.06454717367887497,
-0.5358145833015442,
-0.9203462600708008,
-0.263944149017334,
0.3531898558139801,
-0.03166930004954338,
-0.012849878519773483,
0.9930239915847778,
-0.37538963556289673,
-0.37372639775276184,
0.43760883808135986,
-0.4056616723537445,
-0.11461254209280014,
0.23766174912452698,
0.6607517600059509,
0.2609836757183075,
1.0780258178710938,
0.047673776745796204,
0.7446376085281372,
-0.42983630299568176,
-0.1690879911184311,
0.6210187077522278,
-0.09557965397834778,
-0.0807526484131813,
0.9910784959793091,
-0.14340044558048248,
-1.043013572692871,
0.33768123388290405,
-0.1841602772474289,
-0.40497371554374695,
-0.4497409760951996,
-0.37004324793815613,
-0.3623659312725067,
-0.28511208295822144,
0.29630911350250244,
0.770848274230957,
0.20178702473640442,
0.12466393411159515,
0.7131139636039734,
0.35968396067619324,
-0.6559579372406006,
-0.13323408365249634,
0.03369276225566864,
1.5422687530517578,
-0.16316677629947662,
-0.20497538149356842,
-0.18808357417583466,
0.17196454107761383,
-0.30489054322242737,
0.6524943709373474,
0.42288756370544434,
0.3477611243724823,
0.5365369915962219,
0.3389849066734314,
-0.04816366359591484,
0.49617332220077515,
1.0968258380889893,
-0.09062892198562622,
-0.574708878993988,
-0.2539408206939697,
-0.864169716835022,
-0.61356520652771,
-0.6016520857810974,
0.4612959027290344,
0.8306874632835388,
-0.2084379643201828,
0.19461140036582947,
0.6189830899238586,
-0.8057054281234741,
0.03306444734334946,
-1.4376411437988281,
0.22922557592391968,
-1.3445250988006592,
-0.8184383511543274,
-0.8771953582763672,
-0.17436672747135162,
0.5689206123352051,
0.6662424206733704,
-0.20797809958457947,
0.148471862077713,
-0.6007000803947449,
-0.41460177302360535,
-0.01314665749669075,
-0.2859692871570587,
-0.4330456256866455,
-0.8420841693878174,
-0.42389118671417236,
0.12204712629318237,
-0.3114902973175049,
0.03565431386232376,
-0.19924646615982056,
0.3449269235134125,
0.10088534653186798,
0.5042872428894043,
-0.5935773253440857,
1.1654248237609863,
-0.6105014681816101,
-0.8753625750541687,
0.590126097202301,
0.09021911025047302,
-1.136555552482605,
0.536124050617218,
0.7272654175758362,
-0.008295993320643902,
0.19162996113300323,
0.4161928594112396,
-0.9806317090988159,
0.32809850573539734,
-0.7494913339614868,
-0.11276528984308243,
-0.2192978858947754,
-0.30490565299987793,
-0.6704250574111938,
-0.5862717628479004,
0.29389697313308716,
0.24038203060626984,
-0.7864559888839722,
0.5003108382225037,
-0.2814443111419678,
-0.16980159282684326,
-0.5078549981117249,
0.3221359848976135,
0.1815442442893982,
-0.2959951162338257,
-0.061779964715242386,
0.9367509484291077,
-0.7982393503189087,
-0.1419135481119156,
-0.21861067414283752,
0.2315961718559265,
-0.09481285512447357,
1.123499870300293,
-0.09458844363689423,
-0.6076077818870544,
-0.14840324223041534,
0.20515099167823792,
-0.3849372863769531,
0.1504698395729065,
-0.6218966245651245,
-0.9855809807777405,
-0.5459357500076294,
-0.3904763162136078,
-0.7715857625007629,
0.443642795085907,
0.49794504046440125,
-1.2784098386764526,
-0.5974046587944031,
-0.4820423722267151,
-0.6712177395820618,
0.4920806586742401,
-1.3526123762130737,
0.06734607368707657,
-0.11501091718673706,
-0.47746989130973816,
0.18878841400146484,
-0.09304944425821304,
-0.19748038053512573,
0.5637574791908264,
0.4299640357494354,
0.44290220737457275,
-0.8336235880851746,
-0.6625917553901672,
-0.005388618912547827,
0.3534298837184906,
-1.222347617149353,
0.12186704576015472,
-0.8203094601631165,
0.29009249806404114,
-0.32934263348579407,
-0.255352646112442,
-0.2927466332912445,
0.8184694051742554,
0.12628290057182312,
-0.4815939664840698,
0.00803325604647398,
-0.3043557405471802,
0.14402465522289276,
-0.07216978818178177,
-0.008566557429730892,
0.07678963989019394,
-0.11087115108966827,
0.2043900340795517,
-0.008227148093283176,
-0.4952539801597595,
0.340967059135437,
0.5313957333564758,
-0.11301770806312561,
-0.1360156387090683,
0.38013336062431335,
1.1750682592391968,
-0.08193718641996384,
-0.5707480907440186,
0.9205671548843384,
-0.3648751676082611,
0.43732139468193054,
0.12011770904064178,
-0.6028243899345398,
0.036036416888237,
0.08117671310901642,
0.9132465720176697,
0.9311941266059875,
0.7684357762336731,
0.5095143914222717,
0.5164746046066284,
0.19646920263767242,
0.6532571315765381,
0.8341028690338135,
1.0685807466506958,
0.9109107851982117,
0.18337619304656982,
-0.28827887773513794,
-0.4040275514125824,
-0.37103092670440674,
-0.26373091340065,
-0.4104215204715729,
0.1983441412448883,
-0.3729541003704071,
-0.13700872659683228,
0.13479900360107422,
0.5125625729560852,
-0.16302160918712616,
-0.9314162731170654,
-0.43886294960975647,
0.3323601484298706,
0.009793573059141636,
0.2967871427536011,
0.3807380199432373,
1.1406934261322021,
0.15131875872612,
-0.0809456929564476,
0.20227818191051483,
0.7079305052757263,
-0.13961975276470184,
0.43073180317878723,
0.6919289231300354,
0.8867204785346985,
0.9908298254013062,
0.4508921802043915,
0.028377249836921692,
-0.3745649755001068,
-0.03222741186618805,
0.012754734605550766,
-1.521619200706482,
0.058484628796577454,
-0.0915236696600914,
-0.18002475798130035,
-0.40032222867012024,
-0.772804319858551,
0.21808336675167084,
-0.536312997341156,
0.06046698987483978,
1.3943710327148438,
-0.7978458404541016,
0.3272308111190796,
0.9638644456863403,
0.10021117329597473,
-0.13398072123527527,
0.3054535984992981,
-0.24068310856819153,
-0.0161412563174963,
1.0393091440200806,
1.1267343759536743,
-0.3817096948623657,
0.010484873317182064,
0.40180206298828125,
-0.024008585140109062,
0.4112415611743927,
0.5092943906784058,
-0.17125780880451202,
0.6776225566864014,
-0.7445539236068726,
-0.012425366789102554,
0.24735723435878754,
0.01662340946495533,
-0.17343463003635406,
0.33675986528396606,
0.23019079864025116,
0.8176976442337036,
-0.4162766933441162,
-0.5181929469108582,
1.7501543760299683,
0.5264981389045715,
-0.9414578676223755,
-0.3573625087738037,
0.19522668421268463,
0.21792440116405487,
-0.28537243604660034,
-0.4007909595966339,
0.5834494829177856,
0.7769228219985962,
0.005130839068442583,
0.2346644401550293,
-1.036102294921875,
-0.5005312561988831,
-0.7259496450424194,
0.28007441759109497,
-0.6321924328804016,
0.4659746289253235,
0.27821314334869385,
0.2716985046863556,
0.23829957842826843,
-1.0974156856536865,
0.18990115821361542,
0.15080563724040985,
1.4953134059906006,
-0.10350199043750763,
0.03953547030687332,
0.38932469487190247,
0.9821825623512268,
-0.5299832224845886,
0.729725182056427,
1.0301930904388428,
-0.516960620880127,
1.2582637071609497,
-0.5532189607620239,
-0.012016545049846172,
0.7530247569084167,
-0.2393616884946823,
0.1836257427930832,
-0.41031190752983093,
0.2492782026529312,
-0.21854525804519653,
-0.13153649866580963,
-0.1940121203660965,
-0.6531743407249451,
0.5888515710830688,
-1.2396470308303833,
0.4415908753871918,
-0.26538214087486267,
0.8906075954437256,
-0.3763578534126282,
-0.313226580619812,
3.7750167846679688,
0.9205722808837891,
0.8309358358383179,
0.49696022272109985,
1.308834433555603,
1.1816643476486206,
-0.38836556673049927,
-0.4680238664150238,
0.05988067761063576,
-1.4274146556854248,
-0.7805866599082947,
0.2625279426574707,
-0.1841636598110199,
0.39575839042663574,
-0.7801848649978638,
0.9553517699241638,
-0.18292422592639923,
-0.07407494634389877,
-0.10957520455121994,
-1.033589482307434,
-0.7098076939582825,
0.6044250726699829,
0.5837991833686829,
-0.6993056535720825,
0.12373190373182297,
0.36138442158699036,
0.19947688281536102,
-1.117085576057434,
-0.07068691402673721,
-0.05329067260026932,
-0.6676784157752991,
-1.2393909692764282,
0.5174911022186279,
-0.41364532709121704,
-0.7903477549552917,
0.250323623418808,
-0.08377335220575333,
-0.14384038746356964,
-0.04747860133647919,
-0.053925905376672745,
-0.04053855687379837,
0.07436623424291611,
-0.17778891324996948,
-0.045808710157871246,
-0.6549036502838135,
1.1125894784927368,
-0.6975639462471008,
1.033076286315918,
0.21009573340415955,
-1.028560996055603,
1.161869764328003,
-0.2052948772907257,
0.676179826259613,
-0.0794738382101059,
-0.6233986616134644,
0.08482243865728378,
-0.22558768093585968,
-0.06732108443975449,
0.3657613694667816,
0.2801448702812195,
0.2084941864013672,
-0.3357316553592682,
0.05328187346458435,
0.10027115046977997,
0.2528679072856903,
1.0331571102142334,
0.8417624831199646,
0.3102286458015442,
-0.4780276417732239,
-0.24084706604480743,
-0.4623793065547943,
-0.044582217931747437,
-0.43565550446510315,
0.37940776348114014,
-0.015043710358440876,
-0.3689092695713043,
0.032899994403123856,
0.32584187388420105,
-0.0960233211517334,
-0.11921104043722153,
-0.26659151911735535,
-0.5057183504104614,
0.03126545995473862,
0.28946200013160706,
-0.22483058273792267,
0.899294376373291,
0.28607451915740967,
-0.07910530269145966,
-0.013890459202229977,
0.029799723997712135,
0.33073166012763977,
1.5742946863174438,
0.12544912099838257,
-0.16777822375297546,
-0.5708497166633606
] |
Bosonization and Cluster Updating of Lattice Fermions
|
A lattice fermion model is formulated in Fock space using the Jordan-Wigner representation for the fermion creation and annihilation operators. The resulting path integral is a sum over configurations of lattice site occupation numbers $n(x,t) = 0,1$ which may be viewed as bosonic Ising-like variables. However, as a remnant of Fermi statistics a nonlocal sign factor arises for each configuration. When this factor is included in measured observables the bosonic occupation numbers interact locally, and one can use efficient cluster algorithms to update the bosonized variables.
|
Uwe-Jens Wiese (Universit\"at Bern)
|
hep-lat cond-mat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210019
|
hep-lat/9210020
|
[
-0.09621437638998032,
0.7836293578147888,
0.3455579876899719,
0.304922878742218,
0.11924140900373459,
0.0901661142706871,
-0.4020566940307617,
-0.7220616936683655,
-0.520772397518158,
1.4903322458267212,
0.17533060908317566,
0.06256753206253052,
0.35612431168556213,
-1.370278239250183,
-0.9161189794540405,
0.2164633572101593,
-0.2639675736427307,
-0.7765569686889648,
-0.8798215389251709,
-0.16752587258815765,
0.1930072158575058,
-0.28578853607177734,
-1.0926445722579956,
-0.9835436940193176,
-0.035745441913604736,
0.869399905204773,
-0.2581971287727356,
0.04663391038775444,
1.2764095067977905,
0.692548394203186,
0.507548987865448,
-0.8175869584083557,
-0.2344411015510559,
-0.897560179233551,
-0.3690124452114105,
0.0014682349283248186,
1.2636295557022095,
-0.07236573100090027,
0.02401590161025524,
-0.480947881937027,
1.3505653142929077,
-0.5681970715522766,
0.7236076593399048,
-0.5131142139434814,
-0.1509460061788559,
0.41661614179611206,
-0.5915334224700928,
-0.3902324438095093,
0.33393850922584534,
-1.371949315071106,
-0.1991596817970276,
0.11347553133964539,
0.30966925621032715,
-0.041016992181539536,
-0.25372809171676636,
0.21071527898311615,
-0.3493846654891968,
0.0990629494190216,
-0.08338844031095505,
0.07938408851623535,
-0.2224932760000229,
0.08622781932353973,
0.484453946352005,
-0.9349914193153381,
0.2480395883321762,
0.8417915105819702,
-0.2306816130876541,
0.3245484530925751,
0.27410638332366943,
-1.1439355611801147,
-0.8101013898849487,
-0.5002583861351013,
-0.11775659769773483,
0.2504790425300598,
-0.9268934726715088,
0.40661323070526123,
0.2964763343334198,
-0.3607308268547058,
-0.989571213722229,
-0.34853696823120117,
-0.08843336999416351,
-0.2618226706981659,
-0.6150638461112976,
-0.08174478262662888,
-0.48319610953330994,
-0.3223506212234497,
-0.21078993380069733,
0.5543030500411987,
0.242948517203331,
0.8863179683685303,
0.4263661801815033,
0.37097105383872986,
0.7346000671386719,
-0.32365554571151733,
0.29359060525894165,
0.6233566999435425,
0.48081734776496887,
0.6210880875587463,
-0.022226830944418907,
0.8546655178070068,
0.1256386935710907,
0.821521520614624,
-0.32388973236083984,
0.30037757754325867,
-0.9263235926628113,
0.29215869307518005,
1.2539914846420288,
-0.249383345246315,
0.02269214205443859,
-0.41409561038017273,
0.015672050416469574,
-0.709657609462738,
-0.31806913018226624,
0.49152788519859314,
0.4688248336315155,
0.6786366105079651,
0.3141666650772095,
-0.3258588910102844,
-0.6689035296440125,
-0.08881387859582901,
-0.0029473286122083664,
-0.07052096724510193,
-0.0863352119922638,
0.22986389696598053,
0.02859436720609665,
-0.6151449680328369,
-0.08866745978593826,
0.8102053999900818,
-0.06676991283893585,
-0.4723301827907562,
-0.034014903008937836,
-0.5737114548683167,
-0.43436428904533386,
1.1535388231277466,
0.25273656845092773,
0.22640888392925262,
-0.22863632440567017,
1.173884391784668,
0.7129651308059692,
-0.06248126178979874,
0.4379081726074219,
-0.6943596601486206,
0.5865870714187622,
1.1735435724258423,
-0.5661032795906067,
0.15054252743721008,
0.4228837788105011,
-0.5447772741317749,
-0.2050374150276184,
-0.21803927421569824,
-0.6534883379936218,
0.13564129173755646,
0.023616068065166473,
0.4207959771156311,
0.17500407993793488,
0.22542402148246765,
-0.0773417130112648,
0.817237913608551,
-0.359639972448349,
-1.2458401918411255,
0.9092900156974792,
-0.33420053124427795,
-0.3968585133552551,
0.4494679272174835,
-0.5655163526535034,
0.09233009070158005,
-0.9421599507331848,
0.28008005023002625,
0.325634241104126,
-0.5883924961090088,
0.3327166438102722,
0.8309763669967651,
-0.06449845433235168,
0.36925703287124634,
0.4332377016544342,
-0.017052315175533295,
0.9375112056732178,
-0.3373759090900421,
0.8934576511383057,
-0.08544442802667618,
-0.7893522381782532,
0.10483802855014801,
0.03417538106441498,
0.6873829364776611,
0.5947359204292297,
0.2385285347700119,
-0.7386793494224548,
-0.14360935986042023,
0.34025314450263977,
0.19436946511268616,
0.3140795826911926,
0.717014491558075,
-0.6695630550384521,
0.23346683382987976,
-0.3005013167858124,
-0.14634793996810913,
-1.012966275215149,
0.043652843683958054,
-0.3232439458370209,
-0.7603805065155029,
-0.34463056921958923,
-0.4915899336338043,
-0.459974080324173,
0.6782200932502747,
-1.1898001432418823,
0.40095821022987366,
0.4152691066265106,
0.7847374677658081,
-0.605505108833313,
-0.2402884066104889,
0.14964331686496735,
-0.041623201221227646,
0.7621581554412842,
0.05578343942761421,
-0.4691447913646698,
-0.36037659645080566,
-0.04723739996552467,
0.6530773043632507,
0.8205718398094177,
-0.2292245626449585,
-0.29068654775619507,
0.0385841503739357,
-0.21530836820602417,
0.4521167278289795,
0.04930061474442482,
-0.08421213179826736,
-0.43032410740852356,
0.05453777313232422,
0.5518279671669006,
-0.11597537994384766,
-0.4033393859863281,
0.6558061838150024,
-0.6486990451812744,
0.5878666639328003,
0.6648789644241333,
0.6109711527824402,
0.1419103592634201,
0.348588228225708,
-0.11190952360630035,
0.1710808426141739,
0.5569760203361511,
0.2478434294462204,
0.1534755527973175,
0.531917929649353,
-0.18221741914749146,
0.5298779010772705,
-0.22082343697547913,
0.22500936686992645,
-0.6174983382225037,
0.524431049823761,
-0.8610105514526367,
0.8331319689750671,
0.6792563796043396,
-0.3052310347557068,
-0.9362913966178894,
-0.7939661145210266,
-0.23625530302524567,
0.523246169090271,
-0.43758440017700195,
-0.038565270602703094,
-0.205936998128891,
-0.13615567982196808,
0.10938016325235367,
-0.12750346958637238,
0.016845542937517166,
0.9707682132720947,
-0.6216794848442078,
0.7817569375038147,
-0.03681088611483574,
0.5191012620925903,
-1.291532278060913,
-0.40254491567611694,
-0.7604741454124451,
-0.13286970555782318,
-0.41527560353279114,
-0.1387462317943573,
1.2043901681900024,
-0.4638228416442871,
0.4537339210510254,
0.30890727043151855,
-0.5266368389129639,
0.7550581693649292,
0.05043340474367142,
0.5717355608940125,
0.5216125249862671,
0.21606843173503876,
-0.5773789286613464,
0.5079668760299683,
-0.2756102979183197,
0.07807295024394989,
0.1515352725982666,
-0.25442740321159363,
0.011059950105845928,
-0.10780267417430878,
0.09177180379629135,
0.18676473200321198,
-0.5080207586288452,
-0.6471000909805298,
0.2663094103336334,
-0.17708243429660797,
-0.3025706112384796,
0.3219216763973236,
-0.7935729026794434,
-1.0160269737243652,
-1.5842196941375732,
1.0663533210754395,
0.5833463072776794,
-0.034295618534088135,
0.44787847995758057,
0.7193710803985596,
-0.05056796967983246,
-0.4091103672981262,
-0.1360318958759308,
0.24892450869083405,
-0.6916837692260742,
1.36189603805542,
0.5508728623390198,
-0.3858204185962677,
0.18905748426914215,
-0.8667433857917786,
-0.1270204335451126,
0.8129700422286987,
0.102350614964962,
-0.7557790279388428,
0.20666223764419556,
1.215597152709961,
0.6161469221115112,
-0.9694268107414246,
0.1401359885931015,
-0.6000894904136658,
-0.8545536994934082,
0.7445886731147766,
-0.20599587261676788,
1.1676417589187622,
-0.08476539701223373,
-0.0038218218833208084,
-1.145867943763733,
-0.6013229489326477,
-0.20677027106285095,
-0.03968365862965584,
0.46134525537490845,
0.1403849720954895,
0.08291170001029968,
0.5903360843658447,
0.09206277132034302,
-0.09393061697483063,
0.6363512277603149,
-0.7465133666992188,
0.28030824661254883,
0.5714504718780518,
-0.6682064533233643,
-0.060289256274700165,
0.45850154757499695,
0.2274564951658249,
-0.9412684440612793,
0.2904743552207947,
-0.8685207962989807,
-0.8065628409385681,
-0.20166058838367462,
-0.08412592113018036,
0.4284777343273163,
-0.30073535442352295,
-0.5873604416847229,
0.4115760922431946,
-0.4864594340324402,
-0.9911673069000244,
0.9208083748817444,
-0.27493080496788025,
0.7104581594467163,
-0.5535626411437988,
0.0938948467373848,
0.3915938436985016,
0.19074928760528564,
0.6238121390342712,
0.08688566833734512,
-0.3608655035495758,
0.018865078687667847,
-0.7113226652145386,
0.9206269383430481,
-0.635087788105011,
-0.9372745156288147,
-0.20216533541679382,
1.2103357315063477,
1.4496774673461914,
1.5266971588134766,
1.1564280986785889,
-0.940109133720398,
0.3467150628566742,
-0.5747821927070618,
0.4836224615573883,
-0.4538992643356323,
-0.3494293689727783,
-0.8065018653869629,
-0.5425856113433838,
-0.32918575406074524,
0.020106913521885872,
0.9127470254898071,
0.9952489137649536,
-0.7499340176582336,
-0.26050037145614624,
0.3261488378047943,
0.27681368589401245,
0.3414027690887451,
0.6179519891738892,
0.3003270626068115,
0.7808772325515747,
-0.7803120017051697,
0.07716120779514313,
-0.20120322704315186,
-0.16577205061912537,
-0.4653538763523102,
-0.4569687247276306,
-0.9208691716194153,
-0.5775298476219177,
0.8338567614555359,
-0.11603165417909622,
-0.26179808378219604,
0.5382840633392334,
-0.059863436967134476,
0.43093162775039673,
0.7099481225013733,
-0.5114989876747131,
0.0823410376906395,
0.2653433084487915,
0.02612460032105446,
-0.67997145652771,
-0.2092013955116272,
-0.45101141929626465,
0.7422704100608826,
0.9223166108131409,
-0.7589669227600098,
-0.5703511238098145,
-0.19976332783699036,
0.1345827728509903,
-0.8116477727890015,
0.1475422978401184,
0.5858680605888367,
-0.6763874292373657,
-0.5803488492965698,
0.138447567820549,
0.27826231718063354,
0.06316395103931427,
-0.49575603008270264,
-0.4670727252960205,
0.5243586897850037,
0.9021075963973999,
-0.5498017072677612,
0.5292131900787354,
-0.47427237033843994,
-0.6249585151672363,
-0.23426878452301025,
-0.3650745749473572,
-0.7363865971565247,
-0.08125417679548264,
-0.5944312810897827,
0.4899669289588928,
-0.3836367130279541,
-0.13996946811676025,
0.7795739769935608,
-0.5206407308578491,
0.16289809346199036,
-0.286404550075531,
0.21842417120933533,
0.09122350066900253,
-0.7909454703330994,
0.6645264029502869,
0.3954504728317261,
0.2998952865600586,
0.1351865530014038,
0.5929299592971802,
0.16362637281417847,
-0.19931182265281677,
0.07963024079799652,
-0.32918789982795715,
0.7546716928482056,
-0.10556437075138092,
0.24880997836589813,
-0.051695600152015686,
-0.14271600544452667,
-0.051812395453453064,
-0.6332124471664429,
0.6052747964859009,
0.24248109757900238,
0.80499666929245,
-0.3146667182445526,
-0.2940038740634918,
-0.02181851677596569,
-0.11415347456932068,
-1.051403522491455,
0.0769081637263298,
-0.1188403069972992,
-0.562292218208313,
0.2573641836643219,
-0.6973965167999268,
-0.1635996699333191,
0.2320832759141922,
-0.3190179765224457,
0.01407636795192957,
-0.2614794671535492,
0.959074079990387,
0.45937323570251465,
-0.38581424951553345,
-1.4239733219146729,
0.3872678279876709,
0.33781319856643677,
0.41074368357658386,
-0.41445305943489075,
-0.06884417682886124,
0.4370069205760956,
0.010565487667918205,
-0.4149375259876251,
-0.6041238903999329,
-0.03666228801012039,
-0.4886534810066223,
0.40290650725364685,
0.5575817227363586,
0.44008684158325195,
-0.8470095992088318,
-0.035089340060949326,
0.6303585171699524,
-0.19791394472122192,
-1.3167091608047485,
0.15793083608150482,
1.197659969329834,
-0.7002275586128235,
-0.24012920260429382,
0.01232834067195654,
-0.44515901803970337,
-0.03658350184559822,
0.37002596259117126,
-0.34271055459976196,
-0.3664700388908386,
0.20612546801567078,
-0.09332957118749619,
-0.25948235392570496,
-0.1192471832036972,
0.3239979147911072,
0.34974005818367004,
-0.11274474114179611,
-0.2931719422340393,
-1.135250449180603,
0.1358272284269333,
0.3220122456550598,
-0.3945847153663635,
-0.013781293295323849,
0.639556348323822,
-0.7583286166191101,
0.20598770678043365,
-0.5300502181053162,
-0.4555268883705139,
0.36710458993911743,
0.40168023109436035,
0.2812962532043457,
0.787127673625946,
-0.22604532539844513,
0.25558561086654663,
0.1673235148191452,
0.9940018057823181,
-0.405847430229187,
0.2960852086544037,
-1.4395354986190796,
0.6021623015403748,
-0.45890265703201294,
0.4460658133029938,
-0.7757633328437805,
-0.5057651400566101,
0.2106272429227829,
-0.31958243250846863,
0.8135989904403687,
-0.5555891394615173,
0.18065546452999115,
0.3611558675765991,
-0.32029449939727783,
-0.03937087953090668,
0.6682567000389099,
-0.6265754103660583,
-0.6936073899269104,
-0.5900136232376099,
-1.3084306716918945,
0.48351964354515076,
-0.07911325991153717,
-0.4960123598575592,
-0.7068038582801819,
-0.3379385769367218,
0.5593106746673584,
-0.4119876027107239,
1.1733888387680054,
0.40481990575790405,
-0.05906624719500542,
0.13474604487419128,
0.6572555899620056,
-0.010485871694982052,
-0.3060466945171356,
-0.6901291608810425,
0.6828792095184326,
-0.254177987575531,
-0.6942468881607056,
0.0973706990480423,
-0.1621033251285553,
-0.7011297941207886,
-0.31292131543159485,
0.6249481439590454,
0.05306500941514969,
-0.6293061971664429,
0.3665282130241394,
-0.4148324131965637,
-0.6957418918609619,
-0.38185110688209534,
0.3138774037361145,
-0.45634281635284424,
0.21932969987392426,
0.04920906946063042,
-0.42126521468162537,
0.752945065498352,
0.01804172620177269,
0.01698286645114422,
-0.25620394945144653,
-0.6306841969490051,
0.8019535541534424,
-0.23758265376091003,
-0.5135831236839294,
-0.7876582741737366,
0.002978877630084753,
-0.8415718078613281,
-0.2827084958553314,
-0.37516459822654724,
0.1343267858028412,
0.09193937480449677,
-1.1340643167495728,
0.3305659294128418,
-0.39945051074028015,
-0.9959473013877869,
-0.29045552015304565,
0.059030815958976746,
0.24340207874774933,
0.1492433100938797,
-0.1658826321363449,
-0.5024576187133789,
-1.0275752544403076,
0.2223946452140808,
1.2813833951950073,
-0.26401594281196594,
-0.12867148220539093,
-0.5352162718772888,
-0.2247079610824585,
0.08043222874403,
0.1781267523765564,
0.0074455589056015015,
-0.15163445472717285,
0.15008875727653503,
-0.08932901173830032,
0.665143609046936,
0.46129798889160156,
0.5004288554191589,
1.1382710933685303,
0.20968210697174072,
0.42294180393218994,
-0.8823909759521484,
-0.7312015891075134,
-0.12472380697727203,
0.4211680591106415,
0.9093789458274841,
-0.33972394466400146,
0.07988914102315903,
-0.5493398904800415,
-0.8983396291732788,
-0.4972623586654663,
-0.7180468440055847,
-0.2849605679512024,
-0.799797534942627,
-0.2798083424568176,
-1.2417300939559937,
-0.8274382948875427,
-0.4340263307094574,
0.2670125961303711,
0.6668893694877625,
-0.19119037687778473,
-1.0986287593841553,
0.289322167634964,
0.38427019119262695,
0.010936281643807888,
-0.254686564207077,
-0.6326603293418884,
-0.8803051114082336,
-0.18816889822483063,
-0.6484001278877258,
0.1426714062690735,
0.009219402447342873,
-0.31431421637535095,
0.07549615204334259,
0.13072624802589417,
-0.3109797239303589,
0.5199315547943115,
-0.915591299533844,
-0.3079277575016022,
0.11780739575624466,
-0.40092000365257263,
-0.2395510971546173,
0.15392664074897766,
-0.18940357863903046,
-0.3635242283344269,
0.1359734833240509,
-0.3143458664417267,
-0.0773123949766159,
0.2972993850708008,
-0.5075098276138306,
-0.4236079752445221,
-0.7612738609313965,
0.5513237118721008,
0.004270888399332762,
-0.9220742583274841,
-0.1153232753276825,
0.8925379514694214,
-0.8263490200042725,
-0.10065233707427979,
-0.43839070200920105,
0.16945324838161469,
-0.11819922924041748,
-0.5252909660339355,
0.24097304046154022,
1.4258867502212524,
-0.5796492695808411,
1.1934701204299927,
-0.23243136703968048,
-0.3998473882675171,
-0.6335256695747375,
0.22720812261104584,
-0.29076912999153137,
-0.21278464794158936,
0.5878298282623291,
-0.6245588064193726,
0.2791035771369934,
-0.05803779512643814,
-0.35008448362350464,
0.279134064912796,
-0.21768298745155334,
-0.33863407373428345,
-0.17857365310192108,
-0.5413289666175842,
-0.2025633603334427,
0.34893617033958435,
-0.8718645572662354,
-0.08600617945194244,
-0.31749892234802246,
-0.7588189840316772,
-0.8146432638168335,
-0.38410696387290955,
-1.087304711341858,
-0.10012130439281464,
-0.028125746175646782,
-0.2888820171356201,
-0.45666298270225525,
-0.47112953662872314,
-0.42871105670928955,
-0.028569912537932396,
-0.03528943657875061,
-0.1396525651216507,
-0.6490305662155151,
0.5698859691619873,
0.5758115649223328,
0.480914443731308,
-0.13120998442173004,
0.12497217208147049,
-0.4190240502357483,
0.6637848615646362,
-0.6767499446868896,
-0.566032350063324,
-0.022486833855509758,
0.5535460710525513,
-0.28765496611595154,
-0.005589520558714867,
-0.19544373452663422,
0.3607225716114044,
0.4334051311016083,
-0.06645512580871582,
0.07338980585336685,
-0.07826758921146393,
0.11140621453523636,
0.6775928735733032,
0.3997131884098053,
-0.26693016290664673,
-0.01539148110896349,
0.46539589762687683,
0.42783933877944946,
-0.13784074783325195,
-0.8933941721916199,
0.8880188465118408,
0.6911624670028687,
-0.1671893298625946,
0.9639204144477844,
-0.05443863943219185,
0.7458717226982117,
-0.033360157161951065,
0.08066064119338989,
-0.4403713643550873,
-0.07326410710811615,
0.24984578788280487,
0.15961407124996185,
0.9136054515838623,
0.7801949977874756,
0.5588398575782776,
-0.33910423517227173,
-0.42892158031463623,
0.5022239685058594,
0.7482280731201172,
0.06476102769374847,
0.6862119436264038,
-0.18439029157161713,
0.8620354533195496,
-0.04169375076889992,
0.7620277404785156,
-0.34655508399009705,
-0.004016016144305468,
-0.3381859064102173,
0.5467376708984375,
0.595954954624176,
0.18949277698993683,
-0.631363034248352,
0.04495096951723099,
-0.34496593475341797,
-0.14602859318256378,
0.06969114392995834,
0.4283541440963745,
0.3299218714237213,
0.28209394216537476,
0.8053081035614014,
0.9439151883125305,
-0.4382741153240204,
0.766705334186554,
0.3000132143497467,
0.31610047817230225,
-0.20248067378997803,
0.7286276817321777,
0.40394914150238037,
-0.0328192375600338,
0.20951806008815765,
-0.42817923426628113,
-0.2634131908416748,
0.8354964852333069,
-1.4818593263626099,
0.3630962073802948,
0.35819047689437866,
-0.07226604968309402,
-0.009049721993505955,
-1.4099212884902954,
0.691962718963623,
-0.6037998199462891,
0.26089930534362793,
1.0227382183074951,
0.14216013252735138,
0.11227007955312729,
0.7060075998306274,
-0.27092304825782776,
0.5165140628814697,
0.39369165897369385,
0.2516259551048279,
-0.482181578874588,
0.599741518497467,
1.180806279182434,
0.08388280868530273,
0.4648275077342987,
0.28589341044425964,
-0.7458183169364929,
0.015018349513411522,
-0.3445777893066406,
-0.3005034327507019,
1.4814778566360474,
-0.7382377982139587,
-0.47003746032714844,
0.4778667688369751,
0.3893662393093109,
0.020640213042497635,
-0.11586838215589523,
0.34947633743286133,
0.8699824213981628,
-0.42516669631004333,
-0.9663782715797424,
0.4673270285129547,
0.39829474687576294,
0.011179872788488865,
-0.07647652179002762,
0.38345956802368164,
0.13921576738357544,
0.1971682608127594,
0.16308991611003876,
0.3262248635292053,
0.897750735282898,
-0.06876419484615326,
-0.24450469017028809,
0.022680705413222313,
-0.20381039381027222,
-1.2252609729766846,
-0.8562063574790955,
-0.36732304096221924,
0.8261587023735046,
-0.6408402919769287,
1.0389487743377686,
-0.4241609573364258,
-1.2838492393493652,
-0.055590786039829254,
0.5942781567573547,
1.0095336437225342,
0.23065143823623657,
0.1842927634716034,
1.014448642730713,
1.1127514839172363,
-0.3754230737686157,
0.80924391746521,
0.30557572841644287,
0.08944421261548996,
0.7211513519287109,
-0.37050163745880127,
0.1882362812757492,
0.25223252177238464,
-0.8784641027450562,
0.5910899639129639,
-0.015902945771813393,
0.846838653087616,
-0.6375213265419006,
0.21333208680152893,
-0.48337873816490173,
-0.6322060823440552,
0.12697739899158478,
-0.7970302700996399,
0.6644097566604614,
0.3551218807697296,
-0.010335455648601055,
0.6376398205757141,
0.11464166641235352,
3.821443557739258,
0.5847090482711792,
0.5029465556144714,
-1.0178049802780151,
0.6348209977149963,
0.6436147689819336,
0.000609134673140943,
-0.7488619685173035,
0.39760875701904297,
-0.12260548025369644,
-0.17358921468257904,
0.5572655200958252,
0.5737940669059753,
0.010295050218701363,
-0.029068758711218834,
0.7246468663215637,
-0.21987298130989075,
0.4519578814506531,
0.5089962482452393,
-1.3336282968521118,
-0.7177286148071289,
0.09503796696662903,
0.5453885197639465,
0.0829540491104126,
0.1287413090467453,
0.03639538958668709,
0.31473976373672485,
-0.05565831810235977,
-0.5343471169471741,
0.6583108305931091,
-0.6431972980499268,
-1.0911895036697388,
0.5042532682418823,
-0.5571804642677307,
-0.8554562926292419,
0.6636843681335449,
0.6075712442398071,
-0.013832667842507362,
0.04690259322524071,
0.6781471967697144,
0.2709093987941742,
0.5089149475097656,
-0.3792748749256134,
-0.48509398102760315,
-0.3827306628227234,
0.7855092883110046,
0.014858009293675423,
0.552269458770752,
0.36384958028793335,
-0.8308972120285034,
0.3392804265022278,
-0.10845242440700531,
0.6524037718772888,
0.09307024627923965,
-1.860063076019287,
-0.1040186733007431,
-0.3638995289802551,
-0.4402346909046173,
-0.12470079213380814,
-0.13348990678787231,
0.815799355506897,
0.023730546236038208,
-0.2908227741718292,
0.3661142587661743,
-0.10113486647605896,
0.29941612482070923,
0.3204248547554016,
-0.0018857751274481416,
-0.6914672255516052,
0.07859259098768234,
-0.26347461342811584,
-0.009910233318805695,
-0.6533346772193909,
-0.03024873323738575,
0.173195481300354,
0.14866627752780914,
-0.32489413022994995,
0.8428524136543274,
0.4977337419986725,
0.08215343207120895,
0.37015169858932495,
-0.7543978691101074,
0.13628974556922913,
-0.05541316419839859,
-0.09764473140239716,
0.7447713017463684,
-0.18172217905521393,
-0.37058404088020325,
-0.6341972351074219,
0.31216076016426086,
0.29331251978874207,
1.3585400581359863,
0.1069747656583786,
0.5092148780822754,
-0.3278762996196747
] |
Intermittency Studies in Directed Bond Percolation
|
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the factorial moments for large $1+1$-dimensional lattices allow to handle statistical and boundary effects and show the existence of weak but definite intermittency patterns. The extracted fractal dimensions are in agreement with scaling arguments leading to a new relation linking the intermittency indices to the critical exponents and the fractal dimension of directed percolation clusters.
|
Malte Henkel and Robert Peschanski
|
hep-lat cond-mat hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210020
|
hep-lat/9210021
|
[
0.6922193169593811,
-0.05069189518690109,
0.2933170795440674,
0.6128570437431335,
-0.27113795280456543,
-0.22395829856395721,
-0.11172974109649658,
-0.47407299280166626,
-0.12022778391838074,
1.1169276237487793,
0.5564532279968262,
-0.45847588777542114,
0.3539944589138031,
-0.7780619263648987,
0.17450644075870514,
0.7088975310325623,
0.1400967687368393,
-0.10919379442930222,
-1.242423176765442,
0.5403942465782166,
0.020855195820331573,
-0.20707055926322937,
-0.6989848017692566,
-0.10852912813425064,
-0.5181083083152771,
1.0035459995269775,
0.3591671586036682,
0.4790610373020172,
0.8992528915405273,
0.09471552819013596,
0.39090755581855774,
0.228953555226326,
-0.3572840690612793,
-0.5922505259513855,
-0.11489666998386383,
-0.6933910250663757,
0.21755099296569824,
-0.3606126010417938,
0.775057315826416,
-0.5207951068878174,
0.3638438284397125,
0.05324314162135124,
-0.2199321985244751,
-0.6499305963516235,
-0.8314076066017151,
-0.22160308063030243,
0.24870723485946655,
0.47518545389175415,
-0.09276612848043442,
-1.2658684253692627,
-0.17269684374332428,
0.4977053105831146,
0.2302529215812683,
-0.8926464915275574,
-0.21078532934188843,
-0.2371998280286789,
0.01239822804927826,
-0.06548962742090225,
-0.7884157299995422,
0.2560855448246002,
0.567654550075531,
-0.32260239124298096,
0.24175229668617249,
-0.6245813369750977,
-0.34989461302757263,
0.5786236524581909,
0.009855967015028,
0.5281057953834534,
0.004403345286846161,
-0.4399283826351166,
0.289984792470932,
0.39883336424827576,
-0.7975833415985107,
0.12243528664112091,
-0.6098071336746216,
0.19911590218544006,
0.21151690185070038,
0.1423044502735138,
0.018310025334358215,
-0.2941383123397827,
0.10641420632600784,
0.21815578639507294,
-0.8137839436531067,
0.4191596806049347,
-0.6367502808570862,
-0.3552790582180023,
-0.28739896416664124,
-0.4550730586051941,
0.1603042483329773,
0.3909570574760437,
0.18799988925457,
0.8172018527984619,
-1.2216259241104126,
0.022442981600761414,
0.15383939445018768,
0.2418617159128189,
-0.3386116027832031,
0.16254238784313202,
0.2805735170841217,
0.273326575756073,
0.3940843641757965,
1.1525713205337524,
-0.49440962076187134,
0.723163366317749,
-0.7513465881347656,
0.8805411458015442,
-0.19680505990982056,
-0.08032375574111938,
-0.391642302274704,
-0.8253409266471863,
-0.18632297217845917,
-0.24014854431152344,
0.31721964478492737,
0.9513365030288696,
-0.5803346633911133,
0.6313233375549316,
-0.3616255223751068,
0.06543887406587601,
-0.42594462633132935,
-0.3301973044872284,
0.5594498515129089,
0.0675334706902504,
0.16277344524860382,
0.16957026720046997,
-0.7574991583824158,
0.07695215195417404,
0.21651673316955566,
-0.22518181800842285,
-0.5545018315315247,
0.11786418408155441,
0.3656546473503113,
0.07870221883058548,
-0.47279882431030273,
0.41803789138793945,
-0.8385316133499146,
-0.09963072091341019,
0.04219185560941696,
0.18405164778232574,
0.11250197142362595,
-0.1763981580734253,
0.30557316541671753,
-0.47147998213768005,
0.1872016042470932,
1.158842921257019,
0.08667220920324326,
0.1251269280910492,
0.3961913287639618,
0.8028984069824219,
-0.10012073814868927,
0.07924273610115051,
-0.725814700126648,
0.07617034763097763,
0.1247832179069519,
0.16327746212482452,
0.012478671036660671,
0.19302181899547577,
-0.6413013935089111,
0.6313673853874207,
-0.7045969367027283,
-0.3786281943321228,
-0.10969173908233643,
0.7139721512794495,
-0.18326719105243683,
-0.05022526904940605,
-0.3244597613811493,
-0.0295694712549448,
-0.6498842835426331,
-0.5737189650535583,
1.2422903776168823,
-0.5240629315376282,
-0.22355584800243378,
0.6498981714248657,
-0.05134640634059906,
1.0247328281402588,
0.7765793800354004,
0.5198798775672913,
0.2511708438396454,
-0.06221886724233627,
-0.4954492151737213,
0.2813059389591217,
0.11070375889539719,
-0.4489685893058777,
0.17664065957069397,
0.608781635761261,
-0.3551549017429352,
0.5854449272155762,
0.014248457737267017,
-0.48004278540611267,
0.2308199107646942,
0.16169074177742004,
-0.3895423710346222,
0.4961438775062561,
-0.8958110213279724,
0.893050491809845,
-1.1876957416534424,
0.20950058102607727,
-0.8349764943122864,
0.7519108057022095,
-0.7921252250671387,
-0.7572577595710754,
0.032242801040410995,
0.4537854790687561,
-1.2568256855010986,
-0.005968858953565359,
-0.9320532083511353,
-0.6771592497825623,
1.0292729139328003,
-0.16429990530014038,
-0.693120539188385,
-0.9470385909080505,
0.36589911580085754,
0.05458926782011986,
0.22305136919021606,
-0.07645554840564728,
0.5439630746841431,
0.12137848138809204,
0.39544832706451416,
0.19873256981372833,
0.5018510818481445,
0.40744736790657043,
0.38010263442993164,
0.037567246705293655,
-0.3024715781211853,
0.7106907963752747,
-0.3484935164451599,
-0.3997705280780792,
0.2503195106983185,
0.5208272933959961,
0.13591569662094116,
-0.46411120891571045,
0.43588143587112427,
0.9777860045433044,
0.039046116173267365,
0.515623927116394,
0.6453931927680969,
0.06639163196086884,
0.5549167394638062,
-0.2228548675775528,
0.20366917550563812,
0.06211428716778755,
-0.3194272220134735,
0.5159288644790649,
0.02529466710984707,
0.35856524109840393,
-0.5862203240394592,
0.045896515250205994,
-0.7054726481437683,
0.21088744699954987,
-0.5846765637397766,
0.30179333686828613,
-0.6008703708648682,
0.6823523640632629,
-0.16563813388347626,
0.6530404686927795,
-1.4129996299743652,
0.012937279418110847,
-0.299219012260437,
0.6086743474006653,
0.19274631142616272,
-0.09182800352573395,
0.2951911389827728,
0.37070685625076294,
-0.7510577440261841,
-0.8240739703178406,
-0.28429320454597473,
0.8063341975212097,
0.1588003933429718,
-0.23978103697299957,
0.6112433075904846,
-0.18201789259910583,
-1.0435922145843506,
0.10444286465644836,
-0.9296779036521912,
-0.17303262650966644,
-0.7303504347801208,
0.8032968044281006,
0.7534288167953491,
-0.9173503518104553,
0.38054782152175903,
0.04526665806770325,
-0.18859219551086426,
-0.14258697628974915,
-0.36591440439224243,
0.2000172883272171,
0.3367096781730652,
0.08964608609676361,
-0.9504236578941345,
0.41635143756866455,
-0.8806945085525513,
0.1600605547428131,
-0.5700253248214722,
-0.23367244005203247,
0.4723154306411743,
-0.4094120264053345,
0.36892446875572205,
0.3424752652645111,
-0.15945647656917572,
0.2541491389274597,
0.16339194774627686,
-0.8957846164703369,
-0.09359920024871826,
0.2830035984516144,
-0.20282793045043945,
-0.14455294609069824,
-0.774896502494812,
0.6993735432624817,
0.5403403639793396,
-0.30438151955604553,
0.17155401408672333,
0.3478247821331024,
-0.5349834561347961,
0.7596735954284668,
0.06878916919231415,
-0.22858884930610657,
-0.1213063895702362,
1.0017305612564087,
0.5414997935295105,
-0.3829547166824341,
0.12568089365959167,
-0.38144922256469727,
-0.6271882057189941,
0.3861249089241028,
-0.04036485031247139,
-0.717255711555481,
-0.18713593482971191,
0.9771984219551086,
-0.7173765897750854,
-0.527804970741272,
0.8197543621063232,
-0.8958633542060852,
-0.6873395442962646,
0.18369591236114502,
-0.3979726731777191,
-0.06382257491350174,
-0.12264975160360336,
-0.07827264070510864,
-0.9567096829414368,
0.01093742810189724,
-0.1739107221364975,
0.20949026942253113,
0.5397601127624512,
-0.941839337348938,
0.1320958286523819,
0.7938225269317627,
0.40030181407928467,
-0.8665933609008789,
0.05583251640200615,
-0.5151901245117188,
-0.2460271120071411,
-0.2623121440410614,
-0.7218535542488098,
0.2231476902961731,
-0.7410973310470581,
0.7828255891799927,
-0.18616551160812378,
0.149049773812294,
-0.8321927785873413,
-0.06875891983509064,
-0.16038843989372253,
-0.10270112007856369,
-0.14814800024032593,
0.8641883134841919,
0.7936349511146545,
-0.0725526362657547,
-1.3943544626235962,
-0.6121119856834412,
-0.49805811047554016,
0.10176827758550644,
0.45567139983177185,
-0.8666196465492249,
0.35170361399650574,
-0.007572161499410868,
-0.41294318437576294,
-0.036841727793216705,
-0.07685882598161697,
0.4622677266597748,
0.6288084387779236,
-0.043209291994571686,
1.1000384092330933,
0.006054268218576908,
-0.7823888063430786,
-0.03548973798751831,
0.6998924612998962,
0.7783710956573486,
0.5943934917449951,
0.011829296126961708,
0.04258289188146591,
-0.034844446927309036,
-0.7641794085502625,
-0.6391141414642334,
-0.2646017372608185,
-0.37648534774780273,
0.044824812561273575,
0.08993440866470337,
-0.025222159922122955,
-0.008628753013908863,
0.17628024518489838,
0.5328584909439087,
0.5375901460647583,
-0.0808657705783844,
0.689701497554779,
0.2129090130329132,
0.40970444679260254,
0.8387358784675598,
-0.19015879929065704,
-0.0789116621017456,
-0.6726300120353699,
0.5028183460235596,
0.3362436592578888,
-0.16463449597358704,
-0.37635692954063416,
-0.726364016532898,
-0.773086667060852,
-0.5775009393692017,
0.5934694409370422,
0.2417091727256775,
-0.5939127802848816,
0.37763720750808716,
0.05475301668047905,
-0.06370188295841217,
-0.6362525224685669,
0.04214339703321457,
0.5655936598777771,
0.06378932297229767,
0.5815540552139282,
-1.02330482006073,
0.870387852191925,
-0.501758337020874,
0.10081087797880173,
0.9820555448532104,
-0.9672056436538696,
-1.1526339054107666,
-0.6236719489097595,
-0.05844596028327942,
-0.5565319061279297,
0.4072827994823456,
0.9443023800849915,
0.4590917229652405,
-0.3635777235031128,
-0.7901092171669006,
-0.10515785962343216,
0.613040030002594,
-0.5862387418746948,
0.005411130376160145,
0.22532659769058228,
0.1544131636619568,
0.3144494891166687,
0.44803938269615173,
-0.5895851254463196,
-0.619642972946167,
-0.4020061492919922,
-1.1842749118804932,
0.12920479476451874,
-0.5895497798919678,
0.002028459683060646,
-0.1280282437801361,
-0.010900387540459633,
-0.057016629725694656,
0.7948155403137207,
0.2635131776332855,
-0.22979329526424408,
0.0391131155192852,
0.4508337378501892,
-0.19808965921401978,
0.33523112535476685,
0.2171773612499237,
0.3976653218269348,
0.17530600726604462,
0.3700807988643646,
0.012601112946867943,
-0.02233685739338398,
0.17722339928150177,
-0.20954859256744385,
0.21788334846496582,
-0.04817485436797142,
-0.4917706847190857,
-0.3217090666294098,
-0.19375941157341003,
-0.29608187079429626,
-0.3739408552646637,
-0.7520209550857544,
0.6224216818809509,
-0.029967594891786575,
0.263705313205719,
-0.1069561168551445,
-0.25215834379196167,
-0.9383679032325745,
-0.9831110835075378,
0.05317690595984459,
1.0651071071624756,
-0.27281653881073,
-0.11012923717498779,
0.8648790717124939,
-0.5188741087913513,
0.23720590770244598,
0.42832404375076294,
-0.1570134311914444,
-0.609617292881012,
0.2856779396533966,
1.3340833187103271,
0.09416171908378601,
0.49382731318473816,
-0.7024425864219666,
0.6379100680351257,
-0.21851468086242676,
-0.3996117413043976,
-0.3734704554080963,
-0.5767892599105835,
-0.32735419273376465,
-0.4577259123325348,
0.5484055280685425,
0.23885668814182281,
-0.01825729012489319,
0.19311726093292236,
-0.18885453045368195,
0.4478744566440582,
0.06045868992805481,
-0.11348605155944824,
-0.5478550791740417,
0.765420138835907,
0.25423380732536316,
-0.3238922953605652,
-0.12969088554382324,
0.7584880590438843,
0.23507966101169586,
0.7219244837760925,
0.24107857048511505,
-1.1532561779022217,
0.26530250906944275,
-0.04325921833515167,
0.5640319585800171,
0.016768578439950943,
-0.13119953870773315,
-0.295936644077301,
-0.367709219455719,
0.07798852026462555,
0.5171288251876831,
-0.24721652269363403,
-0.524848997592926,
-0.6272556185722351,
-0.5170109868049622,
0.6301925182342529,
-0.07098852097988129,
0.3933176100254059,
-0.23734444379806519,
-0.4438736140727997,
-0.35567036271095276,
1.2575386762619019,
-0.13924740254878998,
0.41824430227279663,
-0.14679290354251862,
-0.05544234439730644,
0.4134214222431183,
0.5726519823074341,
0.545947253704071,
-0.3032582700252533,
0.2021883726119995,
0.34971585869789124,
0.0911833867430687,
0.44037342071533203,
-0.2953474223613739,
0.15465256571769714,
-0.9933028221130371,
0.8325629830360413,
-0.7197979092597961,
-0.09838154911994934,
0.14935749769210815,
0.3041400909423828,
0.7793188691139221,
-1.139248013496399,
0.5955259799957275,
0.8612167239189148,
0.04638250172138214,
0.9007815718650818,
0.24510012567043304,
-0.034534621983766556,
-0.14632536470890045,
-0.43542322516441345,
-0.37899696826934814,
0.3119775354862213,
-0.06960275024175644,
-0.7159072756767273,
-0.5589481592178345,
-0.3107851445674896,
0.014147826470434666,
-0.3302973508834839,
0.5416870713233948,
0.6893309354782104,
0.11623894423246384,
-0.2368876188993454,
0.028136057779192924,
-0.4731103479862213,
-0.3795284628868103,
-0.12199502438306808,
0.15586364269256592,
-0.27041977643966675,
0.11170664429664612,
0.5671799182891846,
-0.34370896220207214,
-0.8086124062538147,
-0.49703556299209595,
0.03402133658528328,
0.7222518920898438,
-0.1815064549446106,
1.1448005437850952,
0.3994026780128479,
-0.2294084131717682,
-0.493902325630188,
-0.2026195228099823,
0.7463748455047607,
0.34429147839546204,
0.5349317789077759,
0.5714648365974426,
-0.1782570481300354,
-0.3172454237937927,
-0.1342306286096573,
-0.41529345512390137,
0.09536323696374893,
1.0912370681762695,
-0.8757253885269165,
-0.10269284248352051,
0.43199896812438965,
0.00801668781787157,
-0.5410745739936829,
-0.4762073755264282,
-1.4920439720153809,
0.0770488977432251,
-0.7962963581085205,
-0.5996356010437012,
-0.6661033034324646,
-0.6851887106895447,
-0.24312342703342438,
0.13592112064361572,
0.8090845942497253,
-0.18716731667518616,
0.2267540842294693,
-0.006372547242790461,
-0.33351969718933105,
0.1253391057252884,
-0.6771196126937866,
1.252243161201477,
0.19595296680927277,
-0.5337492823600769,
-0.6634184718132019,
0.05015898495912552,
-0.7310106158256531,
-0.24552594125270844,
1.020829200744629,
-0.7203434109687805,
0.5060633420944214,
-0.37096071243286133,
0.21297228336334229,
0.9709025025367737,
1.0219837427139282,
0.14923712611198425,
0.1712815761566162,
-0.5598719716072083,
-0.5605886578559875,
0.14065448939800262,
-0.474859356880188,
0.41171175241470337,
0.7756035327911377,
-0.12051347643136978,
-0.13988101482391357,
-0.12692321836948395,
-0.16387276351451874,
0.1268983781337738,
-1.0496338605880737,
-0.4900329113006592,
-0.772007405757904,
-0.2928048074245453,
-0.3969380557537079,
-0.5932092666625977,
-0.09968182444572449,
0.23885904252529144,
-0.3753434717655182,
0.20490819215774536,
-0.8754535913467407,
0.2315167337656021,
0.061849139630794525,
0.16915789246559143,
-0.7986575365066528,
-0.4760928452014923,
-0.20002233982086182,
-0.23037725687026978,
-0.36308184266090393,
-0.3419242203235626,
-0.5034855008125305,
-0.3241894841194153,
-0.008836164139211178,
0.5910347104072571,
-0.0038888328708708286,
0.8738356828689575,
-0.7051411867141724,
-0.6699951887130737,
0.03906770423054695,
-0.21209470927715302,
-0.6768162250518799,
0.1951824277639389,
0.603972852230072,
0.12740938365459442,
0.8190639019012451,
-0.07737242430448532,
-0.15104587376117706,
0.20773491263389587,
-0.9865076541900635,
0.20379610359668732,
0.49440667033195496,
0.7747085094451904,
-0.4324342906475067,
0.24677009880542755,
0.3561803996562958,
0.13512864708900452,
-0.5090046525001526,
0.4047689437866211,
-0.48321089148521423,
0.14912663400173187,
-0.4076231122016907,
0.1361764818429947,
0.24864141643047333,
0.1948753446340561,
-0.12279537320137024,
0.536885142326355,
-0.4375249147415161,
-0.11913934350013733,
0.2944416105747223,
0.14874693751335144,
-0.1765228807926178,
-0.08299432694911957,
0.40287092328071594,
-0.20200215280056,
0.09784700721502304,
0.39926663041114807,
-0.21794196963310242,
0.26944515109062195,
0.02452252246439457,
-0.035701386630535126,
0.08408556878566742,
0.1332775503396988,
-0.6383305788040161,
0.5458551645278931,
-0.07478935271501541,
-0.44634759426116943,
-0.10745804011821747,
-0.3863186836242676,
-0.5430799126625061,
0.21907757222652435,
-0.6421856880187988,
-0.6819102168083191,
-0.07644244283437729,
0.6056801080703735,
-0.47096458077430725,
0.4158429503440857,
-0.05840723589062691,
0.01808290183544159,
0.05072534829378128,
0.5562310218811035,
-0.6476709842681885,
-0.1946025788784027,
-0.06050858646631241,
0.4792238175868988,
-0.27094563841819763,
-0.3265434205532074,
-0.30467912554740906,
0.7859869599342346,
-0.9153711199760437,
-1.0816173553466797,
-0.3924811780452728,
0.8282170295715332,
-0.18101517856121063,
-0.06898283958435059,
-0.12100405991077423,
0.3729007840156555,
-0.18069429695606232,
0.34040847420692444,
-0.255638062953949,
0.16813406348228455,
-0.719532310962677,
0.44574469327926636,
-0.26903265714645386,
-0.3966324031352997,
0.5864498615264893,
0.3416900336742401,
0.25946542620658875,
-0.041516054421663284,
-0.27853450179100037,
1.233077883720398,
-0.08488595485687256,
0.1874314844608307,
0.3514192998409271,
0.022310249507427216,
0.21239908039569855,
0.2497648149728775,
-0.4246620833873749,
0.038103364408016205,
0.21486440300941467,
0.04193776845932007,
0.879351794719696,
-0.20234990119934082,
0.37367603182792664,
0.8035947680473328,
0.03943042829632759,
-0.19129183888435364,
0.2856064736843109,
-0.008315200917422771,
0.2484092116355896,
0.6458338499069214,
-0.0025585985276848078,
-0.2823733687400818,
0.6730470061302185,
-0.2243013083934784,
0.2224843055009842,
-1.0935975313186646,
-0.399628609418869,
-0.4129599928855896,
-0.32237309217453003,
0.6253296732902527,
-0.26101329922676086,
-0.2949032783508301,
0.14914226531982422,
0.2064608782529831,
0.7238377928733826,
0.02237425558269024,
-1.0258487462997437,
0.195058211684227,
0.5113775730133057,
0.5026066899299622,
-0.2226676046848297,
0.4015296995639801,
0.49754762649536133,
1.0847891569137573,
-0.011751231737434864,
0.7399923801422119,
0.30540981888771057,
0.7911205291748047,
0.5106816291809082,
-0.6106794476509094,
-0.014680136926472187,
0.29283079504966736,
-0.5052464008331299,
0.44792285561561584,
-0.44368353486061096,
-0.22328801453113556,
-0.13776470720767975,
-0.4040195047855377,
0.3177533745765686,
-0.46994006633758545,
-0.2286428064107895,
0.6341251730918884,
-0.22449104487895966,
0.007014944218099117,
0.7802577018737793,
-0.022988982498645782,
0.0374784953892231,
0.5264685750007629,
-0.027422327548265457,
1.0971630811691284,
1.1059577465057373,
1.281437873840332,
0.10097073763608932,
0.17232570052146912,
0.22083066403865814,
-0.39691242575645447,
0.38876456022262573,
0.41447973251342773,
-0.3051293194293976,
0.6848385334014893,
-0.6097604036331177,
-0.19128505885601044,
0.11741690337657928,
0.13785307109355927,
-0.42476120591163635,
-0.05143231153488159,
0.39786964654922485,
0.2315087616443634,
-1.236452579498291,
-0.015458496287465096,
1.5167161226272583,
0.572547972202301,
0.14526964724063873,
-0.7596438527107239,
0.14676600694656372,
-0.005590399261564016,
-0.4261499345302582,
-0.7116515636444092,
0.5546068549156189,
-0.5255120992660522,
-0.2132243663072586,
-0.13305863738059998,
-0.2733194828033447,
-0.5622372031211853,
-1.1395164728164673,
0.3332863450050354,
-0.7310488820075989,
0.26767733693122864,
0.3546873927116394,
0.516832709312439,
-0.26794227957725525,
-0.9833779335021973,
-0.37159156799316406,
-0.2503404915332794,
0.8471702933311462,
-0.033181559294462204,
0.4394160807132721,
0.7827688455581665,
-0.5172193050384521,
-0.4384426772594452,
0.046484701335430145,
0.43284788727760315,
-0.5363588929176331,
0.4951461851596832,
-0.3826074004173279,
0.5196881294250488,
0.3920961916446686,
-0.37109455466270447,
-0.3078775405883789,
-0.29812493920326233,
0.08107796311378479,
0.14411497116088867,
-0.21733292937278748,
-0.5464986562728882,
-0.48125240206718445,
-0.3853054940700531,
-0.545573353767395,
-0.09557367861270905,
0.323347270488739,
0.30019262433052063,
-0.01102113351225853,
-1.1441941261291504,
4.265982151031494,
-0.04277770593762398,
0.5474129319190979,
-0.42098283767700195,
0.6175265908241272,
1.1412322521209717,
-0.4587711989879608,
-0.5315002799034119,
-0.20591293275356293,
-0.14632558822631836,
-0.15918827056884766,
-0.16579870879650116,
0.24705597758293152,
0.06531108915805817,
0.18102200329303741,
0.5236439108848572,
0.17407773435115814,
-0.26977768540382385,
0.3216078281402588,
-0.29107823967933655,
-0.6380401253700256,
0.067833311855793,
0.1805562973022461,
0.09022145718336105,
0.2934378385543823,
-0.17061004042625427,
0.05993059650063515,
-0.7478746771812439,
-0.9414004683494568,
-0.6638728976249695,
0.0699925348162651,
-0.24021227657794952,
0.3590235412120819,
-0.1930135190486908,
-0.9227539896965027,
0.5120219588279724,
0.5605669617652893,
-0.19525790214538574,
0.29705142974853516,
0.27846744656562805,
-0.2670193314552307,
-0.35866573452949524,
0.7421616911888123,
0.06186247989535332,
0.12229414284229279,
1.09028959274292,
-0.06393484026193619,
0.7342830300331116,
0.6528093218803406,
-0.4524926245212555,
0.6792176961898804,
-0.1786390244960785,
0.06689672917127609,
-0.387922078371048,
-0.7386869192123413,
0.17061644792556763,
-0.7828941941261292,
0.06425007432699203,
-0.33141574263572693,
0.003451407188549638,
0.3292514681816101,
-0.5287024974822998,
-0.1540701687335968,
-0.20091086626052856,
-0.3061354458332062,
0.11418506503105164,
0.08474995195865631,
0.41850125789642334,
0.3133976459503174,
0.02962687239050865,
-0.09249697625637054,
0.08387699723243713,
-0.3815614879131317,
0.42608439922332764,
0.014317139983177185,
-0.0963374525308609,
-0.4015148878097534,
0.22070194780826569,
0.2583445906639099,
-0.045407071709632874,
0.21161912381649017,
0.2899702489376068,
-0.6025557518005371,
0.18131348490715027,
0.3487282693386078,
1.1886463165283203,
-0.4921863079071045,
-0.10273369401693344,
-0.4894038140773773,
0.2032976746559143,
0.5914599299430847,
1.4910885095596313,
0.0003521685430314392,
0.07705625891685486,
-0.6602503657341003
] |
The String Tension in Gauge Theories: a Suggestion for a New Measurement Method
|
We discuss a new method for testing confinement and measuring the string tension (in the Coulomb gauge). Our numerical simulations demonstrate that the problems related to Gribov copies are not harmful and that the method is effective in the case of pure gauge Q.C.D.. We discuss the relevance of the method for studying gauge theories coupled to fermionic matter.
|
E. Marinari, M. L. Paciello, G. Parisi and B. Taglienti
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210021
|
hep-lat/9210022
|
[
-0.05193405970931053,
-0.21148423850536346,
0.19674168527126312,
0.3219219744205475,
0.0941573902964592,
-0.5002449154853821,
0.049791231751441956,
-0.8476828932762146,
-1.035979151725769,
1.2006442546844482,
-0.08313940465450287,
-0.28634700179100037,
0.5874671936035156,
-0.9181068539619446,
-0.36176860332489014,
0.07219330966472626,
0.08204273134469986,
-0.8416699767112732,
-1.398417592048645,
0.5622929334640503,
-0.23999544978141785,
0.05261419340968132,
-0.4701910614967346,
-0.2962024509906769,
-0.2756412625312805,
0.9778175950050354,
0.18375222384929657,
0.4358036518096924,
0.6587660312652588,
0.6461405754089355,
0.2035960704088211,
-0.6909603476524353,
-0.18997907638549805,
-0.4294092357158661,
-0.4098392724990845,
0.08867157995700836,
-0.5438738465309143,
-0.32590657472610474,
0.795070469379425,
0.13551084697246552,
0.728804349899292,
-0.4282761812210083,
-0.39700379967689514,
-0.025309255346655846,
-0.07634163647890091,
0.08196064829826355,
-0.43807539343833923,
0.48689374327659607,
-0.1445865035057068,
-1.0608916282653809,
0.46241697669029236,
0.2982305884361267,
0.13722801208496094,
-0.447308748960495,
0.20059272646903992,
-0.36538824439048767,
0.15012378990650177,
0.3947891891002655,
-0.4915289282798767,
-0.48608314990997314,
0.2992945611476898,
0.24513588845729828,
0.6296661496162415,
-0.5234112739562988,
-0.49507418274879456,
0.978751540184021,
-0.41499412059783936,
1.0342196226119995,
-0.3338121771812439,
-0.12871578335762024,
0.0021550736855715513,
-0.2742120027542114,
-0.6183870434761047,
0.38913393020629883,
-0.8349308371543884,
-0.03329174593091011,
-0.05144830048084259,
-0.13145151734352112,
-0.2923256456851959,
-0.18164294958114624,
-0.1195274293422699,
0.12354184687137604,
0.014806065708398819,
0.12569960951805115,
0.2347978949546814,
-0.2443714141845703,
-0.6104514002799988,
-0.5303530693054199,
-0.584854781627655,
0.648910641670227,
0.31556862592697144,
0.7118380665779114,
-1.0786992311477661,
-0.004836203530430794,
0.5319002866744995,
0.34240829944610596,
-0.1274658888578415,
0.27880150079727173,
0.01255861483514309,
-0.17467625439167023,
0.2825264036655426,
1.088128924369812,
-0.3497268259525299,
0.7244024276733398,
-0.9664435982704163,
0.44075387716293335,
-0.1378171443939209,
0.43607887625694275,
0.019308974966406822,
-0.8205432891845703,
0.07169616222381592,
-0.3027612864971161,
0.6865895390510559,
0.45863407850265503,
0.3513408303260803,
0.4321117401123047,
-0.7867081761360168,
-0.11235102266073227,
-0.9040024280548096,
-0.3559586703777313,
0.45042112469673157,
0.06954750418663025,
0.3764125108718872,
0.501711368560791,
-0.3801915943622589,
-0.1615639626979828,
0.15904569625854492,
0.4455343186855316,
-0.15695622563362122,
1.1731435060501099,
0.2729431688785553,
0.1062961220741272,
-0.6054075956344604,
0.20172546803951263,
-1.162587285041809,
-0.030997227877378464,
-0.12513688206672668,
0.21635113656520844,
0.4223759174346924,
-0.11636943370103836,
0.8467116355895996,
-0.691494345664978,
-0.06414807587862015,
0.7947810888290405,
0.24453501403331757,
-0.2570025324821472,
0.46961700916290283,
0.25764235854148865,
0.06092754006385803,
0.2585832476615906,
-0.3533723056316376,
0.011592302471399307,
0.2898508608341217,
0.11465731263160706,
-0.12791137397289276,
0.4353715777397156,
-0.5453419089317322,
0.14787398278713226,
-0.35708901286125183,
-0.38512033224105835,
0.5088430643081665,
0.2837086319923401,
-0.23485010862350464,
0.27546995878219604,
-0.48723775148391724,
-0.42926934361457825,
-0.19435077905654907,
-0.3539181351661682,
0.3504147231578827,
-0.29438114166259766,
0.049520932137966156,
0.46832039952278137,
-0.3168201446533203,
0.8997963666915894,
-0.008527392521500587,
-0.15305091440677643,
0.3275679349899292,
-0.3263799250125885,
-0.5213931202888489,
0.028849365189671516,
-0.009037851355969906,
-0.8899163007736206,
0.25951382517814636,
0.2048034816980362,
-0.5567379593849182,
-0.08857784420251846,
0.16284041106700897,
-0.38370242714881897,
0.24827179312705994,
0.33315134048461914,
-0.08692672848701477,
0.4085110127925873,
-0.3529551029205322,
0.6010477542877197,
-0.4722933769226074,
0.17479360103607178,
-1.1465243101119995,
0.4290182590484619,
-0.12402977049350739,
-0.016938339918851852,
-0.025751525536179543,
0.28970298171043396,
-1.314025640487671,
0.39460599422454834,
-1.0156571865081787,
-0.30514204502105713,
0.42166945338249207,
0.3597230017185211,
-0.41256681084632874,
-0.016158942133188248,
0.4396646320819855,
-0.4907451272010803,
0.013679923489689827,
-0.448163777589798,
0.2577376663684845,
0.3211672306060791,
0.10937079042196274,
0.03927553817629814,
0.5074538588523865,
0.5817267894744873,
0.4479963481426239,
-0.1111682876944542,
0.4241674542427063,
0.6344705820083618,
-0.507495105266571,
-0.47473469376564026,
0.17325866222381592,
0.6743389368057251,
0.35059666633605957,
-0.43108320236206055,
0.22090674936771393,
0.46770423650741577,
0.029196666553616524,
0.9074374437332153,
0.5589478015899658,
-0.06379347294569016,
0.43254345655441284,
0.6025213003158569,
0.3094311058521271,
0.16786733269691467,
-0.18619273602962494,
-0.31103602051734924,
0.5612162351608276,
-0.08613688498735428,
-0.308112233877182,
0.20260611176490784,
-0.35624757409095764,
0.3920292854309082,
-0.5371618866920471,
0.15355631709098816,
-0.396469384431839,
0.041298702359199524,
-0.4218743145465851,
0.3870184123516083,
-1.5090253353118896,
-0.12950651347637177,
-0.054484330117702484,
0.2792899012565613,
-0.33936622738838196,
-0.13872668147087097,
-0.27527469396591187,
0.34982892870903015,
-0.24007593095302582,
-0.18206477165222168,
-0.43772614002227783,
0.734225869178772,
-0.1361856311559677,
-0.007660238537937403,
0.5813169479370117,
-0.32303255796432495,
-0.9961068630218506,
0.3211670219898224,
-0.8006335496902466,
-0.2705012261867523,
-0.47534310817718506,
0.6387064456939697,
0.23474571108818054,
-0.6626641154289246,
0.5595685243606567,
0.31169116497039795,
-0.202146515250206,
-0.03723639249801636,
-0.02129450812935829,
0.27244246006011963,
0.34377390146255493,
0.679119884967804,
-0.812666118144989,
0.1318952888250351,
-0.5295356512069702,
0.016087697818875313,
-0.5609144568443298,
-0.06734201312065125,
0.29467567801475525,
-0.3956112861633301,
0.3093595802783966,
-0.027271343395113945,
-0.5008238554000854,
-0.20664744079113007,
0.2870117127895355,
-0.1457170844078064,
0.06572512537240982,
0.15760110318660736,
-0.3136947453022003,
0.3584299385547638,
-0.7794984579086304,
0.5777140259742737,
-0.031408634036779404,
-0.354105144739151,
0.2097661793231964,
0.06610668450593948,
-0.7509647607803345,
0.6300382614135742,
0.4231213331222534,
-0.339270681142807,
0.07731199264526367,
0.5747648477554321,
0.5312804579734802,
0.22694672644138336,
-0.024492425844073296,
-0.06347808241844177,
-0.26664310693740845,
0.15297311544418335,
0.3140029311180115,
-0.4167204797267914,
0.0010293804807588458,
0.33368200063705444,
-0.17226149141788483,
-0.23991753160953522,
0.9315659403800964,
-1.2566291093826294,
-0.7420324683189392,
-0.07488219439983368,
-0.7683581709861755,
0.23223434388637543,
-0.22968770563602448,
0.06976812332868576,
-1.2004473209381104,
-0.3006373941898346,
0.4499775171279907,
0.346244215965271,
0.3808903396129608,
0.10106004774570465,
0.36434340476989746,
-0.013109114021062851,
0.5509166717529297,
-0.5317708253860474,
0.1355813592672348,
-0.14315113425254822,
-0.7366628646850586,
-0.4881293475627899,
-0.19159573316574097,
0.388247013092041,
-0.03140171617269516,
0.14677269756793976,
-0.10264627635478973,
0.39062634110450745,
-0.7086493372917175,
-0.12269018590450287,
-0.45961427688598633,
-0.5354769825935364,
0.10453803837299347,
0.7933936715126038,
-0.24901451170444489,
-0.1414036750793457,
-0.615469753742218,
-0.046464093029499054,
-0.048221737146377563,
0.3443712890148163,
0.09869532287120819,
-0.4088728427886963,
0.017567770555615425,
-0.2143120914697647,
-0.6166277527809143,
0.28588420152664185,
-0.00928297359496355,
0.4986281394958496,
1.3049249649047852,
0.06357849389314651,
0.7427931427955627,
-0.015066375955939293,
-0.12054122984409332,
-0.6096466779708862,
1.242857813835144,
0.6316372752189636,
0.08403905481100082,
0.494122177362442,
-0.16725894808769226,
-0.05678076297044754,
-0.5188941359519958,
-0.4407399892807007,
-0.5209760665893555,
-0.4341256022453308,
0.6571595072746277,
-0.2296949326992035,
0.2369455099105835,
0.30867859721183777,
0.23775123059749603,
0.015023713000118732,
-0.03994977846741676,
-0.023285357281565666,
0.4262361228466034,
-0.03627981245517731,
0.03714027255773544,
0.022092552855610847,
-0.15764011442661285,
0.4807462692260742,
-0.1349642127752304,
0.13881981372833252,
-0.008329161442816257,
0.05782485753297806,
-0.28725266456604004,
-0.3594641089439392,
-0.11951262503862381,
-0.4826015830039978,
0.6436490416526794,
0.1617722362279892,
-0.2903023660182953,
0.2977098524570465,
0.49518346786499023,
0.6874475479125977,
-0.5623323321342468,
0.4263269007205963,
0.5983689427375793,
0.7469045519828796,
0.5979042053222656,
-0.6750993728637695,
0.44395169615745544,
-0.10930176824331284,
0.269768625497818,
0.4528702199459076,
-0.9957373738288879,
-0.4751840829849243,
-0.2698764503002167,
0.012033448554575443,
-0.26916563510894775,
-0.04968450218439102,
0.6754680275917053,
0.6458765864372253,
0.32240989804267883,
-0.925511360168457,
-0.12506036460399628,
1.164350986480713,
-0.5737018585205078,
-0.4938868582248688,
0.21593308448791504,
-0.4219391345977783,
0.1528288871049881,
0.0586162768304348,
-0.22556257247924805,
-0.5329011678695679,
-0.021481145173311234,
-0.7607733607292175,
0.40395599603652954,
0.03812568634748459,
-0.6161983609199524,
-0.4562925100326538,
0.12756764888763428,
-0.3084617853164673,
0.32010418176651,
0.2891683280467987,
-0.47641685605049133,
-0.34256625175476074,
-0.41261354088783264,
-0.2577064633369446,
0.062467753887176514,
0.22540543973445892,
0.2676539123058319,
1.0324821472167969,
0.6542854309082031,
0.7018706202507019,
0.2904422879219055,
0.2352737933397293,
-0.1258772313594818,
0.03771442174911499,
0.357025682926178,
-0.20294858515262604,
-0.8451272249221802,
-0.32319775223731995,
-0.12086473405361176,
-0.7502535581588745,
-0.24856653809547424,
0.4785882234573364,
-0.31592103838920593,
0.42419496178627014,
0.07774332165718079,
-0.6094604730606079,
-0.8223667144775391,
-0.4842304587364197,
-0.841826319694519,
0.667264997959137,
-0.16720633208751678,
-0.19020304083824158,
0.4327908456325531,
0.3538559675216675,
0.21286821365356445,
-0.7299932837486267,
-0.5208208560943604,
-0.5841282606124878,
0.15153491497039795,
0.520684540271759,
0.6600411534309387,
0.2385508269071579,
-0.3005756139755249,
1.0385648012161255,
-0.3168487846851349,
0.16558903455734253,
-0.11387768387794495,
-0.6986221671104431,
-0.3323620855808258,
-0.5180653929710388,
0.564225435256958,
0.027727346867322922,
-0.2678276598453522,
0.21087317168712616,
-0.3785285949707031,
0.1150844395160675,
-0.09059159457683563,
-0.43486303091049194,
0.06949464976787567,
0.1563582420349121,
0.44550541043281555,
0.11804944276809692,
0.1448814868927002,
0.5302555561065674,
0.4707854092121124,
0.36264768242836,
0.048146333545446396,
-0.9896297454833984,
0.6510176658630371,
-0.3210587501525879,
0.5710182189941406,
-0.9878361225128174,
0.357296884059906,
0.37495821714401245,
-0.27545616030693054,
0.06625383347272873,
0.9632266163825989,
-0.30618998408317566,
-0.6275671720504761,
-0.16086728870868683,
0.0869319960474968,
-0.29755958914756775,
-0.4927513301372528,
-0.051958318799734116,
-0.18444505333900452,
-0.5919434428215027,
-0.5909671783447266,
1.008156180381775,
-0.13304229080677032,
0.7139798402786255,
-0.007775445934385061,
-0.06991134583950043,
0.12178829312324524,
0.2823864221572876,
0.6361426115036011,
0.15564849972724915,
0.3724185526371002,
0.29379940032958984,
-0.0928676649928093,
0.47553205490112305,
-0.46247684955596924,
0.1838093400001526,
-0.7068062424659729,
0.830416738986969,
-0.6314812898635864,
-0.5495344996452332,
0.31314998865127563,
0.9600203633308411,
0.5338977575302124,
-0.7887184619903564,
0.7100322246551514,
0.4825229048728943,
-0.10115694999694824,
0.36001113057136536,
0.6569719910621643,
-0.46603813767433167,
-0.10517306625843048,
-0.6015611886978149,
-0.8771324753761292,
0.2834184765815735,
0.11708005517721176,
-0.16085314750671387,
-0.24662412703037262,
-0.22396093606948853,
-0.045864373445510864,
-0.032298099249601364,
0.0947420746088028,
-0.27325835824012756,
0.3586929142475128,
0.09877248108386993,
-0.3353605568408966,
0.3386373817920685,
-0.3643020987510681,
0.4241754114627838,
-0.0045531862415373325,
0.008139549754559994,
-0.17169523239135742,
0.32104140520095825,
-0.3407663404941559,
-0.4620910882949829,
0.04055091366171837,
0.09030210226774216,
0.26160120964050293,
-0.1288161426782608,
1.0477501153945923,
-0.09535151720046997,
-0.3345436751842499,
0.13977080583572388,
-0.2788470983505249,
0.4394219219684601,
0.028285449370741844,
0.5099993348121643,
0.5617708563804626,
0.2531760334968567,
0.009873798117041588,
0.26741063594818115,
-0.04596228525042534,
-0.2859986126422882,
0.5096091628074646,
-0.5005565881729126,
0.28663963079452515,
0.8391749858856201,
-0.030580712482333183,
-0.3975597023963928,
-0.05700988322496414,
-0.9767745137214661,
-0.5812705755233765,
0.07336974143981934,
-0.41585904359817505,
-0.26813745498657227,
-0.16708900034427643,
-0.3868923485279083,
0.22329501807689667,
0.7437112927436829,
0.3060319423675537,
-0.1512300968170166,
0.5403317213058472,
-0.4683246910572052,
-0.3424718976020813,
-0.1415356695652008,
1.1159340143203735,
0.019694678485393524,
-0.8602280616760254,
0.1667598932981491,
-0.02353016845881939,
-0.6149994134902954,
-0.4307069778442383,
0.6201292276382446,
-0.44192472100257874,
0.5584606528282166,
-0.5340424180030823,
-0.11181933432817459,
0.23281735181808472,
0.748153805732727,
0.250133216381073,
-0.19797702133655548,
-0.03244001790881157,
-0.5840865969657898,
0.2497270256280899,
-0.278374582529068,
0.09058533608913422,
0.33754679560661316,
-0.17631103098392487,
0.4294249713420868,
-0.26993075013160706,
-0.5860838890075684,
-0.2459692656993866,
-0.7579820156097412,
-0.2248920351266861,
-1.3101658821105957,
-0.1805989146232605,
-0.3624579608440399,
0.03218759596347809,
0.12334088236093521,
0.5981076955795288,
-0.495172917842865,
0.2244994193315506,
-0.36508187651634216,
0.04685032367706299,
0.1800582855939865,
-0.022434284910559654,
-0.1457379013299942,
-1.136938452720642,
-0.39367640018463135,
-0.38299816846847534,
-0.5452649593353271,
-0.48890945315361023,
-0.19329752027988434,
-0.18330177664756775,
-0.21014392375946045,
0.3612253665924072,
-0.004166288301348686,
0.38404127955436707,
-0.7237515449523926,
-0.8656085133552551,
-0.0024952914100140333,
0.3625509440898895,
-0.7614486217498779,
0.6891012191772461,
0.6281920075416565,
0.5910658240318298,
0.5080583095550537,
-0.38352566957473755,
-0.20462188124656677,
-0.07001622766256332,
-0.81798255443573,
0.0404643751680851,
0.4809614419937134,
0.5042601823806763,
-0.15341737866401672,
-0.7992315292358398,
-0.044192828238010406,
0.6602975726127625,
-1.0010526180267334,
0.1536363959312439,
-0.4274697005748749,
0.47343355417251587,
-0.5322861671447754,
0.20314812660217285,
0.09221197664737701,
-0.11288483440876007,
0.24356141686439514,
1.3540115356445312,
-0.25867196917533875,
-0.014354974962770939,
0.4118328392505646,
0.5191903114318848,
-1.1237576007843018,
-0.25961804389953613,
0.3960553705692291,
0.20396383106708527,
0.017805911600589752,
0.4612797498703003,
-0.2129308432340622,
0.4170691967010498,
0.2538231611251831,
-0.6260036826133728,
-0.2740786671638489,
-0.9290283918380737,
-0.49310052394866943,
0.45816710591316223,
0.6019595861434937,
-0.671336829662323,
0.03332246467471123,
-0.7847684621810913,
-0.9038222432136536,
0.1795116364955902,
-0.195738285779953,
-0.003784891916438937,
-0.42544376850128174,
-0.6410408020019531,
-0.03699803724884987,
0.1664094477891922,
-0.12118634581565857,
0.12274283915758133,
0.09253480285406113,
0.5615394711494446,
0.06105220317840576,
-0.47713232040405273,
-0.1800415962934494,
-0.06527344882488251,
-0.6133362054824829,
-0.15355893969535828,
-0.4869540333747864,
0.435057669878006,
-0.4375061094760895,
-0.8778607249259949,
-0.4884818196296692,
0.5670486688613892,
-0.09074260294437408,
-0.465127170085907,
-0.11314369738101959,
-0.739391565322876,
-0.1830333024263382,
-0.164700448513031,
-0.6972953677177429,
-0.3675387501716614,
-0.7292292714118958,
-0.202538400888443,
-0.11436016857624054,
-0.5369173288345337,
0.3120102286338806,
-0.7155243754386902,
-0.39351415634155273,
-0.3348752558231354,
-0.47316160798072815,
1.3924767971038818,
0.2350941002368927,
-0.3768012821674347,
0.4224518835544586,
0.11314766108989716,
-0.35115504264831543,
0.33939459919929504,
-0.5387684106826782,
-0.14358866214752197,
0.4502377212047577,
0.5055127739906311,
0.7118932008743286,
0.2804490327835083,
0.36083555221557617,
0.3101675510406494,
0.4605698883533478,
0.5495939254760742,
0.2995856702327728,
0.48204320669174194,
0.16854731738567352,
0.8541251420974731,
-0.0060475068166852,
0.040314752608537674,
0.3320122957229614,
0.08910422772169113,
0.5505187511444092,
-0.21150702238082886,
-0.15205317735671997,
0.18252281844615936,
0.16355523467063904,
0.19255173206329346,
-1.1442134380340576,
-0.5484983921051025,
-0.30419033765792847,
-0.1331019103527069,
0.38266700506210327,
-0.016401924192905426,
-0.30343717336654663,
0.3064720928668976,
0.333515465259552,
-0.12606529891490936,
-0.140745609998703,
0.45743313431739807,
0.03971299156546593,
1.2651302814483643,
0.7103700637817383,
0.49551185965538025,
0.21334432065486908,
0.12683157622814178,
0.13694363832473755,
-0.5779849290847778,
0.044409431517124176,
0.35793623328208923,
-0.8982828855514526,
0.20697477459907532,
-0.2586030960083008,
-0.02574712038040161,
-0.14591391384601593,
0.09319183230400085,
-0.01994401589035988,
-0.4298602342605591,
0.008572748862206936,
0.44028139114379883,
-0.5088257193565369,
0.3882046937942505,
0.34924301505088806,
0.2745356857776642,
0.08361127227544785,
0.22392086684703827,
-0.2145450860261917,
-0.11100161075592041,
1.3046728372573853,
0.9797406196594238,
-0.18115784227848053,
0.36403775215148926,
0.37432584166526794,
-0.40403687953948975,
0.35522374510765076,
0.5112194418907166,
0.22945328056812286,
0.16976095736026764,
-0.43363261222839355,
-0.5161232352256775,
0.2968983054161072,
0.03896579146385193,
0.28654152154922485,
-0.04008133336901665,
0.4162515103816986,
0.01700899377465248,
-0.5302242040634155,
-0.03781147673726082,
1.409072756767273,
0.05603154003620148,
-0.3614186942577362,
-0.5368179678916931,
-0.1354910135269165,
-0.30460402369499207,
-0.4688822627067566,
-0.4543865919113159,
0.6800920963287354,
0.2947697341442108,
0.073673315346241,
-0.04381434619426727,
-0.48531436920166016,
-0.781361997127533,
-0.7816689014434814,
0.2857345640659332,
-0.7690653800964355,
0.25502726435661316,
0.5117978453636169,
-0.22070790827274323,
0.4638867676258087,
-0.4318748116493225,
0.12691564857959747,
0.34880775213241577,
0.9808225631713867,
-0.4014257788658142,
-0.2505369484424591,
0.31095248460769653,
0.10672084242105484,
-0.6465410590171814,
0.9399843215942383,
1.0123209953308105,
-0.49754229187965393,
0.26626965403556824,
-0.7413671016693115,
0.3877072334289551,
0.5300483107566833,
-0.1320255845785141,
0.4023567736148834,
-0.039886973798274994,
-0.08053842186927795,
0.2539656460285187,
-0.16820257902145386,
0.3702496886253357,
-0.5864250063896179,
0.6150223612785339,
-0.282007098197937,
0.0029395294841378927,
0.2472711056470871,
0.1906214952468872,
-0.067069411277771,
-0.8615163564682007,
4.522373676300049,
0.5901896953582764,
0.6629626750946045,
0.2846760153770447,
0.4253652095794678,
1.0849217176437378,
-0.30880722403526306,
-0.4859556257724762,
0.6185111403465271,
-0.641603410243988,
-0.5984079837799072,
-0.042490825057029724,
0.12538769841194153,
-0.5287538766860962,
-0.46214571595191956,
0.7480546236038208,
-0.4896594285964966,
0.05781682953238487,
0.05835428461432457,
-0.5862780213356018,
-0.5713629722595215,
0.5432021021842957,
0.04203978553414345,
0.10617547482252121,
-0.3053508996963501,
0.5796351432800293,
0.21312321722507477,
-0.8978838920593262,
-0.5056249499320984,
0.07392261177301407,
-1.052459955215454,
-0.7574376463890076,
0.25962474942207336,
-0.12893980741500854,
-1.010711431503296,
0.34329116344451904,
0.18780431151390076,
-0.3749636709690094,
0.07425480335950851,
-0.06003497168421745,
-0.3177627623081207,
-0.6418121457099915,
0.6586380004882812,
-0.0929693654179573,
-0.41363683342933655,
0.9425485730171204,
0.02949940226972103,
0.40308743715286255,
0.4205353558063507,
-0.20632116496562958,
0.33550772070884705,
0.22663147747516632,
0.5811660289764404,
-0.1651768982410431,
-0.8211479783058167,
0.1491841822862625,
-0.28118500113487244,
0.2995184361934662,
0.11755664646625519,
-0.5159335136413574,
0.3740238547325134,
-0.6311739087104797,
-0.1469484567642212,
-0.3282112181186676,
0.034029994159936905,
0.186717689037323,
0.5492269396781921,
0.5928937196731567,
-0.2314782738685608,
-0.6244213581085205,
0.15706802904605865,
-0.7803188562393188,
-0.5174015164375305,
-0.010820110328495502,
0.04276643693447113,
0.024993406608700752,
-0.24649813771247864,
0.22315804660320282,
0.017441026866436005,
-0.03025941550731659,
0.3197651207447052,
-0.009734983555972576,
-0.5949982404708862,
0.3580077886581421,
0.2572330832481384,
0.5973400473594666,
-0.248920276761055,
0.20427192747592926,
0.02942740172147751,
0.10888069868087769,
0.16975048184394836,
1.1026283502578735,
0.0008833669126033783,
0.2209806591272354,
-0.47419366240501404
] |
Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions
|
The fermion mass spectrum is studied in the quenched approximation in the strong coupling vortex phase (VXS) of a globally U(1)$_L \otimes$U(1)$_R$ symmetric scalar-fermion model in two dimensions. In this phase fermion doublers can be completely removed from the physical spectrum by means of a strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase consists most probably only of a massive Dirac fermion which has charge zero with respect to the $U(1)_L$ group. We give evidence that the fermion which is charged with respect to that subgroup is absent in the VXS phase. When the $U(1)_L$ gauge fields are turned on, the neutral fermion may couple chirally to the massive vector boson state in the confinement phase. The outcome is very similar to our findings in the strong coupling symmetric phase (PMS) of fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the exception that in four dimensions the neutral fermion does most probably decouple from the bosonic bound states.
|
Wolfgang Bock, Asit K. De, Erich Focht and Jan Smit
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210022
|
hep-lat/9210023
|
[
0.5550316572189331,
0.5140961408615112,
0.059003859758377075,
0.06828111410140991,
-0.2170402556657791,
-0.20349742472171783,
-0.00012058625725330785,
-0.15900124609470367,
-0.9070066213607788,
1.4898086786270142,
1.2172422409057617,
-0.11510811001062393,
0.7125539779663086,
-0.9180644154548645,
-0.3162360191345215,
0.6030229926109314,
-0.06173703446984291,
-0.3138062357902527,
-1.2394448518753052,
-0.1538621485233307,
-0.029185423627495766,
-0.2765887975692749,
-1.5357328653335571,
-0.1803874969482422,
-0.4318617284297943,
0.88406902551651,
0.17086830735206604,
0.07049828767776489,
1.3319653272628784,
0.5004761815071106,
0.23028233647346497,
-0.9724438190460205,
0.006528831087052822,
-0.5046374201774597,
0.10101047903299332,
-0.4100583791732788,
0.5299220681190491,
-0.2833267152309418,
0.6865416765213013,
-0.6430849432945251,
1.291779637336731,
0.1604871153831482,
0.2580556273460388,
-0.39936593174934387,
-0.753849446773529,
-0.18495973944664001,
-0.5320420265197754,
-0.24723613262176514,
-0.4017382562160492,
-0.8009466528892517,
0.47622305154800415,
-0.02762756310403347,
0.31498435139656067,
-0.8211142420768738,
-0.0794181227684021,
-0.6494012475013733,
-0.15991075336933136,
-0.03355800732970238,
-0.23980750143527985,
-0.4513823091983795,
0.5855044722557068,
-0.3345643877983093,
0.5521076321601868,
-0.5681097507476807,
0.2595251500606537,
0.8889719843864441,
0.17323826253414154,
0.33544644713401794,
0.16162748634815216,
0.1843288242816925,
-0.5393148064613342,
-0.742281973361969,
-0.4399415850639343,
0.40994322299957275,
-0.32169169187545776,
0.3023858666419983,
-0.05514371395111084,
-0.42542770504951477,
-1.3081622123718262,
-0.08524105697870255,
0.17603567242622375,
-0.7296639680862427,
-0.5900624394416809,
0.5644127726554871,
0.010168012231588364,
-0.16882842779159546,
0.12064099311828613,
-0.3582550585269928,
0.1436893343925476,
0.606481671333313,
0.10644342005252838,
0.878703773021698,
0.1719835251569748,
-0.15683279931545258,
0.42172884941101074,
0.8705772161483765,
0.24368928372859955,
0.06592084467411041,
0.47061362862586975,
-0.024005142971873283,
-0.2638130187988281,
0.8936425447463989,
-0.29380401968955994,
0.46795856952667236,
-0.5140581130981445,
0.15951809287071228,
0.2569771707057953,
0.5295500755310059,
-0.20022039115428925,
-0.408300518989563,
-0.08942004293203354,
-0.5191177725791931,
0.7794424295425415,
1.2367273569107056,
0.1829265058040619,
0.41312068700790405,
0.4578445255756378,
-0.16337746381759644,
-0.3788589537143707,
-0.12684395909309387,
0.3118792176246643,
0.336902379989624,
0.17680834233760834,
0.9346412420272827,
0.15951083600521088,
-0.13715192675590515,
0.10923603177070618,
0.813099205493927,
-0.6081690788269043,
0.3442440629005432,
-0.030213188380002975,
0.07678572833538055,
-0.5714587569236755,
0.5786915421485901,
-0.42446354031562805,
0.4894942045211792,
-0.0027339516673237085,
0.5754592418670654,
0.23098626732826233,
-0.43665117025375366,
0.5684719085693359,
-0.5461235642433167,
0.13660340011119843,
0.7371872067451477,
-0.1764778196811676,
0.2077084481716156,
0.11648207902908325,
0.3324471712112427,
0.0021548359654843807,
0.6224319934844971,
-1.1465808153152466,
-0.057525891810655594,
-0.3082588016986847,
0.4627281725406647,
0.04549983888864517,
0.325900137424469,
-0.6057515740394592,
0.7850708365440369,
-0.9270244836807251,
-0.7727898359298706,
0.36352407932281494,
-0.19794444739818573,
-0.4017581641674042,
0.2713463306427002,
-0.3296965956687927,
0.41671252250671387,
-0.6399003267288208,
-0.6300402879714966,
-0.08578124642372131,
-0.5388122200965881,
0.4299291670322418,
0.1742921620607376,
-0.15522253513336182,
0.9942989945411682,
-0.4296424388885498,
0.1327938437461853,
0.8738049864768982,
-0.8300967812538147,
-0.32930704951286316,
0.0840931087732315,
-0.6049249172210693,
-0.8420725464820862,
0.5973852276802063,
-0.25464755296707153,
0.14686478674411774,
0.5094738006591797,
-0.4600104093551636,
0.1725710779428482,
-0.19117484986782074,
0.17100495100021362,
-0.2841736376285553,
0.5651636123657227,
-0.23814508318901062,
0.5403311848640442,
-0.7488583326339722,
0.059768110513687134,
-0.9134387969970703,
0.5934504866600037,
-0.6527548432350159,
-0.8529177904129028,
-0.04540799558162689,
0.06184582784771919,
-1.133187174797058,
0.5008617639541626,
-1.2370316982269287,
0.22187747061252594,
0.4995962679386139,
-0.04508083686232567,
-0.6657524704933167,
-0.5922899842262268,
0.41467729210853577,
0.08244506269693375,
0.1738469898700714,
-0.49578455090522766,
-0.024596475064754486,
0.1185910701751709,
-0.1509263962507248,
0.08236391842365265,
0.2614716589450836,
0.2577509582042694,
0.4821121096611023,
0.2752743065357208,
0.0992363765835762,
1.0423052310943604,
-0.2081460803747177,
-0.48128247261047363,
-0.02402305044233799,
0.5172396898269653,
0.2913150489330292,
0.03328796848654747,
-0.11945783346891403,
0.9315258264541626,
-0.24395303428173065,
0.5610467791557312,
0.4396184980869293,
0.389570951461792,
0.8158600926399231,
0.8754823803901672,
0.5580158829689026,
0.2364388108253479,
0.21718604862689972,
-0.4091182053089142,
0.6066311597824097,
0.4379027187824249,
0.5726184248924255,
0.5033559799194336,
-0.3984856605529785,
0.06924773752689362,
-0.47876015305519104,
0.8966741561889648,
-0.2987162172794342,
1.1672981977462769,
0.009129820391535759,
0.8316928744316101,
-0.911255419254303,
0.10849966108798981,
0.05782637745141983,
0.29061415791511536,
0.027966612949967384,
-0.6950238943099976,
-0.16257426142692566,
0.09741935133934021,
-0.6082001328468323,
-0.16865026950836182,
-0.1331344097852707,
0.943954586982727,
0.024133669212460518,
0.11988507956266403,
0.05663904920220375,
-0.22055329382419586,
-1.1285918951034546,
-0.22871094942092896,
-0.7955173254013062,
-0.16195666790008545,
-0.6173803210258484,
0.07749373465776443,
1.0788997411727905,
-1.1551196575164795,
0.8721135258674622,
0.28720948100090027,
-0.7153699994087219,
0.2787737250328064,
-0.6093040108680725,
0.4381020963191986,
0.42123648524284363,
-0.35962212085723877,
-0.7114171385765076,
0.20969390869140625,
-0.3908933103084564,
0.4240171015262604,
0.12310730665922165,
0.07372492551803589,
0.5540199875831604,
-0.7563934326171875,
0.4152577519416809,
-0.5094490051269531,
-0.5972033143043518,
0.0839647576212883,
-0.42456236481666565,
-0.2524249851703644,
-0.017544660717248917,
1.1844916343688965,
-0.2178688943386078,
-0.21316641569137573,
-1.0653706789016724,
0.5523605346679688,
-0.14087744057178497,
-0.3247711658477783,
0.8481230735778809,
0.3039528429508209,
-0.596855640411377,
0.10533669590950012,
-0.14612239599227905,
0.052417583763599396,
-0.07549858093261719,
0.8170730471611023,
0.6324405670166016,
0.5257330536842346,
0.6066655516624451,
-0.41845548152923584,
-0.3011973202228546,
0.006830047816038132,
0.19055679440498352,
-0.05640612915158272,
-0.10336967557668686,
1.0939158201217651,
-0.22496472299098969,
-0.6912089586257935,
0.6933732032775879,
-0.5548520088195801,
-0.985717236995697,
0.24077025055885315,
-0.3762807846069336,
0.7086387872695923,
0.08172512799501419,
-0.20066313445568085,
-0.7199650406837463,
0.1550973653793335,
0.1606902927160263,
0.6604178547859192,
0.013374898582696915,
-0.85744708776474,
0.8311309218406677,
0.29506614804267883,
0.5384321808815002,
-0.03749176859855652,
0.3082925081253052,
-0.25817984342575073,
-0.6640515327453613,
0.2579803168773651,
-0.8522442579269409,
-0.063073068857193,
-0.1612088829278946,
0.6513456702232361,
0.16650798916816711,
0.6180444955825806,
0.13425587117671967,
-0.6522022485733032,
-0.8227255344390869,
-0.26222649216651917,
0.7474037408828735,
0.5688201785087585,
-0.03425906226038933,
0.6141930818557739,
-0.7500205039978027,
-0.21442632377147675,
0.5988725423812866,
-0.2849675416946411,
0.8228243589401245,
-0.7894282341003418,
0.08850349485874176,
-0.03099280409514904,
0.0006095858989283442,
-0.08508799225091934,
-0.1636587232351303,
0.5313258171081543,
0.40726715326309204,
0.04651772603392601,
1.1547393798828125,
-1.247969627380371,
-0.6987534165382385,
-0.1620595008134842,
0.7263518571853638,
0.8394007682800293,
0.5692176818847656,
0.5154021382331848,
-0.7600142955780029,
0.2663253843784332,
-0.27902379631996155,
-0.6761528253555298,
-0.6595199108123779,
-0.7725286483764648,
-0.17856678366661072,
-0.46793368458747864,
-0.25248417258262634,
-0.40967312455177307,
-0.011925734579563141,
-0.08559184521436691,
0.5460585951805115,
0.0334046334028244,
0.4796697497367859,
0.16263648867607117,
0.8371291756629944,
0.9044714570045471,
0.18166226148605347,
-0.25488269329071045,
-0.8067247271537781,
-0.19392047822475433,
0.22340361773967743,
0.14545083045959473,
-0.3537954092025757,
-0.39887675642967224,
-0.4349480867385864,
-0.7750803828239441,
1.0653034448623657,
-0.15348057448863983,
-0.5995328426361084,
0.9163234829902649,
-0.7039957642555237,
0.25513210892677307,
-0.23061856627464294,
-0.016095122322440147,
0.21591150760650635,
0.16953422129154205,
0.2618665099143982,
-1.2888219356536865,
0.8585872650146484,
-0.5951274037361145,
0.45487454533576965,
0.5978708863258362,
-1.0651379823684692,
-1.0258342027664185,
-0.7690192461013794,
-0.47521644830703735,
-0.5646407604217529,
-0.03179849684238434,
0.5459378361701965,
0.06470507383346558,
-0.056229282170534134,
-0.7660166025161743,
-0.39837101101875305,
0.36945176124572754,
-0.5362771153450012,
-0.0630137100815773,
0.24443268775939941,
0.1680811494588852,
0.026101678609848022,
-0.04458806291222572,
0.08282385766506195,
-0.03944703936576843,
0.0208742618560791,
-0.06656070053577423,
0.17480389773845673,
-0.7269908785820007,
-0.7073372602462769,
-0.3195447027683258,
-0.17782951891422272,
-0.8312361240386963,
0.4470040798187256,
-0.623424768447876,
0.2645014524459839,
-0.06764031201601028,
0.2577614486217499,
-0.7592025399208069,
-0.3521374762058258,
0.29658043384552,
-0.2099868208169937,
0.2854560613632202,
0.7075296640396118,
0.2581160068511963,
0.3410106301307678,
1.027622103691101,
-0.2297433614730835,
0.44264334440231323,
0.5434125065803528,
0.15495334565639496,
-0.18164747953414917,
-0.3650713264942169,
-0.08148667216300964,
-0.6886541247367859,
-1.0627212524414062,
0.03168071433901787,
-0.2742249071598053,
0.6104551553726196,
-0.21098069846630096,
-0.5120360851287842,
-0.24612101912498474,
-0.7679505944252014,
-0.7170330286026001,
0.2683236300945282,
0.11403830349445343,
-0.4516702890396118,
0.6188833117485046,
-0.07797495275735855,
-0.06149411201477051,
0.14736701548099518,
-0.37659984827041626,
-0.22166478633880615,
0.2886432409286499,
0.3219633102416992,
-0.09183523803949356,
1.0098001956939697,
-0.31642693281173706,
0.6079580783843994,
-0.06919752806425095,
-0.06246662512421608,
-0.2699761688709259,
-1.0797092914581299,
-0.1584482043981552,
-0.2541961967945099,
-0.5668512582778931,
-0.4231042265892029,
-0.05643078312277794,
-0.27416184544563293,
0.27717992663383484,
-0.22573746740818024,
-0.015778914093971252,
-0.6219756007194519,
-0.3110242486000061,
1.1644309759140015,
-0.1355227679014206,
-0.14574256539344788,
0.44579023122787476,
0.6752498149871826,
0.17602577805519104,
0.1765594482421875,
0.3661424517631531,
-0.9144738912582397,
0.5425525903701782,
-0.09354232251644135,
0.3805553615093231,
-0.7663905620574951,
0.25550615787506104,
0.15730169415473938,
-0.9353813529014587,
0.1429131180047989,
0.9376348257064819,
0.6689919233322144,
0.23527075350284576,
0.3453181982040405,
-0.20671918988227844,
0.28674083948135376,
-0.45265626907348633,
-0.4558909833431244,
-0.25291043519973755,
-0.3497660756111145,
-0.6827166080474854,
0.5810115933418274,
-0.02158571034669876,
0.0659666359424591,
0.44290369749069214,
-0.20084063708782196,
0.16701477766036987,
0.8663603067398071,
0.1388176530599594,
-0.7417730093002319,
0.7793896198272705,
1.1083122491836548,
0.23325741291046143,
-0.2932216227054596,
-0.7787609696388245,
0.5737035274505615,
-1.0333510637283325,
1.2201663255691528,
-0.22768615186214447,
-0.23412160575389862,
-0.19683398306369781,
0.24158452451229095,
0.9486727714538574,
-0.9844849705696106,
0.26828691363334656,
-0.085267074406147,
0.02060946822166443,
0.6445522904396057,
0.6827787160873413,
-0.6212208867073059,
-0.662881076335907,
-1.1974984407424927,
-1.0946215391159058,
0.5209633111953735,
-0.061960041522979736,
-0.031705230474472046,
-0.838245153427124,
-0.2771204113960266,
0.46919533610343933,
0.20495299994945526,
1.0335955619812012,
0.07683927565813065,
0.00045303930528461933,
-0.4218416213989258,
0.3923666179180145,
0.06992673128843307,
-0.6672985553741455,
0.5675716996192932,
0.19837985932826996,
0.07998406141996384,
-0.15296544134616852,
-0.5044738054275513,
-0.3776609003543854,
-0.8783502578735352,
-0.1792253851890564,
0.35078367590904236,
-0.16689759492874146,
-0.14222444593906403,
0.6124970316886902,
-0.4980024993419647,
-0.28734591603279114,
-0.20216743648052216,
-0.18638254702091217,
-0.2964690327644348,
0.28493532538414,
0.8396007418632507,
0.5577792525291443,
0.10797939449548721,
0.032962068915367126,
0.27702274918556213,
-0.8320777416229248,
-0.41802123188972473,
0.4354623854160309,
-0.18939727544784546,
-0.382553368806839,
0.05994599312543869,
0.11386413127183914,
-0.7948604226112366,
-0.22929635643959045,
-0.7396495938301086,
0.15623733401298523,
0.10180368274450302,
-0.509384036064148,
-0.14699478447437286,
-0.09627930074930191,
-0.04979758709669113,
0.5739976167678833,
0.36638253927230835,
-0.2603750228881836,
0.14535360038280487,
-0.10128407925367355,
-0.5196033120155334,
-0.6084317564964294,
0.20465849339962006,
1.248915433883667,
-0.3308833837509155,
-0.16202545166015625,
-0.242949977517128,
-0.5407336950302124,
-0.706664502620697,
0.4374855160713196,
0.5828483700752258,
-0.32101672887802124,
0.35723474621772766,
0.590140163898468,
0.6723169684410095,
-0.0904366672039032,
0.9480105042457581,
0.5015478134155273,
0.07772726565599442,
0.09884542226791382,
-1.05878484249115,
-0.23698940873146057,
0.19203715026378632,
0.5216441750526428,
0.5444144606590271,
0.039914220571517944,
0.25896352529525757,
0.08059339225292206,
-0.4998549818992615,
0.11794702708721161,
-1.0746111869812012,
0.4251551032066345,
-0.9815071821212769,
0.09646041691303253,
-0.5763888955116272,
-0.45593205094337463,
0.4565313160419464,
0.4073444604873657,
0.08382213860750198,
-0.20034803450107574,
-0.5114851593971252,
0.08171256631612778,
0.3202156722545624,
0.0912357047200203,
0.11510976403951645,
-1.029552936553955,
-0.6896183490753174,
-0.3364547789096832,
-0.22265848517417908,
-0.08397744596004486,
-0.5128469467163086,
0.04397919774055481,
-0.03514403849840164,
0.3563362956047058,
-0.7393993735313416,
0.2412489354610443,
-0.31141942739486694,
-0.6224684715270996,
0.479211688041687,
-0.2595408260822296,
-0.6478453874588013,
0.02453608065843582,
-0.47211959958076477,
0.6622661352157593,
-0.12034090608358383,
-0.23921513557434082,
-0.31546300649642944,
0.28309905529022217,
-0.9781941771507263,
-0.605593740940094,
-0.1937500387430191,
0.5084803104400635,
-0.22749567031860352,
-0.42713484168052673,
0.758716881275177,
-0.26355794072151184,
-1.097331166267395,
0.10992542654275894,
-0.3342810869216919,
0.068741075694561,
0.011287723667919636,
0.08219864964485168,
0.012986092828214169,
0.547494649887085,
0.19184935092926025,
1.1095216274261475,
-0.4690478444099426,
-0.6282980442047119,
-0.3548908531665802,
0.17417891323566437,
-0.6113633513450623,
0.7447591423988342,
0.15711578726768494,
-0.35152605175971985,
0.085540771484375,
0.7939006686210632,
-0.3083232343196869,
0.22090034186840057,
-0.32934263348579407,
-0.09056305140256882,
-0.09497876465320587,
-0.3114608824253082,
-0.3451247811317444,
1.0432500839233398,
0.2234009951353073,
-0.6651290655136108,
-0.38051220774650574,
-0.5289175510406494,
-0.5098709464073181,
0.45246708393096924,
-0.8269075751304626,
0.06732142716646194,
-0.1824524849653244,
-0.7827644944190979,
0.3783470392227173,
0.4410204589366913,
-0.028003279119729996,
-0.05422711744904518,
0.3205905258655548,
-0.1153857409954071,
-0.38066092133522034,
-0.014141411520540714,
-0.6331019997596741,
0.2824823260307312,
-0.16493988037109375,
-0.5464911460876465,
-0.398906946182251,
0.3916296660900116,
-1.1058413982391357,
-0.5384092330932617,
0.14007535576820374,
0.6032535433769226,
-0.10935819894075394,
-0.23809604346752167,
-0.43110841512680054,
-0.1673187017440796,
0.02881789207458496,
-0.09255791455507278,
-0.48429006338119507,
-0.20075243711471558,
0.07473493367433548,
0.43830445408821106,
-0.5378196835517883,
-0.9078790545463562,
0.25042590498924255,
0.32613271474838257,
0.2744068503379822,
0.22481349110603333,
-0.4945733845233917,
0.4409312903881073,
-0.20426204800605774,
-0.8366475105285645,
1.254724144935608,
0.002062092535197735,
0.5725446939468384,
0.6476214528083801,
-0.28206533193588257,
0.36914655566215515,
0.0916798785328865,
0.6644951105117798,
1.1000863313674927,
0.1542305052280426,
-0.2950455844402313,
0.20716938376426697,
0.5515482425689697,
0.40715470910072327,
0.3911982774734497,
0.3482053279876709,
0.311646044254303,
0.06355812400579453,
0.17007620632648468,
0.048271629959344864,
0.22007636725902557,
0.24078021943569183,
-0.4425920844078064,
-0.06774187833070755,
0.08296480774879456,
-0.09070917963981628,
0.08157884329557419,
0.1699446588754654,
-0.4947628974914551,
-0.4760073125362396,
-0.4455048739910126,
0.28070878982543945,
0.23789620399475098,
0.190024271607399,
0.1282183676958084,
0.8901324272155762,
0.7415406107902527,
0.09130117297172546,
-0.37880754470825195,
0.5074340105056763,
0.22758060693740845,
0.8279283046722412,
0.07444832473993301,
0.6933445334434509,
0.7044342756271362,
0.3152143657207489,
0.13545352220535278,
-0.7090765833854675,
0.3100748658180237,
-0.0353795550763607,
-1.6109590530395508,
0.5528433322906494,
-0.2799077033996582,
-0.18426044285297394,
0.008745302446186543,
-0.252649188041687,
0.7626174688339233,
-0.7585951089859009,
0.5174630284309387,
0.8070207834243774,
-0.20293904840946198,
0.020835524424910545,
0.19372163712978363,
0.06877387315034866,
1.0479007959365845,
0.56048184633255,
0.07756704092025757,
0.08780703693628311,
0.9046469330787659,
1.1441162824630737,
0.23753492534160614,
0.021943848580121994,
-0.004664155654609203,
-0.3425317108631134,
-0.0676111951470375,
0.3673925995826721,
-0.41357851028442383,
1.0459972620010376,
-0.35933151841163635,
-1.1041406393051147,
-0.025082219392061234,
0.4118833541870117,
-0.3151565492153168,
-0.08089905977249146,
-0.12833727896213531,
0.5425912737846375,
-0.7806603312492371,
-0.42592623829841614,
1.0405317544937134,
0.5491600632667542,
-0.7100551724433899,
-0.731663703918457,
-0.13667550683021545,
-0.048846591264009476,
-0.11264932155609131,
-0.4122083783149719,
0.44480079412460327,
0.18769939243793488,
0.2997072637081146,
-0.03984243795275688,
-0.737302303314209,
-0.5248846411705017,
-0.574751079082489,
-0.15501008927822113,
-0.8720078468322754,
0.7093908190727234,
-0.3794409930706024,
0.2888129651546478,
0.26014021039009094,
-0.5406964421272278,
0.25388118624687195,
-0.03255549073219299,
0.566426157951355,
-0.654653012752533,
0.15074029564857483,
0.9727280139923096,
0.41050201654434204,
-0.4661288559436798,
0.7312191128730774,
1.0065317153930664,
-0.5720574259757996,
0.8553576469421387,
0.06211515888571739,
0.12147253006696701,
-0.034369584172964096,
0.03790218010544777,
0.29328739643096924,
-0.022042106837034225,
0.07383061200380325,
-0.07521427422761917,
-0.40840113162994385,
-0.25204959511756897,
-1.1846086978912354,
0.025441672652959824,
-0.33631595969200134,
0.1786520779132843,
-0.009039701893925667,
0.376830518245697,
0.4882439374923706,
-0.42622658610343933,
4.114972114562988,
0.8844165205955505,
1.0695199966430664,
-0.5572695136070251,
0.4536786675453186,
0.5694789290428162,
-0.4120354652404785,
-1.0371127128601074,
0.39969465136528015,
-0.7924714684486389,
-0.367931067943573,
0.09307829290628433,
0.3546018600463867,
-0.626204252243042,
-0.24097642302513123,
0.3815701901912689,
-0.03258552774786949,
0.11440856754779816,
0.3901236951351166,
-1.118346095085144,
-0.3596082627773285,
0.6862833499908447,
0.15841060876846313,
-0.35861337184906006,
0.4194927513599396,
-0.035632893443107605,
0.505752444267273,
-1.0612763166427612,
-0.4900568425655365,
0.04266052693128586,
-0.7225539088249207,
-0.7712506651878357,
-0.504324734210968,
-0.2810046672821045,
-0.44527342915534973,
0.8730992674827576,
-0.24376405775547028,
-0.6784430146217346,
0.25535377860069275,
0.26270100474357605,
-0.3972005248069763,
0.10123369842767715,
-0.07309633493423462,
0.3408795893192291,
-1.2173511981964111,
1.2434568405151367,
-0.01849307119846344,
1.0893772840499878,
0.3629891872406006,
-0.34833666682243347,
0.7712828516960144,
0.1274208277463913,
0.6839156746864319,
-0.48864713311195374,
-1.228684663772583,
0.45361557602882385,
-0.6585459113121033,
-0.39101383090019226,
-0.42729365825653076,
0.3433421552181244,
1.0836317539215088,
-0.15166553854942322,
-0.2207297682762146,
-0.0649578720331192,
0.06979100406169891,
0.6657623648643494,
0.3492003083229065,
-0.003585991682484746,
-1.086761713027954,
0.40859895944595337,
-0.10313282907009125,
-0.39162421226501465,
-0.743512749671936,
0.02654266729950905,
-0.1954103708267212,
-0.3955496847629547,
-0.5411809682846069,
0.2355193942785263,
0.4154368042945862,
0.34011900424957275,
0.2619074583053589,
-0.34856441617012024,
-0.13648350536823273,
-0.11604481190443039,
-0.12841631472110748,
0.8561157584190369,
-0.12802883982658386,
0.2422463595867157,
0.13651758432388306,
-0.2060101330280304,
-0.08394782245159149,
0.7634084820747375,
0.23643426597118378,
-0.35011398792266846,
-0.8148248195648193
] |
Scattering in a Simple 2-d Lattice Model
|
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.
|
C.R. Gattringer, I. Hip and C.B. Lang
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210023
|
hep-lat/9210024
|
[
0.0033961583394557238,
-0.3396555483341217,
0.5451515913009644,
-0.09830240905284882,
0.24035997688770294,
-0.366426944732666,
0.0732870027422905,
0.21679182350635529,
-0.4516793191432953,
1.369353175163269,
0.7141831517219543,
0.6308127641677856,
-0.19922149181365967,
-0.7846668362617493,
0.19405381381511688,
0.6885132789611816,
-0.3818073272705078,
-0.45109617710113525,
-1.3473827838897705,
0.5829404592514038,
0.41137605905532837,
0.5860744118690491,
-1.483000636100769,
-0.7517815828323364,
-0.09032172709703445,
0.5286493897438049,
0.9107184410095215,
0.3895626664161682,
0.9185361266136169,
0.5338748097419739,
0.5272022485733032,
0.11188465356826782,
-0.1269284188747406,
0.27109795808792114,
-0.48067861795425415,
0.5367840528488159,
-0.16745439171791077,
-0.0825408399105072,
0.781673789024353,
-0.08568529039621353,
0.5674009919166565,
-0.13292428851127625,
-0.42102816700935364,
-0.21235378086566925,
-0.8635861873626709,
0.16988016664981842,
0.11549743264913559,
0.2555233836174011,
-0.357303261756897,
-1.0426678657531738,
-0.027489183470606804,
-0.37793782353401184,
0.5790056586265564,
-1.0863648653030396,
-0.8136765956878662,
-0.12479760497808456,
0.2140396386384964,
-0.42036959528923035,
-0.4383949041366577,
-0.2017064094543457,
0.20552676916122437,
0.12014929205179214,
0.3950835168361664,
-1.0615726709365845,
-0.21484781801700592,
0.20788264274597168,
-0.15445783734321594,
0.9850977063179016,
0.14784418046474457,
-0.4943021237850189,
-0.29720598459243774,
-0.155421644449234,
-0.7315229177474976,
0.4114614427089691,
-0.41784659028053284,
0.6165147423744202,
-0.06875753402709961,
-0.549850583076477,
-1.2530517578125,
-0.5992425084114075,
-0.32175925374031067,
0.41506069898605347,
-0.19279636442661285,
0.6139308214187622,
-0.9452124834060669,
-0.7169166207313538,
-0.05426417663693428,
-0.197970911860466,
-0.04740343615412712,
0.061612319201231,
-0.02444065921008587,
0.3441617488861084,
-0.419411838054657,
0.15912964940071106,
0.9483270049095154,
0.7620836496353149,
-0.32365700602531433,
0.9633992910385132,
0.3539612889289856,
-0.4704398512840271,
-0.05854577571153641,
1.2791049480438232,
-0.4484409689903259,
0.7774512767791748,
-0.10204394906759262,
0.4859125316143036,
-0.006814755033701658,
-0.39970242977142334,
-0.6314924955368042,
-0.8921387195587158,
0.5104149580001831,
-0.5585199594497681,
0.746840238571167,
0.4381687641143799,
0.3420993685722351,
0.5265452861785889,
-0.43027523159980774,
0.16072119772434235,
-0.7028761506080627,
-0.5685638189315796,
0.6455320715904236,
-0.10518704354763031,
0.4364929795265198,
0.4572419226169586,
0.13649213314056396,
-0.3831813931465149,
0.580733060836792,
0.4783659279346466,
-0.28081509470939636,
0.5760165452957153,
0.8665876984596252,
-0.049700602889060974,
0.04159209877252579,
0.16698934137821198,
-0.6985412836074829,
-0.1306707113981247,
-0.7644716501235962,
0.13679566979408264,
0.19271481037139893,
-0.17515088617801666,
0.765461266040802,
-0.6339512467384338,
0.4207649230957031,
1.2338848114013672,
-0.03290119767189026,
0.33801987767219543,
0.032743778079748154,
0.009442958980798721,
-0.3576846718788147,
0.5247352123260498,
-0.2317131757736206,
-0.3528529107570648,
-0.2994018793106079,
0.4174283444881439,
0.018076645210385323,
0.6173514723777771,
-0.6104938387870789,
0.5701504945755005,
-0.7718576788902283,
-0.4096154570579529,
0.42060238122940063,
-0.420829176902771,
-0.6234303116798401,
0.867660403251648,
-0.8292588591575623,
0.4428272247314453,
-0.3717770278453827,
-0.13344217836856842,
-0.024427779018878937,
-0.039999574422836304,
-0.2485235035419464,
0.2344019114971161,
-1.1449090242385864,
1.0904070138931274,
0.6642646789550781,
0.5402003526687622,
0.21048188209533691,
-0.7075156569480896,
-0.03226037696003914,
0.6112408638000488,
-0.07982270419597626,
-1.1032923460006714,
0.5272161960601807,
0.4493122696876526,
-0.7528990507125854,
-0.012310006655752659,
0.20888403058052063,
-0.32915619015693665,
0.10976793617010117,
0.28625327348709106,
-0.3964442014694214,
-0.027679920196533203,
0.2902659475803375,
0.9348000288009644,
-0.9848853945732117,
0.4991799294948578,
-0.9467369914054871,
-0.27394089102745056,
-0.6876627802848816,
0.04189346358180046,
0.15549536049365997,
0.3668213188648224,
-0.5767672061920166,
0.15742117166519165,
-1.1517423391342163,
0.026537176221609116,
0.37129151821136475,
0.44348207116127014,
-0.9567472338676453,
0.1589752733707428,
0.5425629019737244,
-0.6811019778251648,
0.5600742101669312,
-0.520563006401062,
0.7685486674308777,
0.2139948010444641,
-0.4649765193462372,
0.7180527448654175,
-0.09754181653261185,
0.4269126355648041,
0.489125519990921,
0.977524995803833,
-0.5731428265571594,
0.5792822241783142,
-0.35162368416786194,
-0.46427565813064575,
-0.02151680178940296,
0.9717332124710083,
0.2882544994354248,
0.6111202836036682,
0.2585698068141937,
0.15788927674293518,
0.0543334074318409,
0.814302384853363,
1.025220513343811,
0.0912843570113182,
1.0116373300552368,
0.45122241973876953,
0.9765839576721191,
0.8509390354156494,
-0.4046218693256378,
-0.28961125016212463,
0.6479029059410095,
-0.28960981965065,
-0.22603915631771088,
0.09280108660459518,
-0.7240900993347168,
0.48513567447662354,
-0.8892632722854614,
0.7797651886940002,
-0.4632927477359772,
0.22745807468891144,
-0.24973469972610474,
-0.07609989494085312,
-1.2163747549057007,
-0.42710044980049133,
-0.3363366723060608,
0.09903262555599213,
-0.0873737707734108,
-0.02422736957669258,
-0.18083588778972626,
-0.2724393308162689,
0.1271771341562271,
-0.8571549654006958,
-0.6205868721008301,
0.6723318099975586,
-0.17619790136814117,
-0.43058347702026367,
0.25360891222953796,
-0.4255128800868988,
-1.344277024269104,
-0.04423009976744652,
-0.9436119198799133,
-0.15600329637527466,
-0.6812338829040527,
0.05884573236107826,
0.27339714765548706,
-0.23645944893360138,
0.2075597494840622,
0.0018130068201571703,
-0.06820901483297348,
0.49928387999534607,
-0.736335277557373,
0.37960729002952576,
0.7893319725990295,
-0.0015429535415023565,
-1.2830053567886353,
0.057898201048374176,
-0.8781992793083191,
-0.16212426126003265,
0.04449167102575302,
-0.18080876767635345,
1.5470225811004639,
-0.08356408774852753,
0.03720957413315773,
0.0820235088467598,
-0.5581270456314087,
0.27873367071151733,
-0.11019954830408096,
-0.43340015411376953,
-0.06171668320894241,
0.21291965246200562,
0.48652076721191406,
0.23110607266426086,
-1.190807580947876,
0.9419957399368286,
0.5343912243843079,
-0.28363096714019775,
0.22626791894435883,
-0.32766595482826233,
-0.6710962653160095,
0.6756258010864258,
0.5324841737747192,
-0.007351053413003683,
-0.27202853560447693,
0.7757259011268616,
0.4373559057712555,
0.16272364556789398,
-0.870490550994873,
-0.0872117429971695,
-0.5172564387321472,
0.4808540642261505,
-0.1323326826095581,
-0.7149713635444641,
-0.19424721598625183,
0.5055562853813171,
-0.09897428005933762,
-0.5760610103607178,
0.5865800380706787,
-0.517255425453186,
-0.6534423232078552,
-0.25305214524269104,
-0.5225481390953064,
0.5224213600158691,
0.21676002442836761,
0.18809343874454498,
-1.0682246685028076,
0.005139211192727089,
0.29422295093536377,
0.175630122423172,
0.1343105435371399,
0.35714003443717957,
0.5305254459381104,
0.5190867185592651,
0.575992226600647,
-0.17675943672657013,
0.13577508926391602,
-0.1088767945766449,
-0.40163546800613403,
0.9940115809440613,
-0.5194759368896484,
-0.160471573472023,
-0.04998140037059784,
0.03088727593421936,
-0.015177952125668526,
0.4788782000541687,
-0.26645427942276,
-0.4695579707622528,
-0.8856445550918579,
-0.43105170130729675,
1.0276222229003906,
0.9290667772293091,
-0.38314634561538696,
-0.5383912920951843,
-0.8661317229270935,
-0.19929687678813934,
-0.1385771632194519,
0.7148250937461853,
0.6080522537231445,
-0.9738513231277466,
0.24336101114749908,
0.20183977484703064,
-0.06699316948652267,
0.17060747742652893,
-0.571100652217865,
0.08919045329093933,
0.4802402853965759,
-0.0034335937816649675,
0.27497750520706177,
-0.33087024092674255,
-0.5424555540084839,
0.12385718524456024,
1.1674216985702515,
0.7107158899307251,
0.753853976726532,
0.19163937866687775,
-0.35984137654304504,
0.2014954835176468,
-0.2920847535133362,
-0.4438917934894562,
-0.056981515139341354,
-0.24311496317386627,
-0.4051242768764496,
-0.18298140168190002,
-0.16134676337242126,
0.4282437562942505,
0.26776355504989624,
0.4229300618171692,
0.3308711051940918,
0.06572944670915604,
-0.06612533330917358,
0.7409304976463318,
0.4938335716724396,
0.5489667654037476,
-0.7005361914634705,
-0.057359740138053894,
-0.7663464546203613,
0.17389971017837524,
0.7924183011054993,
0.5295671820640564,
0.26448091864585876,
-1.0067821741104126,
-0.11839285492897034,
-0.25761663913726807,
0.5042567253112793,
0.035314835608005524,
-1.0697929859161377,
0.34599804878234863,
0.06843522936105728,
0.6603319048881531,
-0.369871586561203,
0.0006689223228022456,
0.6642933487892151,
0.10384403169155121,
0.10552099347114563,
-0.522447407245636,
-0.5444572567939758,
-1.0929814577102661,
0.5186572074890137,
0.010081016458570957,
-0.785060703754425,
-0.9044867753982544,
-0.6991627216339111,
-0.1265891045331955,
-0.016700899228453636,
0.38093966245651245,
0.697019100189209,
0.12341012060642242,
0.6866163611412048,
-0.8021511435508728,
-0.06324218958616257,
0.7970006465911865,
-0.4142319858074188,
-0.3029992878437042,
0.35006874799728394,
-0.6192595958709717,
-0.07323621213436127,
0.9056053757667542,
-0.0458015576004982,
-0.9129704833030701,
0.22883661091327667,
-0.33730214834213257,
-0.004698131699115038,
-0.40512266755104065,
-0.7894042134284973,
-0.7325562238693237,
-0.31579774618148804,
-0.2717140018939972,
0.5874285697937012,
-0.03998560830950737,
0.3736710250377655,
-0.07914642244577408,
-0.2995882034301758,
-0.058326005935668945,
0.600316047668457,
0.2718510627746582,
0.22870130836963654,
1.1035720109939575,
0.6643983125686646,
0.08917129784822464,
-0.08425669372081757,
-0.03162422403693199,
-0.14466308057308197,
-0.19606231153011322,
0.5502611398696899,
0.04171034321188927,
-0.4201318323612213,
-0.4124661684036255,
-0.2787766754627228,
-0.9732481837272644,
-0.7795817255973816,
0.3426198661327362,
-0.20111091434955597,
0.6548908948898315,
0.2843024730682373,
-0.6889680624008179,
-0.4855768382549286,
-0.8876103162765503,
-0.7225828170776367,
0.43105047941207886,
0.2404869645833969,
-0.3624117076396942,
0.6901941895484924,
-0.4223990738391876,
-0.1361459493637085,
-0.4884120225906372,
0.10273643583059311,
-0.5048637390136719,
-0.1252884864807129,
0.7348658442497253,
0.5235077738761902,
1.178268313407898,
-1.0664862394332886,
0.3411886990070343,
-0.3548889458179474,
0.2194409966468811,
-0.7612743377685547,
-0.1425045132637024,
-0.21277140080928802,
-0.4382919669151306,
-0.14428752660751343,
-0.2678264379501343,
-0.47989681363105774,
0.16414710879325867,
0.2142907828092575,
0.020139915868639946,
-0.4109175205230713,
-0.8421465158462524,
-0.14541251957416534,
0.5753235816955566,
0.48994848132133484,
-0.43715357780456543,
-0.3054138720035553,
0.24570488929748535,
0.21475103497505188,
0.17028933763504028,
-0.3792610168457031,
-0.25043386220932007,
-0.01504481490701437,
-0.7121807336807251,
0.9130279421806335,
-1.2287819385528564,
-0.23218291997909546,
-0.30709654092788696,
-0.7207275032997131,
0.9549525380134583,
0.16973668336868286,
-0.2396954894065857,
-0.27921342849731445,
-0.20834064483642578,
-0.3299744129180908,
0.768897533416748,
-0.36367374658584595,
0.18101608753204346,
-1.1626514196395874,
-0.2126718908548355,
0.16805002093315125,
0.49550166726112366,
0.44955334067344666,
0.3560965359210968,
0.19620877504348755,
-0.18667000532150269,
-0.042349815368652344,
0.48803552985191345,
-0.04580201953649521,
0.03814003989100456,
0.29316169023513794,
0.2711607813835144,
0.26525914669036865,
0.08729296177625656,
-0.26687559485435486,
0.6526976227760315,
-0.8728153705596924,
0.4301658272743225,
-0.36561527848243713,
0.04155512899160385,
0.2541704475879669,
0.13059377670288086,
0.8167846202850342,
-0.70606929063797,
-0.030802972614765167,
0.38802534341812134,
-0.38787102699279785,
0.689046323299408,
0.3397042751312256,
-0.6273431777954102,
-0.73056960105896,
-0.15371981263160706,
-1.015221118927002,
0.29910239577293396,
-0.3018135726451874,
-0.12783506512641907,
-0.8406628370285034,
-0.8124455213546753,
0.4435572028160095,
0.2771088182926178,
0.40614715218544006,
0.313256174325943,
0.18403156101703644,
0.34257054328918457,
-0.3635490834712982,
-0.07463810592889786,
-0.46372732520103455,
-0.23213374614715576,
-0.23694191873073578,
-0.07640838623046875,
-0.07301374524831772,
0.5609583854675293,
-0.5322394371032715,
-0.9027009010314941,
-0.4035148620605469,
0.3344958424568176,
0.19723035395145416,
-0.20149114727973938,
0.45758891105651855,
-0.3886208236217499,
0.14725127816200256,
-0.5841434597969055,
-0.14381036162376404,
0.013945739716291428,
-0.11729294806718826,
0.7156589031219482,
0.8071665167808533,
0.19639495015144348,
0.47934839129447937,
0.6001464128494263,
-0.5068244338035583,
-0.15299853682518005,
0.0944179892539978,
-0.236493319272995,
-0.33608582615852356,
0.6203455328941345,
-0.5150885581970215,
-0.4373038709163666,
-0.28653836250305176,
-1.13918137550354,
-0.13168232142925262,
-0.15771090984344482,
-0.050109751522541046,
0.2062867432832718,
-0.0779084712266922,
0.07905889302492142,
0.6309891939163208,
0.5733138918876648,
0.1320258229970932,
-0.0510529987514019,
0.42941924929618835,
-0.5365363359451294,
-0.0734802782535553,
0.20673096179962158,
0.7508739829063416,
-0.11462729424238205,
-0.3636983633041382,
-0.35960546135902405,
0.2853696048259735,
-0.6199897527694702,
-0.2751658260822296,
0.31803423166275024,
-0.4013093113899231,
0.2681591510772705,
0.19549427926540375,
0.5382154583930969,
0.7454923987388611,
0.18398401141166687,
0.2374030202627182,
-0.6585114598274231,
-0.456989049911499,
-0.5320150852203369,
-0.04112126678228378,
-0.8191969990730286,
0.14301784336566925,
0.6265166401863098,
0.0196590106934309,
0.5582299828529358,
0.20912998914718628,
0.5069384574890137,
-0.3095780313014984,
-0.907925546169281,
-0.533747673034668,
-1.4875372648239136,
0.07292869687080383,
-0.5561704635620117,
-0.47682780027389526,
0.16260755062103271,
0.7345348000526428,
-0.2386731505393982,
0.0640951618552208,
-0.14243271946907043,
-0.5297091007232666,
-0.12847985327243805,
0.7762119770050049,
-0.016022542491555214,
-0.5706954002380371,
-0.2893107831478119,
-0.19807714223861694,
0.15666453540325165,
-0.29433929920196533,
-0.28515347838401794,
-0.122477225959301,
0.39287880063056946,
0.569465696811676,
0.4491877853870392,
0.271211177110672,
-0.38430720567703247,
-0.7102336287498474,
0.47323256731033325,
-0.08463466912508011,
-1.2312324047088623,
0.8294987678527832,
0.14155834913253784,
0.8647745847702026,
0.6573514342308044,
0.41894763708114624,
-1.0012918710708618,
0.38104838132858276,
-0.8175467848777771,
-0.29005011916160583,
0.473125159740448,
-0.037942979484796524,
-0.41939449310302734,
-0.5268059968948364,
0.39367908239364624,
-0.4750664532184601,
-0.8185929656028748,
0.8033528923988342,
-0.20388709008693695,
0.13968618214130402,
-0.07753194868564606,
0.5019401907920837,
0.06717738509178162,
-0.17579370737075806,
0.2253178507089615,
0.7053079009056091,
-0.39479270577430725,
-0.016568629071116447,
0.43066608905792236,
0.3203996419906616,
-0.2742193937301636,
-0.09682677686214447,
0.40682873129844666,
-0.08699171990156174,
0.10022801905870438,
0.510939359664917,
0.3849545121192932,
0.2608228325843811,
0.16866599023342133,
-0.8078567981719971,
-0.16793487966060638,
-0.3629968464374542,
-0.28588974475860596,
0.5719224810600281,
0.045186471194028854,
-0.9038081169128418,
0.4190247654914856,
-0.7206881642341614,
-0.5453658103942871,
-0.3243240416049957,
-1.3269457817077637,
0.012112673372030258,
0.8422893285751343,
-0.12041505426168442,
0.7237219214439392,
0.5629495978355408,
-0.3628958463668823,
-0.13307960331439972,
-0.010406381450593472,
1.1808522939682007,
0.40800008177757263,
-0.42219093441963196,
0.11064726859331131,
-0.2668650150299072,
-1.0186123847961426,
-0.46873706579208374,
-0.04725255072116852,
0.22585344314575195,
-0.4346422255039215,
-0.7558280229568481,
-0.04089987650513649,
0.24341562390327454,
-0.34732773900032043,
0.3938343822956085,
0.21847011148929596,
-0.3130043148994446,
-0.11050320416688919,
-0.419076144695282,
0.1985381543636322,
-0.019151834771037102,
-0.7449947595596313,
0.36160123348236084,
-0.37810733914375305,
-0.9551252722740173,
-0.09888263046741486,
0.18203723430633545,
0.35197576880455017,
-0.17071327567100525,
-0.025522198528051376,
0.807421863079071,
0.6546140909194946,
-0.4863867461681366,
0.24924030900001526,
-0.3900067210197449,
-0.09332206845283508,
0.052150677889585495,
-0.2836156189441681,
0.9071671962738037,
0.6999983191490173,
0.7397045493125916,
0.9070637822151184,
0.05360567942261696,
0.12301725149154663,
0.11485974490642548,
0.7430298328399658,
0.40160301327705383,
-0.030755504965782166,
-0.06613738089799881,
0.6590606570243835,
0.7029216289520264,
-0.09166844934225082,
-0.4309351146221161,
0.05993719398975372,
-0.2803388833999634,
-0.051108218729496,
0.20537354052066803,
-0.3472347855567932,
-0.05788111686706543,
0.2301018089056015,
0.1623152792453766,
-0.15921403467655182,
-0.437182754278183,
-0.06555533409118652,
0.18442335724830627,
0.729234516620636,
-0.04747416451573372,
-0.2919102907180786,
0.4708220958709717,
0.5382024645805359,
-0.3816315531730652,
0.07431794703006744,
0.7638033628463745,
0.18326926231384277,
0.7483698129653931,
0.989286482334137,
0.37382030487060547,
0.4958883225917816,
0.1442740112543106,
0.23494216799736023,
-0.8133625388145447,
0.058782435953617096,
0.28761541843414307,
-0.9436582326889038,
0.2808699905872345,
-0.03543751686811447,
-0.3402690589427948,
-0.7532007098197937,
-0.4202500879764557,
0.05970069766044617,
-0.14106722176074982,
0.14829280972480774,
0.46063825488090515,
-0.7027343511581421,
0.0504034198820591,
0.7182461619377136,
-0.18308964371681213,
0.3970019519329071,
0.4893772006034851,
-0.04733928665518761,
0.11178651452064514,
0.7995790839195251,
0.7831882834434509,
0.34753671288490295,
0.305325984954834,
-0.3525993824005127,
-0.6360470652580261,
0.5034646391868591,
0.645143449306488,
0.16842220723628998,
0.14316527545452118,
-0.7390524744987488,
-0.1403132826089859,
0.23370914161205292,
0.13850697875022888,
0.11288521438837051,
-0.5896373987197876,
0.36197197437286377,
0.5581660270690918,
-0.24226008355617523,
-0.08013471961021423,
0.9354312419891357,
0.42056167125701904,
-0.916944146156311,
0.08603782206773758,
-0.11117922514677048,
-1.0357664823532104,
-0.3537810742855072,
-1.2251057624816895,
0.6631274223327637,
-0.2348576784133911,
0.2655336558818817,
-0.3080132305622101,
-0.26993632316589355,
-0.6856792569160461,
-0.5417820811271667,
0.6558747291564941,
-0.9242377877235413,
0.38178715109825134,
0.708434522151947,
-0.2521073818206787,
0.6148675680160522,
-0.5251360535621643,
-0.23883840441703796,
-0.29175496101379395,
0.762173593044281,
0.3875390291213989,
0.428976446390152,
0.6895385980606079,
0.4699203372001648,
-0.3535166084766388,
0.053171463310718536,
0.8075893521308899,
-0.5720264315605164,
0.8421237468719482,
-0.20267020165920258,
-0.26964008808135986,
0.3993177115917206,
-0.08763045072555542,
0.31685519218444824,
-0.11110519617795944,
-0.051726873964071274,
0.0908021405339241,
0.07099518924951553,
-0.6060546040534973,
-0.5683075189590454,
0.4379989802837372,
-0.7851638793945312,
0.2842230498790741,
-0.43980100750923157,
0.5011090636253357,
0.5403482913970947,
-0.6125280857086182,
4.135087490081787,
1.273010492324829,
0.22952762246131897,
0.550667941570282,
0.5873296856880188,
1.4754998683929443,
-0.5794954299926758,
-0.006791605614125729,
0.2236611694097519,
-1.0392818450927734,
-0.265188992023468,
-0.12293653190135956,
0.14687895774841309,
-0.3823188543319702,
-1.054082989692688,
0.7144697904586792,
-0.24834765493869781,
-0.01991606131196022,
-0.4988403916358948,
-0.6609962582588196,
-0.966628909111023,
0.44245070219039917,
0.005787078756839037,
-0.059924542903900146,
0.09710628539323807,
0.16245907545089722,
0.09155261516571045,
-0.14390583336353302,
-0.2951754629611969,
-0.37385979294776917,
-0.3317525088787079,
-0.7693042755126953,
-0.09628131985664368,
-0.19304774701595306,
-1.1856876611709595,
-0.030402563512325287,
-0.04610258713364601,
-0.58022141456604,
0.518523097038269,
0.3109305202960968,
-0.3976854681968689,
-0.4174453616142273,
0.17488084733486176,
-0.31273290514945984,
-0.6001764535903931,
0.6627914905548096,
0.0181485153734684,
0.47534096240997314,
0.40766671299934387,
-0.6589903235435486,
0.37165653705596924,
-0.060407329350709915,
0.6528784036636353,
-1.3695034980773926,
-0.8327746391296387,
-0.3882264196872711,
-0.6167962551116943,
0.48554304242134094,
0.9791631698608398,
0.1417798548936844,
0.02202160656452179,
0.220118910074234,
-0.5087236762046814,
0.05577211081981659,
-0.16106027364730835,
0.9881966710090637,
0.31779634952545166,
0.4064073860645294,
-0.1678471565246582,
-0.04457250237464905,
-0.04011717811226845,
-0.3342512845993042,
-0.29084083437919617,
0.31826773285865784,
0.09406322985887527,
0.004005845636129379,
-0.08050252497196198,
0.11302174627780914,
-0.2800695300102234,
0.6016908288002014,
-0.516069769859314,
-0.05863141641020775,
-0.023866651579737663,
-0.12359242141246796,
-0.26159244775772095,
0.3972618281841278,
0.2651112377643585,
-0.37911292910575867,
-0.26252636313438416,
0.5649530291557312,
0.15328525006771088,
1.442286491394043,
0.26775333285331726,
-0.4025419056415558,
-0.5002772808074951
] |
Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model
|
By carrying out character expansion and integration over all link variables, the partition function of 3-dimensional pure SU(2) lattice gauge theory is rewritten in terms of 6j symbols. The result is Ponzano-Regge model of 3-dimensional gravity with a term that explicitly breaks general coordinate invariance. Conversely, we show that dual of Ponzano-Regge model is an SU(2) lattice gauge theory where all plaquette variables are constrained to the identity matrix and therefore the model needs no further regularization. Our techniques are applicable to other models with non-abelian symmetries in any dimension and provide duality transform for the partition function.
|
Ramesh Anishetty, Srinath Cheluvaraja, H.S. Sharatchandra and Manu Mathur
|
hep-lat cond-mat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210024
|
hep-lat/9210025
|
[
0.7400856018066406,
0.13267089426517487,
-0.42833295464515686,
-0.14429767429828644,
0.5129305124282837,
-0.4529862701892853,
-0.2990611493587494,
-0.3609411120414734,
-0.675481379032135,
1.7322534322738647,
0.8244615197181702,
0.1908574104309082,
0.14004836976528168,
-1.198237419128418,
-0.0152249401435256,
0.251361221075058,
-0.5899685621261597,
-0.8136213421821594,
-0.8762145638465881,
0.29066208004951477,
0.4872845709323883,
-0.07168879359960556,
-1.4112884998321533,
-0.3502897620201111,
-0.32751527428627014,
1.0966565608978271,
0.6562128663063049,
0.05794917792081833,
1.5025804042816162,
0.5788361430168152,
0.5039976835250854,
-0.15905261039733887,
-0.19532454013824463,
-0.45980304479599,
-0.5069512724876404,
-0.2041473090648651,
-0.0796307772397995,
0.1514977514743805,
0.10776612162590027,
-1.0315313339233398,
0.5967720746994019,
-0.5573400259017944,
0.2486281841993332,
-0.15830160677433014,
-0.6162700057029724,
-0.137657031416893,
0.10242736339569092,
0.2504343092441559,
0.43840986490249634,
-1.2941919565200806,
0.06817369908094406,
0.17088496685028076,
-0.10395902395248413,
-0.38534843921661377,
-0.9546517729759216,
-0.2920379936695099,
0.1193530410528183,
0.5541649460792542,
-0.9103915095329285,
-0.5860416293144226,
1.6397608518600464,
0.1583261936903,
0.44605088233947754,
-1.131522536277771,
0.8647719621658325,
1.06816565990448,
-0.29572615027427673,
0.16103053092956543,
0.4771471917629242,
-0.2950235605239868,
-0.22968049347400665,
-0.5253380537033081,
-0.3404659032821655,
0.14290788769721985,
-0.41977250576019287,
0.780788004398346,
0.29592666029930115,
-0.4193793833255768,
-1.2134865522384644,
-0.5311827659606934,
0.23001687228679657,
-0.16126014292240143,
-0.43429553508758545,
0.5983046293258667,
-0.18820084631443024,
0.0032268879003822803,
0.6898836493492126,
-0.688873827457428,
-0.00950809009373188,
0.00388155784457922,
0.2251235991716385,
0.2640010118484497,
0.26091623306274414,
0.36812570691108704,
0.6039435863494873,
1.0734723806381226,
-0.08661917597055435,
1.0371943712234497,
0.14722010493278503,
0.11577834188938141,
-0.261319100856781,
1.8177293539047241,
-1.4076827764511108,
0.3748006224632263,
-0.41079723834991455,
-0.36565327644348145,
-0.06760889291763306,
-0.13026881217956543,
-0.2868298590183258,
-0.6964306235313416,
0.22223515808582306,
-0.17059551179409027,
-0.17034131288528442,
0.6120673418045044,
0.2781812846660614,
1.2669634819030762,
0.2246047407388687,
0.37073662877082825,
-0.5191394686698914,
-0.37945929169654846,
0.04462730884552002,
0.2068328559398651,
0.377730131149292,
0.46720585227012634,
0.19222263991832733,
-0.5963358879089355,
0.3019731342792511,
0.40846145153045654,
-1.115465760231018,
0.24403081834316254,
-0.09938295930624008,
0.02646820992231369,
-0.4001639783382416,
0.407504677772522,
-0.19993801414966583,
-0.07659406214952469,
-0.011106684803962708,
0.8506244421005249,
0.15132415294647217,
-0.01133059710264206,
0.5336394906044006,
-0.6014142036437988,
0.08515465259552002,
1.2618547677993774,
-0.14007671177387238,
0.18269433081150055,
0.28607112169265747,
-0.539847195148468,
-0.4557943344116211,
0.8427655696868896,
-0.8569551706314087,
-0.5221261978149414,
-0.4624820947647095,
0.7684676051139832,
0.06801088154315948,
0.5006651282310486,
-0.7405632734298706,
0.35225868225097656,
-0.536468505859375,
-0.41589951515197754,
-0.5494180917739868,
-0.09793715924024582,
-0.3832033574581146,
0.725504994392395,
-0.3207377791404724,
0.3013649880886078,
-0.2367306798696518,
0.03760140389204025,
0.4936135411262512,
-0.9743457436561584,
-0.09461700916290283,
-0.3493565320968628,
-0.02266194485127926,
0.6251912713050842,
0.5841800570487976,
0.5378465056419373,
0.1280476450920105,
-0.6308278441429138,
0.25439712405204773,
-0.02955041453242302,
0.4264841079711914,
-0.3152415156364441,
0.7920987606048584,
-0.408029705286026,
-0.5672061443328857,
-0.5364156365394592,
-0.2915482223033905,
-0.31616589426994324,
0.11120741069316864,
0.9373380541801453,
-0.1981869786977768,
0.704121470451355,
-0.3352290093898773,
0.8531201481819153,
-0.32180869579315186,
0.0795564204454422,
-0.45482662320137024,
-0.11935564130544662,
-0.8759832978248596,
-0.8218139410018921,
0.09708420187234879,
0.394989550113678,
-0.27926263213157654,
-0.03370295837521553,
-1.3829058408737183,
0.44650495052337646,
0.17816489934921265,
-0.4751853048801422,
-0.7387368679046631,
-0.32357895374298096,
0.5222898125648499,
-0.3970523774623871,
0.5659287571907043,
-0.6538310050964355,
0.8478133678436279,
0.6658011078834534,
-0.35332047939300537,
-0.28527751564979553,
0.500422477722168,
-0.35907161235809326,
1.4639472961425781,
-0.037061907351017,
-0.14640073478221893,
0.7335858345031738,
-0.2943982481956482,
-0.16231758892536163,
0.022201625630259514,
0.7010079622268677,
0.6701158285140991,
0.4988134503364563,
0.15611812472343445,
0.07470408082008362,
-0.027518030256032944,
0.5123594403266907,
0.7878903150558472,
0.30611395835876465,
0.6403371691703796,
0.5946382284164429,
0.6360717415809631,
0.5056858658790588,
0.22230294346809387,
0.21323053538799286,
0.5851602554321289,
0.37752559781074524,
0.13493521511554718,
0.39268776774406433,
-0.613242506980896,
-0.024819275364279747,
-0.5979099869728088,
-0.09031251817941666,
-0.5340650677680969,
0.6934986710548401,
-0.25234559178352356,
0.20911690592765808,
-0.28977668285369873,
-0.10680823028087616,
0.12467168271541595,
0.3160802125930786,
-0.25977572798728943,
-0.3838740587234497,
0.2559363543987274,
0.3763467073440552,
-0.3324926793575287,
-0.691834568977356,
-0.6865823268890381,
1.4786137342453003,
-0.32073506712913513,
0.19798216223716736,
0.8306226134300232,
-0.38597023487091064,
-1.300463318824768,
-0.08247821778059006,
-0.7607465386390686,
-0.005775798112154007,
0.022454196587204933,
-0.22163544595241547,
0.5963362455368042,
-0.5605732798576355,
0.3623555898666382,
-0.019827239215373993,
-0.44514790177345276,
0.33919021487236023,
-0.0027810547035187483,
0.5209346413612366,
0.33582016825675964,
0.051921796053647995,
-1.22748601436615,
0.08470402657985687,
-0.5403568148612976,
-0.14165546000003815,
0.1606534719467163,
0.2823987603187561,
0.7266068458557129,
0.10357681661844254,
0.47748076915740967,
-0.13410668075084686,
-0.29951080679893494,
-0.09267986565828323,
-0.2911423444747925,
-0.6668248772621155,
0.36989232897758484,
0.6360200643539429,
0.3914262056350708,
-0.44591811299324036,
-0.1725579798221588,
0.30150511860847473,
0.5280609130859375,
-0.6504465937614441,
0.7785950899124146,
0.194399893283844,
-0.675391674041748,
-0.3042808771133423,
-0.4385349452495575,
0.15162748098373413,
-0.04181522876024246,
0.9066144824028015,
1.1843154430389404,
-0.1015983521938324,
-0.08590979874134064,
-0.3729216456413269,
-0.5459907650947571,
-0.22138801217079163,
-0.42094799876213074,
-0.5856867432594299,
-0.3553145229816437,
0.9488758444786072,
-0.3300255239009857,
-0.7375668287277222,
0.7065560817718506,
-0.7962862849235535,
-0.7145782709121704,
0.35157543420791626,
-0.692682683467865,
0.5782672762870789,
0.11523006111383438,
0.1338108628988266,
-0.4781232476234436,
0.006094884127378464,
-0.22706887125968933,
0.5941390991210938,
0.22711525857448578,
-0.24726779758930206,
0.7470930218696594,
0.5344443321228027,
0.3147813379764557,
-0.903754711151123,
0.34837251901626587,
-0.4012470841407776,
0.29235050082206726,
0.49416714906692505,
-0.5016610622406006,
0.16080217063426971,
0.09094645082950592,
0.19584207236766815,
-0.20173430442810059,
0.43328577280044556,
-0.13584934175014496,
-0.27394890785217285,
-0.35920053720474243,
0.12904976308345795,
0.7385457158088684,
1.1723765134811401,
0.1401396244764328,
0.0379708893597126,
-0.6474751830101013,
-0.37134408950805664,
0.6047556400299072,
-0.24806612730026245,
0.9132136106491089,
-1.2644070386886597,
1.0325053930282593,
0.27450716495513916,
-0.5898268222808838,
-0.2440718114376068,
0.5036535263061523,
-0.16189879179000854,
-0.11940202116966248,
1.0763896703720093,
1.0370336771011353,
-0.6316618919372559,
-0.9777891635894775,
0.21773743629455566,
1.220603108406067,
0.5734366178512573,
1.3005450963974,
0.19867217540740967,
-0.12104127556085587,
-0.2867870032787323,
-0.49758556485176086,
-0.20359303057193756,
-0.37269502878189087,
-0.6157633662223816,
-0.5083394646644592,
-0.20284870266914368,
0.23188558220863342,
-0.38332200050354004,
0.7701841592788696,
0.5516340732574463,
0.5822661519050598,
-0.16964425146579742,
0.8803160786628723,
-0.5264734625816345,
0.7816375494003296,
0.986616313457489,
0.5670391321182251,
-0.02320338413119316,
-1.2584383487701416,
0.25945669412612915,
0.5416501760482788,
-0.08560891449451447,
-0.005359424278140068,
-0.5029047131538391,
0.06210660934448242,
-0.1929626166820526,
0.4757902920246124,
-0.2033432424068451,
-0.6172057390213013,
0.4989921450614929,
-0.22220344841480255,
0.8494588732719421,
-0.7408338785171509,
-0.17149293422698975,
1.3783448934555054,
0.7548919320106506,
-0.1835699826478958,
-1.4535249471664429,
0.42272669076919556,
-0.9779337644577026,
0.5182295441627502,
0.7686953544616699,
-0.4225873351097107,
-0.48277178406715393,
-0.7519139647483826,
-0.517200231552124,
-0.5912271738052368,
0.5124956369400024,
0.9003241658210754,
-0.08483017981052399,
-0.13426730036735535,
-0.617128849029541,
-0.22702741622924805,
0.23724408447742462,
0.283978134393692,
-0.49583277106285095,
0.6150299906730652,
-0.12121780961751938,
-0.35917678475379944,
0.9721385836601257,
-0.06925670057535172,
0.2209179550409317,
0.030614474788308144,
-0.011280275881290436,
-0.07794889807701111,
-1.019973874092102,
-0.8544553518295288,
-0.5486217737197876,
-0.32064536213874817,
-0.5857202410697937,
1.1964281797409058,
0.04158312454819679,
0.38983088731765747,
-0.18581697344779968,
0.5873706936836243,
-0.658902645111084,
-0.11250673234462738,
0.11449635028839111,
0.1401432901620865,
-0.044418323785066605,
0.8911312818527222,
-0.024385616183280945,
0.323937326669693,
0.8993083238601685,
-0.11183290183544159,
0.1227942556142807,
0.5188897252082825,
0.5001567602157593,
0.13579638302326202,
-0.48254501819610596,
0.06288278102874756,
-0.4966587722301483,
-0.8196616172790527,
0.14300039410591125,
-0.7315361499786377,
1.1451284885406494,
-0.2555527687072754,
-0.6261240243911743,
-0.5793750286102295,
-0.21953846514225006,
-0.32144683599472046,
0.4925883710384369,
-0.2122812569141388,
-0.1263507753610611,
0.20765313506126404,
-0.8104482293128967,
-0.04346612095832825,
0.3691893517971039,
0.17962145805358887,
0.23456139862537384,
0.6589527130126953,
0.7290396094322205,
-0.28688570857048035,
0.3717765808105469,
-0.7921766638755798,
0.5258464813232422,
-0.6281330585479736,
-0.09121421724557877,
-0.6480463743209839,
-0.8669010996818542,
-0.431674987077713,
0.3075476288795471,
-0.22884951531887054,
-0.4378073513507843,
0.13348768651485443,
-0.02174338325858116,
0.2141660898923874,
-0.34612563252449036,
-0.28990545868873596,
-0.5105593800544739,
-0.5752913355827332,
0.9112735390663147,
-0.15026797354221344,
-1.185427188873291,
-0.46416521072387695,
0.261287122964859,
0.25442832708358765,
-0.032380495220422745,
0.17478418350219727,
-1.2432563304901123,
0.23231111466884613,
-0.6355220675468445,
0.3116740584373474,
-1.1153013706207275,
-0.4563333988189697,
0.08640594035387039,
-1.1063727140426636,
0.1495174765586853,
0.4474059045314789,
0.7561839818954468,
-0.3543015420436859,
0.08008620142936707,
-0.4432726502418518,
1.023892879486084,
-0.5375826954841614,
-0.324526846408844,
-0.5338875651359558,
-0.16737066209316254,
-0.09811004251241684,
0.5636476278305054,
-0.4205976724624634,
-0.10026521980762482,
-0.2766602039337158,
0.47731515765190125,
0.2796570062637329,
0.8890560269355774,
0.4412206709384918,
-0.4280705451965332,
-0.3119361400604248,
0.15739887952804565,
-0.18385708332061768,
0.6683791279792786,
-0.3697252571582794,
0.5077146291732788,
-0.9587850570678711,
0.6595296263694763,
-0.7707369923591614,
0.12776793539524078,
-0.3466304838657379,
-0.49744024872779846,
0.9377520680427551,
-0.8312581777572632,
0.8490844368934631,
0.47757595777511597,
-0.020179374143481255,
0.5462377667427063,
0.5211650133132935,
-0.3431972563266754,
-0.3455946445465088,
-0.7279134392738342,
-0.7186942100524902,
1.3039307594299316,
-0.5338099002838135,
-0.587672233581543,
-1.0009523630142212,
-0.7456870079040527,
0.3207625448703766,
-0.01808580569922924,
0.05938892066478729,
0.6877633333206177,
0.21900247037410736,
0.08281689882278442,
-0.5534672737121582,
-0.408275306224823,
-0.0393148772418499,
0.24796409904956818,
0.45049408078193665,
-0.39119237661361694,
-0.47815296053886414,
-0.06147104501724243,
-0.6447411179542542,
-1.382404088973999,
-0.1762978583574295,
0.9032285809516907,
0.21424473822116852,
-0.30679696798324585,
0.8888237476348877,
-0.8324191570281982,
-0.6994860172271729,
-0.6087783575057983,
-0.0466739758849144,
-0.17680425941944122,
0.24446077644824982,
0.698341965675354,
0.21201331913471222,
0.31067341566085815,
-0.4852398931980133,
0.3655281960964203,
-0.7135634422302246,
0.007819149643182755,
0.9548606276512146,
-0.6141268014907837,
-0.3276349604129791,
0.15982501208782196,
-0.1571974903345108,
-0.9546480774879456,
-0.5958915948867798,
-0.44135552644729614,
0.3596874177455902,
-0.10609867423772812,
-0.5439881682395935,
0.05059308931231499,
-0.08824902772903442,
0.05254095792770386,
0.662300169467926,
0.521217942237854,
-0.5988887548446655,
-0.20762290060520172,
0.4727792739868164,
-0.3477128744125366,
-0.27400195598602295,
0.45442551374435425,
1.2290781736373901,
-0.06328892707824707,
-0.6898927688598633,
0.09453210234642029,
-0.3433467745780945,
0.025366967543959618,
-0.10490752756595612,
0.16510970890522003,
-0.41615408658981323,
0.5306255221366882,
0.7578887343406677,
0.5028226971626282,
0.6240391731262207,
0.5351000428199768,
0.6846948266029358,
-0.4263893961906433,
-0.4598267078399658,
-0.8505352735519409,
-0.9611738324165344,
-0.12095405161380768,
-0.022305622696876526,
0.45598846673965454,
0.3616194725036621,
0.3278900682926178,
0.3922472894191742,
-0.5828967690467834,
-0.11129642277956009,
-0.9136835336685181,
0.10301166027784348,
-0.9909610152244568,
-0.5203740000724792,
-0.3055182695388794,
-0.36278843879699707,
0.055627088993787766,
0.5378526449203491,
-0.19095298647880554,
-0.457781583070755,
0.1414184868335724,
-0.46896713972091675,
-0.400911808013916,
-0.20305871963500977,
0.23421959578990936,
-0.7284452319145203,
-1.366955280303955,
-0.4079267978668213,
-0.5266857147216797,
-0.6156919598579407,
0.3300952613353729,
0.30602189898490906,
0.01799439638853073,
0.7516920566558838,
-0.33175307512283325,
0.927076518535614,
-0.7462220788002014,
-0.22371789813041687,
0.13088755309581757,
-0.39076152443885803,
-0.9780704379081726,
0.00009738975495565683,
-0.41942232847213745,
0.35731375217437744,
0.630159854888916,
0.011305359192192554,
-0.26499783992767334,
0.4188973605632782,
-1.196467399597168,
-0.31468895077705383,
0.3655135929584503,
0.7062435746192932,
-0.6668172478675842,
-1.44048011302948,
0.051392145454883575,
0.17634625732898712,
-1.1423611640930176,
0.05260958895087242,
0.13150492310523987,
-0.0043363370932638645,
-0.7639792561531067,
0.7186664938926697,
-0.14972905814647675,
0.9290353059768677,
0.3200531601905823,
0.4616941213607788,
-0.44985201954841614,
-0.055122099816799164,
-0.42488718032836914,
-0.1186738908290863,
-0.19980637729167938,
-0.03576916828751564,
-0.4771619141101837,
-1.0856446027755737,
-0.10518378764390945,
0.4234059453010559,
-0.3028908371925354,
-0.41056761145591736,
-0.09709588438272476,
0.13701097667217255,
0.015822969377040863,
-0.7012191414833069,
-0.5421380996704102,
0.8953797817230225,
0.45656368136405945,
-0.35534074902534485,
-0.5423693656921387,
-0.4053010642528534,
-0.7002752423286438,
-0.0412152074277401,
-1.194029688835144,
-0.3872591257095337,
-0.20651769638061523,
-0.5495538711547852,
0.13752970099449158,
-0.1667071282863617,
-0.004823936149477959,
0.6288377046585083,
-0.1738424003124237,
0.527256190776825,
-0.3849523365497589,
0.0025407117791473866,
-0.2048853039741516,
0.3584248125553131,
-1.44444739818573,
-0.3522509038448334,
-0.3804912269115448,
0.16457577049732208,
-0.9963794350624084,
-0.878251314163208,
-0.2583427429199219,
0.38471561670303345,
0.11980892717838287,
0.16983307898044586,
-0.4056984782218933,
0.2949511706829071,
0.023891355842351913,
0.018927982077002525,
-1.0744415521621704,
0.2228182852268219,
-0.5950136184692383,
0.3800506591796875,
0.36339253187179565,
-1.2910914421081543,
0.3281499743461609,
0.7673406004905701,
0.9610471725463867,
-0.14160406589508057,
-0.4975281059741974,
0.5823699831962585,
-0.3326238691806793,
-1.1314682960510254,
0.9728437662124634,
0.32406526803970337,
0.8208058476448059,
-0.23686492443084717,
-0.12438879162073135,
0.8563770055770874,
0.6126140356063843,
0.15241743624210358,
0.6154552102088928,
0.2963261902332306,
0.5044875144958496,
0.40517550706863403,
0.65495765209198,
-0.1343415379524231,
0.23905988037586212,
0.4712870121002197,
0.09459110349416733,
-0.36287975311279297,
-0.39989951252937317,
0.3819195032119751,
-0.31685304641723633,
-0.01935923472046852,
0.27645906805992126,
-0.04706556349992752,
-0.08968508243560791,
-0.31761491298675537,
-0.93439120054245,
0.5428414344787598,
-0.9119915962219238,
-0.6754775643348694,
-0.9232189059257507,
0.8522675037384033,
0.16840852797031403,
-0.12360404431819916,
-0.10386201739311218,
0.17701347172260284,
0.2620159685611725,
0.47841939330101013,
-0.07088986784219742,
0.5967686772346497,
0.5552197098731995,
0.5765929818153381,
0.39854979515075684,
1.115749716758728,
0.6103447079658508,
0.18364867568016052,
0.033530402928590775,
-1.012740135192871,
0.43458089232444763,
0.39077654480934143,
-1.4848631620407104,
-0.48252442479133606,
-0.5946308970451355,
-0.21719710528850555,
-0.2792503237724304,
-0.602379560470581,
0.42504075169563293,
-0.9490585327148438,
-0.08799183368682861,
1.270376443862915,
0.45935818552970886,
-0.3580710291862488,
0.5743120312690735,
-0.08478737622499466,
0.669115424156189,
0.8933518528938293,
-0.02271081507205963,
-0.14691832661628723,
1.0690467357635498,
1.3303821086883545,
0.008657988160848618,
0.5958161354064941,
0.11837223917245865,
-0.5726775527000427,
0.3414093554019928,
0.5578655004501343,
-0.6372928023338318,
0.8852746486663818,
-0.5537330508232117,
-0.653461754322052,
0.11820077896118164,
0.06571073830127716,
-0.5521001219749451,
-0.4856586754322052,
0.05723640322685242,
0.6677475571632385,
-0.5983151793479919,
-0.5457568168640137,
1.6405869722366333,
0.11369264870882034,
-0.4925253689289093,
-0.09187568724155426,
0.4372059106826782,
0.1534985601902008,
0.1356639862060547,
-1.1472738981246948,
-0.0021482794545590878,
-0.23913626372814178,
-0.0173984095454216,
-0.49355533719062805,
-1.1317662000656128,
-0.18931064009666443,
-0.9221617579460144,
-0.297508180141449,
-0.43448710441589355,
1.1295816898345947,
0.6638420820236206,
0.3043553829193115,
0.4587898552417755,
-0.5354631543159485,
0.006640496663749218,
0.3597806394100189,
0.6935722827911377,
0.4134056568145752,
0.3551880419254303,
0.9682211875915527,
1.0928012132644653,
-0.6768824458122253,
0.006866883020848036,
0.4681207537651062,
-0.5029093623161316,
0.42715492844581604,
0.0477173738181591,
0.4867374300956726,
0.04906993731856346,
-0.4004925489425659,
0.21744127571582794,
0.669854462146759,
0.6060991287231445,
-0.5668550729751587,
-0.056687064468860626,
0.1081683486700058,
-0.7423821687698364,
0.2748876214027405,
-0.8768924474716187,
0.15682554244995117,
0.6596180200576782,
0.3950716555118561,
-0.026269782334566116,
-0.32962244749069214,
3.6943159103393555,
1.1512455940246582,
1.0741190910339355,
-0.4073217809200287,
1.346556544303894,
0.905188798904419,
0.04759460687637329,
-0.015466530807316303,
0.37223538756370544,
-0.42237502336502075,
-0.03165733814239502,
0.5290957689285278,
0.5620905756950378,
-0.08670616894960403,
-0.6450898051261902,
0.02201375551521778,
-0.49570542573928833,
0.14666375517845154,
0.13105382025241852,
-1.0659552812576294,
-0.9091595411300659,
0.47579827904701233,
0.18312513828277588,
-0.10535385459661484,
0.14510804414749146,
0.03388916701078415,
-0.0931762084364891,
-1.0132285356521606,
-0.34194323420524597,
-0.24151068925857544,
-0.3002893328666687,
-0.5990679860115051,
0.09495275467634201,
-0.228323295712471,
-0.6064150333404541,
0.851673424243927,
0.5853797197341919,
-0.5210683941841125,
-0.09800731390714645,
0.4500299096107483,
-0.3386428952217102,
-0.717736542224884,
-0.3320159912109375,
0.09527825564146042,
-0.34221670031547546,
1.0835261344909668,
-0.201190784573555,
0.2724650800228119,
0.005507525522261858,
-0.9352908730506897,
0.4305468797683716,
0.004103563725948334,
1.0647116899490356,
-0.17081639170646667,
-1.1152263879776,
-0.1596430391073227,
-0.8981103301048279,
-0.8904261589050293,
0.13962185382843018,
0.28240036964416504,
0.9029240608215332,
-0.42683351039886475,
-0.5123398900032043,
0.8780040740966797,
-0.1348424106836319,
0.3661430776119232,
0.3162975609302521,
-0.7379423379898071,
-0.2834292948246002,
0.3160305321216583,
-0.13354648649692535,
0.5422490835189819,
-0.03359256684780121,
0.47664928436279297,
-0.12499338388442993,
0.005196660757064819,
-0.08564557880163193,
0.7074940204620361,
-0.006854422856122255,
0.7632303833961487,
-0.3269582688808441,
-0.44942909479141235,
0.49096396565437317,
0.11230999231338501,
-0.4135385751724243,
1.0392701625823975,
-0.1225750744342804,
-0.11387740075588226,
-0.07888562977313995,
0.4207163155078888,
0.15308967232704163,
1.3430109024047852,
-0.04031120613217354,
-0.2519907057285309,
-0.28547415137290955
] |
Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo
|
We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to overcome critial slowing down for a given model. Our method is introduced in the context of spin models. A multigrid Monte Carlo procedure for nonabelian lattice gauge theory is described, and its kinematics is analyzed in detail.
|
Martin Grabenstein and Klaus Pinn
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210025
|
hep-lat/9210026
|
[
0.33058732748031616,
0.058799419552087784,
-0.09696698188781738,
0.3090501129627228,
-0.25357916951179504,
0.17279262840747833,
0.24550652503967285,
-0.2449388951063156,
-0.8172076940536499,
1.1579588651657104,
0.7365065813064575,
-0.2219683676958084,
0.10809263586997986,
-0.6021296977996826,
-0.16342362761497498,
0.6119722723960876,
0.07867404818534851,
-0.5701024532318115,
-1.2525864839553833,
0.674745500087738,
0.12066732347011566,
-0.45323559641838074,
-1.361413598060608,
0.02417471632361412,
-0.39478254318237305,
0.5854762196540833,
0.022334516048431396,
0.3503977358341217,
0.8353978395462036,
0.7998018860816956,
0.5135849714279175,
-0.2937764525413513,
-0.25005966424942017,
-0.16479092836380005,
-0.310927152633667,
-0.6755671501159668,
-0.38317781686782837,
-0.13713543117046356,
0.6528133749961853,
-0.37807726860046387,
1.1122797727584839,
-0.2822140157222748,
0.32864826917648315,
-0.12930862605571747,
-0.6315520405769348,
-0.16118678450584412,
-0.15669673681259155,
0.2237156182527542,
-0.1097177267074585,
-1.1197339296340942,
0.059878211468458176,
0.5256698131561279,
0.09109091013669968,
-0.9170750975608826,
-0.4023970365524292,
-0.05506758391857147,
0.025494005531072617,
-0.11774766445159912,
-0.7697729468345642,
-0.517907977104187,
0.5594863891601562,
0.07363668084144592,
0.4987069070339203,
-0.8994914889335632,
-0.11791488528251648,
1.3652387857437134,
0.16574764251708984,
0.5083460211753845,
0.3255300521850586,
-0.04111681506037712,
0.003932983614504337,
-0.4250074625015259,
-0.6868500113487244,
-0.07664437592029572,
-0.98347008228302,
0.35937705636024475,
0.26244303584098816,
-0.26987558603286743,
-0.6412602663040161,
0.05129731073975563,
-0.036425985395908356,
0.047309063374996185,
-0.7168610692024231,
0.205572247505188,
-0.7063742280006409,
-0.5703723430633545,
0.43070852756500244,
-0.5266593098640442,
0.41752687096595764,
0.5887404084205627,
-0.703444242477417,
0.6087255477905273,
-0.6111701726913452,
0.5803027749061584,
0.5055543780326843,
0.6962542533874512,
0.11478282511234283,
0.4344463348388672,
-0.03049650602042675,
0.01772799901664257,
-0.3250812590122223,
0.39678463339805603,
-1.0247406959533691,
-0.16750167310237885,
-0.6821759343147278,
0.4979861080646515,
-0.37012505531311035,
0.3011993169784546,
-0.28397685289382935,
-1.1297158002853394,
0.7112596035003662,
-0.07060721516609192,
0.053999923169612885,
0.668328583240509,
0.25741130113601685,
0.3599226474761963,
-0.6309295892715454,
0.526207447052002,
-0.6822389364242554,
-0.3156493902206421,
-0.08578229695558548,
0.34423336386680603,
0.5184275507926941,
0.5563088059425354,
0.06530051678419113,
0.04317045584321022,
0.45897573232650757,
0.39322927594184875,
-0.7548992037773132,
0.30625125765800476,
0.13031357526779175,
-0.47125449776649475,
-0.23876765370368958,
1.2749218940734863,
-0.24741575121879578,
0.23377563059329987,
-0.5646266341209412,
0.4529949128627777,
0.3033193349838257,
-0.24650628864765167,
0.801673412322998,
-0.6900293231010437,
-0.36038002371788025,
1.126484751701355,
-0.3884725570678711,
-0.047066062688827515,
0.2158576399087906,
0.22343628108501434,
-0.22755157947540283,
0.2649776041507721,
-0.26271340250968933,
-0.31846368312835693,
-0.27962803840637207,
0.40297627449035645,
-0.40057238936424255,
0.17972122132778168,
-0.8796972632408142,
-0.41639864444732666,
-0.08709757030010223,
-0.565512478351593,
0.35530611872673035,
0.08609562367200851,
-0.4681251347064972,
0.21478882431983948,
-0.3125750720500946,
0.37480661273002625,
-0.4935685098171234,
0.42299604415893555,
0.7242913842201233,
-0.97581547498703,
-0.15226559340953827,
0.37783876061439514,
-0.29377102851867676,
0.6282012462615967,
0.5946573615074158,
-0.005852320697158575,
0.6994928121566772,
-0.942225992679596,
-0.07134370505809784,
0.18094700574874878,
-0.37734872102737427,
0.2414335161447525,
0.5105485320091248,
0.0839841216802597,
-0.1886235773563385,
-0.6425929069519043,
0.20263861119747162,
0.09383808821439743,
0.2718470096588135,
-0.17768946290016174,
-0.43736451864242554,
0.23488067090511322,
-0.5369313955307007,
0.5519728064537048,
-0.3548847734928131,
-0.08317498862743378,
-1.3951013088226318,
0.2415728121995926,
-0.47173380851745605,
-0.5021349787712097,
0.309780478477478,
0.5298815965652466,
-0.7005420923233032,
0.6123213171958923,
-1.1754621267318726,
0.07205469161272049,
0.8898703455924988,
-0.10215310007333755,
-0.7410644292831421,
0.32768791913986206,
0.5240175127983093,
-0.5260568261146545,
0.09903305023908615,
-0.5453738570213318,
0.1518227756023407,
0.16117781400680542,
-0.25590401887893677,
0.16851197183132172,
0.3623427152633667,
0.4439411759376526,
0.4121876657009125,
-0.09690608084201813,
-0.3229365050792694,
0.6020346283912659,
0.39360421895980835,
-0.26329532265663147,
0.40324318408966064,
0.06918896734714508,
0.08156940340995789,
-0.026195118203759193,
-0.25357961654663086,
0.3283774256706238,
-0.29315057396888733,
0.16751499474048615,
0.6360993385314941,
0.12283304333686829,
0.3828621208667755,
0.3873870372772217,
0.03086715005338192,
0.33149251341819763,
0.3341824412345886,
-0.13081616163253784,
-0.08800909668207169,
-0.5085228085517883,
-0.6306821703910828,
0.1370246261358261,
0.17040027678012848,
-0.04258214309811592,
-0.5297844409942627,
0.6961416006088257,
0.23315970599651337,
0.7142804861068726,
0.1332731544971466,
0.9860110282897949,
-1.3710403442382812,
-0.1317785531282425,
-0.686843752861023,
-0.1102716252207756,
-0.4058596193790436,
0.046625543385744095,
0.19887083768844604,
-0.009694166481494904,
-0.20076346397399902,
-0.7475160360336304,
-0.5090870261192322,
0.5631446838378906,
-0.5795597434043884,
0.0727677196264267,
1.355339527130127,
-0.39659351110458374,
-0.8017794489860535,
0.13908961415290833,
-1.0107769966125488,
0.007427565287798643,
-0.5354536771774292,
-0.28456854820251465,
0.5383967161178589,
-0.6557488441467285,
0.1433168351650238,
-0.2513163387775421,
-0.27492934465408325,
0.6823497414588928,
-0.0647144615650177,
0.12885572016239166,
0.3978478014469147,
0.4685612916946411,
-0.7655019760131836,
0.24226464331150055,
-0.7123435735702515,
-0.11088155955076218,
0.04657221585512161,
-0.1850774735212326,
0.2663407623767853,
0.11804986745119095,
0.5058403611183167,
0.8638107180595398,
-0.6978908777236938,
0.20124810934066772,
0.36171022057533264,
-0.7287607192993164,
0.4176672101020813,
-0.04088116064667702,
0.42728349566459656,
0.3092281222343445,
-1.308364748954773,
0.39111876487731934,
0.5637757182121277,
-0.4698665738105774,
0.5359724760055542,
0.29795244336128235,
-0.5073975920677185,
0.1978563368320465,
-0.5579469799995422,
0.11955229192972183,
-0.23020556569099426,
0.9690192937850952,
0.36825135350227356,
-0.0951056256890297,
-0.21571241319179535,
-0.14272426068782806,
-0.23438897728919983,
-0.27648234367370605,
0.034605544060468674,
-0.1662171334028244,
-0.2812085449695587,
0.757684051990509,
-0.11847737431526184,
-0.5666772723197937,
0.46147599816322327,
-0.8718559741973877,
-0.823289155960083,
0.44521698355674744,
-0.9051260352134705,
0.21962526440620422,
0.04060598090291023,
-0.010632915422320366,
-0.6108923554420471,
0.15835370123386383,
-0.7500494122505188,
0.31432196497917175,
0.545918881893158,
-0.19473643600940704,
0.19735164940357208,
0.09303431957960129,
0.197801411151886,
-0.12346809357404709,
0.12227188050746918,
-0.051689185202121735,
-0.4778200387954712,
0.516905665397644,
-0.12064669281244278,
0.7054982781410217,
0.0741562694311142,
0.4523961544036865,
-0.3796076774597168,
0.291221022605896,
-0.12561602890491486,
-0.3388507664203644,
-0.7939677238464355,
-0.406316876411438,
0.26143911480903625,
0.8249403238296509,
-0.18149101734161377,
-0.22376666963100433,
-0.30783572793006897,
0.4654347002506256,
0.5439193844795227,
0.09355977922677994,
0.15999159216880798,
-0.34149864315986633,
-0.17308254539966583,
-0.10489625483751297,
-0.636353611946106,
0.12071478366851807,
0.02398933283984661,
0.4677145183086395,
0.7538843154907227,
0.4030423164367676,
0.3141136169433594,
-0.1710626631975174,
-0.024090902879834175,
0.2543163597583771,
0.9905703067779541,
0.6976617574691772,
0.7821356654167175,
0.2993263900279999,
0.013984458521008492,
0.1620306670665741,
-0.6861723065376282,
0.08735931664705276,
-0.6212887763977051,
-0.5825080871582031,
0.28743425011634827,
-0.1178242638707161,
-0.020830806344747543,
0.13275857269763947,
-0.08621136099100113,
0.7444353103637695,
0.11711925268173218,
0.2898408770561218,
0.08021170645952225,
-0.05568215250968933,
0.0681028738617897,
0.4574565291404724,
0.1318625509738922,
0.5458530187606812,
-1.2377099990844727,
0.21554802358150482,
0.10718764364719391,
0.3382687568664551,
0.04823661595582962,
-0.6950952410697937,
0.2431998997926712,
-0.9411221146583557,
0.5974768996238708,
0.06204375997185707,
-0.37613219022750854,
0.192580446600914,
0.34687426686286926,
0.5925459861755371,
0.0185574721544981,
0.566623330116272,
0.30440011620521545,
0.14164680242538452,
-0.1983041763305664,
-1.0403245687484741,
0.12855541706085205,
-0.46628713607788086,
0.1660478264093399,
0.714011549949646,
-0.4374886155128479,
-0.6985232830047607,
-0.9384990334510803,
0.022021958604454994,
-0.030481819063425064,
0.14219433069229126,
1.388505458831787,
0.6413038372993469,
0.18565362691879272,
-0.9112130403518677,
-0.36204588413238525,
0.7818917632102966,
-0.3273877501487732,
-0.78998202085495,
0.7900751233100891,
-0.03536536917090416,
-0.0448896586894989,
0.5300300121307373,
-0.39121493697166443,
-0.6280107498168945,
0.5003837943077087,
-0.7575704455375671,
0.22516943514347076,
-0.1699341982603073,
-0.6960155367851257,
-0.4844208061695099,
-0.054103583097457886,
-0.719693124294281,
0.7484338283538818,
0.22171272337436676,
-0.3687652051448822,
-0.3027876913547516,
-0.0714108943939209,
-0.4651603400707245,
-0.27548301219940186,
0.243471160531044,
-0.1544623076915741,
0.9797105193138123,
1.0642073154449463,
0.5481547713279724,
0.061926379799842834,
0.6184630990028381,
0.20995670557022095,
-0.23128053545951843,
0.15979953110218048,
0.04102887585759163,
-0.49295443296432495,
-0.3351985216140747,
-0.37996408343315125,
-0.7723791003227234,
-0.38061344623565674,
-0.1193016842007637,
0.2454516440629959,
0.6609346270561218,
0.3112977147102356,
-0.4902484714984894,
-0.6730487942695618,
-0.30191540718078613,
-0.6361695528030396,
0.7916468977928162,
-0.403219610452652,
-0.15747739374637604,
0.8905103802680969,
-0.5210744738578796,
0.2608725428581238,
-0.4674462676048279,
-0.2190569043159485,
0.13238714635372162,
0.7641174793243408,
0.6979398727416992,
0.908636212348938,
0.28489914536476135,
-1.3128217458724976,
0.6741719245910645,
-0.3137267827987671,
-0.19222106039524078,
-0.29467546939849854,
-0.694914698600769,
-0.40339863300323486,
0.24591410160064697,
0.356449693441391,
-0.01610538735985756,
-0.03138040378689766,
-0.13807745277881622,
-0.34086787700653076,
-0.3982599079608917,
0.16775240004062653,
-0.4695548117160797,
0.3315388858318329,
0.40938910841941833,
0.4755416810512543,
-0.9569843411445618,
-0.060631364583969116,
0.056273236870765686,
-0.013704217039048672,
-0.4437781572341919,
0.13219161331653595,
-0.3085322082042694,
0.019260015338659286,
-0.8675372004508972,
0.2682226002216339,
-0.5761157870292664,
-0.40731576085090637,
-0.24450843036174774,
-0.4858177602291107,
0.11860009282827377,
0.3682081699371338,
0.5782594680786133,
0.3080993592739105,
-0.5343215465545654,
-0.5105218887329102,
0.38597720861434937,
-0.8111569285392761,
-0.5757967233657837,
-0.2677944302558899,
-0.36036139726638794,
-0.22406704723834991,
0.9223567247390747,
-0.8057258725166321,
0.10098859667778015,
-0.403240442276001,
0.009034602902829647,
0.08348070085048676,
0.6463181972503662,
0.9191094636917114,
0.031199607998132706,
0.14365138113498688,
0.21318000555038452,
-0.02825838513672352,
0.6919482946395874,
-0.6250042915344238,
0.6145637631416321,
-0.6121605038642883,
1.0032813549041748,
-0.9878736138343811,
-0.09570404887199402,
0.1592203825712204,
-0.1751779317855835,
0.770997941493988,
-0.13085031509399414,
0.6051375865936279,
1.0218751430511475,
-0.4679161012172699,
0.12840847671031952,
-0.19391044974327087,
-0.5556183457374573,
-0.1416475474834442,
-0.34706753492355347,
-0.35800838470458984,
0.9784561991691589,
-0.14804597198963165,
0.2380809634923935,
-0.6662736535072327,
-1.0131304264068604,
0.07236219942569733,
0.03819884732365608,
0.11609936505556107,
0.40284115076065063,
0.2879045605659485,
0.1922762095928192,
0.6402868628501892,
0.10694845020771027,
-0.8062357902526855,
0.20853328704833984,
-0.199942484498024,
0.10679373145103455,
0.41207411885261536,
-0.29174160957336426,
-0.3758929669857025,
-0.3173133432865143,
-0.12618842720985413,
0.23785904049873352,
0.2487766146659851,
0.06736107915639877,
0.38608473539352417,
-0.3811645805835724,
-0.6067914366722107,
-0.23306825757026672,
0.5424825549125671,
-0.09945211559534073,
0.02558501623570919,
0.7896322011947632,
0.41837775707244873,
-0.4995681047439575,
0.2433960735797882,
-0.1421373039484024,
-0.37171125411987305,
-0.7310124635696411,
0.6938392519950867,
-0.7747219800949097,
-0.1797209084033966,
0.7163676619529724,
0.39081183075904846,
-0.5197083950042725,
0.10981328785419464,
-1.0810285806655884,
-0.18654300272464752,
-0.021973934024572372,
0.5432448387145996,
-0.4954451024532318,
-0.024900255724787712,
-0.3501793146133423,
0.20090745389461517,
0.6957531571388245,
0.43612241744995117,
0.17595097422599792,
-0.2055499255657196,
0.3717067241668701,
-0.48112788796424866,
0.3239479064941406,
1.1992069482803345,
-0.25117945671081543,
-1.0757497549057007,
0.6908431649208069,
0.7148391008377075,
-0.21932731568813324,
-0.531741201877594,
0.3453565239906311,
-0.7827320694923401,
0.1927519291639328,
0.2691531181335449,
-0.05546494945883751,
-0.15825319290161133,
0.010933264158666134,
0.08493657410144806,
0.937382161617279,
-0.549811065196991,
-0.6794161796569824,
0.03232765942811966,
0.1530539095401764,
0.16909396648406982,
0.6795262098312378,
0.5502214431762695,
0.5065383315086365,
0.1696341633796692,
0.07156943529844284,
-0.05350256711244583,
-0.21628542244434357,
0.2454988956451416,
-0.9179050326347351,
-0.25262129306793213,
-0.8666952848434448,
-0.16780084371566772,
0.7315707802772522,
0.9805372953414917,
-0.24650336802005768,
-0.15107744932174683,
-0.39966830611228943,
0.31821203231811523,
-0.05646233260631561,
-0.1462981402873993,
0.25175249576568604,
-1.169581413269043,
0.19822439551353455,
0.06015780195593834,
-0.4128406345844269,
-1.0499577522277832,
0.011538236401975155,
0.08462664484977722,
-0.33323508501052856,
1.0327683687210083,
-0.09867122769355774,
0.5287606716156006,
-0.9238812327384949,
-0.4655861556529999,
-0.500072181224823,
0.21018166840076447,
-0.6087543964385986,
0.40317273139953613,
-0.22107529640197754,
0.8832248449325562,
0.529654324054718,
-0.7981442809104919,
-0.4737951457500458,
0.49978554248809814,
-0.33951741456985474,
-0.10946735739707947,
0.05801676586270332,
0.368744432926178,
-0.02749377116560936,
-1.1726951599121094,
-0.2318866103887558,
0.2824787497520447,
-0.7290095686912537,
0.03084205649793148,
-0.48103415966033936,
0.45036694407463074,
-0.4756571054458618,
0.10494428873062134,
0.2537558674812317,
0.4039030969142914,
0.41409599781036377,
0.8786578178405762,
-0.19628845155239105,
0.01016854029148817,
0.04608209431171417,
0.30133214592933655,
0.08883405476808548,
0.19675788283348083,
0.302725613117218,
-0.6977387070655823,
0.22068975865840912,
0.5284606218338013,
0.14885815978050232,
-0.28555405139923096,
0.3329411745071411,
-0.2715633511543274,
0.38219591975212097,
-0.049096353352069855,
-0.6780267357826233,
0.7566018104553223,
0.5970968008041382,
-0.4829443693161011,
-0.593588650226593,
-0.8138805627822876,
-1.0964972972869873,
0.30305230617523193,
-0.518193244934082,
-0.49623242020606995,
0.1629040539264679,
-0.3139682114124298,
0.46520450711250305,
0.8967720866203308,
-0.38149866461753845,
0.16831199824810028,
0.33179205656051636,
-0.03329355642199516,
1.144650936126709,
0.21442879736423492,
-0.6981405019760132,
0.054598644375801086,
-0.9486731290817261,
-0.467128187417984,
-0.6085054874420166,
0.6606855392456055,
-0.9930500388145447,
-1.5464926958084106,
-0.760890007019043,
0.7811076641082764,
0.045844439417123795,
0.1543269157409668,
-0.4127679765224457,
-0.9455384016036987,
-0.28189778327941895,
-0.22790800034999847,
-0.8563737273216248,
-0.22115889191627502,
-0.6785210371017456,
0.2966247498989105,
-0.24363446235656738,
-0.7188459038734436,
0.6222978234291077,
-0.2417033612728119,
0.44745567440986633,
0.007659832946956158,
0.20747900009155273,
1.2165061235427856,
0.08052844554185867,
-0.34102562069892883,
0.7163801193237305,
0.2559134364128113,
0.24369409680366516,
0.5918442606925964,
-0.6979179382324219,
0.30053088068962097,
0.3156678080558777,
0.08091015368700027,
0.34700995683670044,
0.4653390944004059,
0.19040988385677338,
0.4209732413291931,
0.08923381567001343,
-0.11418493092060089,
-0.08012235164642334,
0.2962754964828491,
-0.21594828367233276,
0.18429461121559143,
-0.6146308779716492,
0.05054138973355293,
-0.4662168622016907,
0.10021005570888519,
0.7428509593009949,
-0.22083616256713867,
-0.3694991171360016,
-0.2739580273628235,
0.005992364604026079,
-0.002161328447982669,
-0.8715592622756958,
-0.15400509536266327,
-0.10076077282428741,
0.2551192045211792,
0.3041922450065613,
0.027492888271808624,
-0.026740787550807,
0.5713868737220764,
0.6751837730407715,
-0.11793680489063263,
-0.4882095158100128,
0.38998350501060486,
0.13133041560649872,
1.2958709001541138,
1.1308531761169434,
0.09373008459806442,
0.1949995905160904,
-0.18468649685382843,
-0.08483924716711044,
-1.0844382047653198,
0.351417601108551,
0.6624036431312561,
-0.9732099175453186,
0.3933871388435364,
-0.3270966112613678,
-0.46689125895500183,
-1.1676560640335083,
-0.4568993151187897,
0.4145726263523102,
-0.6587880253791809,
0.12871213257312775,
0.45509281754493713,
-0.6680753231048584,
0.6801509857177734,
0.1884257197380066,
0.43228814005851746,
0.45034876465797424,
0.3175647258758545,
0.24103708565235138,
0.10329676419496536,
0.9356566071510315,
1.2234342098236084,
0.6401602625846863,
-0.10773446410894394,
-0.3407902419567108,
-0.6383121609687805,
0.7546533942222595,
0.6907912492752075,
0.06266482174396515,
0.4918985664844513,
-0.20091618597507477,
-0.8136194348335266,
0.3341570198535919,
-0.09506899118423462,
-0.22361114621162415,
-0.4660206437110901,
0.12937279045581818,
0.1446472853422165,
-0.1643112748861313,
-0.6944915652275085,
1.6218154430389404,
0.19582216441631317,
-0.7787254452705383,
-0.5079672336578369,
0.6659442186355591,
-0.5311794877052307,
-0.20081768929958344,
-1.1425318717956543,
0.15235649049282074,
0.1267722249031067,
0.3210796117782593,
0.13528093695640564,
-0.5791652798652649,
-0.6477994918823242,
-0.9604465961456299,
0.4224764406681061,
-0.4674377143383026,
0.5701434016227722,
0.31659629940986633,
0.160220667719841,
0.28000515699386597,
-0.41020476818084717,
0.3956204354763031,
0.16298657655715942,
0.724123477935791,
-0.2566244900226593,
-0.01857776753604412,
0.14078323543071747,
0.33584094047546387,
-1.186583161354065,
0.8564541935920715,
0.631915271282196,
-0.6497383713722229,
0.48055246472358704,
-0.7866265773773193,
0.890191912651062,
0.5077239871025085,
0.13663919270038605,
0.3857940435409546,
0.03903733938932419,
0.302763432264328,
-0.20722579956054688,
-0.29353803396224976,
-0.642939567565918,
-1.0518289804458618,
0.1574678122997284,
-0.47051891684532166,
0.048956532031297684,
0.0892271026968956,
0.19891422986984253,
0.45322877168655396,
-0.9698730707168579,
4.195825099945068,
0.8065803050994873,
0.45650771260261536,
0.4515362083911896,
0.991028904914856,
0.725336492061615,
-0.41200628876686096,
0.03062412515282631,
0.13755300641059875,
-0.3607238233089447,
-0.46017858386039734,
0.3424191474914551,
0.3692546486854553,
-0.07469669729471207,
-0.0975908488035202,
0.6340430974960327,
-0.4028221070766449,
-0.2515226900577545,
0.2623399496078491,
-1.1678698062896729,
-0.6308393478393555,
-0.39507079124450684,
0.5138698816299438,
-0.17777150869369507,
0.41050997376441956,
-0.17932447791099548,
0.040517259389162064,
-0.1342465728521347,
0.11298812180757523,
-0.3634962737560272,
-0.1524103879928589,
-0.9618022441864014,
0.47511669993400574,
-0.09955116361379623,
-1.238052248954773,
0.6994083523750305,
0.16729451715946198,
0.29067280888557434,
0.19054841995239258,
-0.2388266921043396,
-0.06731247156858444,
-0.6506636142730713,
-0.08100540190935135,
-0.0708385556936264,
-0.3889797031879425,
0.6299437880516052,
0.16786843538284302,
0.4363842308521271,
0.4256472587585449,
-0.8924418091773987,
0.6700379252433777,
0.23496204614639282,
0.9394271373748779,
-0.2942051887512207,
-1.0322726964950562,
-0.04729524254798889,
-0.7541859745979309,
-0.002092340961098671,
0.2276419699192047,
-0.24069084227085114,
-0.08808550238609314,
-0.30192822217941284,
-0.2732958197593689,
0.4379570186138153,
0.19258472323417664,
-0.2000991255044937,
-0.04607882350683212,
0.20391139388084412,
-0.49936774373054504,
-0.20366284251213074,
-0.27028387784957886,
0.2693401575088501,
-0.08285435289144516,
0.0785374566912651,
-0.032200489193201065,
0.12981772422790527,
-0.07212000340223312,
0.5936527252197266,
-0.49839603900909424,
0.3965342044830322,
0.1825510561466217,
-0.27946361899375916,
-0.40764933824539185,
0.6161807775497437,
-0.15411733090877533,
0.6520561575889587,
-0.7072547674179077,
0.5621905326843262,
-0.26770585775375366,
0.1501966267824173,
-0.018100515007972717,
0.9088499546051025,
0.2765054404735565,
0.7980813980102539,
-0.8450642228126526
] |
Regularization dependence of the Higgs mass triviality bound
|
We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff effects at four percent in several regularized models with tunable couplings in the bare action yield triviality bounds displaying a large degree of universality. Extrapolating from $N=\infty$ to $N=4$ we conservatively estimate that a Higgs particle with mass up to $0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff effects, indicating that strong scalar self interactions in the standard model are not ruled out. We also present preliminary numerical results of the physical $N=4$ case for the $F_4$ lattice that are in agreement with the large $N$ expectations. Note: The full ps file is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lat92_proc.ps (to get it type: get lat92_proc.ps)
|
Urs M. Heller, Markus Klomfass, Herbert Neuberger and Pavlos Vranas
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210026
|
hep-lat/9210027
|
[
0.2842985689640045,
0.08558067679405212,
0.11492978036403656,
0.4822571873664856,
0.12565073370933533,
0.04259420931339264,
0.0442582368850708,
-0.46268516778945923,
-0.6645719408988953,
1.5124536752700806,
0.7538655400276184,
-0.2142029106616974,
0.42675623297691345,
-0.6323527097702026,
-0.4522393047809601,
0.5206823945045471,
0.06861552596092224,
-0.6949576139450073,
-1.6056252717971802,
0.18019631505012512,
0.6859744191169739,
-0.14178387820720673,
-0.842940628528595,
-0.39722350239753723,
-0.48265379667282104,
0.5353119969367981,
0.6517394185066223,
-0.047996968030929565,
0.9657909870147705,
0.8152716159820557,
0.9884761571884155,
-0.5547351837158203,
0.0036672919522970915,
-0.7358458042144775,
-0.2383486032485962,
0.33027392625808716,
-0.16749757528305054,
-0.15363724529743195,
0.6746383905410767,
-0.7266754508018494,
0.9564284682273865,
-0.34374141693115234,
0.45556584000587463,
-0.042865607887506485,
-0.3284749686717987,
0.6162811517715454,
-0.10333852469921112,
-0.05424364283680916,
-0.5238723158836365,
-0.8256598711013794,
0.8201468586921692,
0.2167225033044815,
0.1570553481578827,
-0.5972551703453064,
-0.06302754580974579,
0.2664388418197632,
-0.29751014709472656,
0.7456541657447815,
-0.43228796124458313,
0.4217437207698822,
0.6945510506629944,
-0.1940261274576187,
0.8888454437255859,
-0.5369808673858643,
0.30036523938179016,
1.0179309844970703,
0.03693043813109398,
0.8014540076255798,
0.006107311230152845,
-0.6879400014877319,
-0.48106399178504944,
0.07093365490436554,
0.12222153693437576,
-0.018374422565102577,
-1.106017827987671,
1.033248782157898,
-0.012792832218110561,
-0.03610290214419365,
-0.8112484812736511,
-0.5421757102012634,
-0.18641266226768494,
0.35424748063087463,
-0.22343893349170685,
0.7999259233474731,
-0.17243382334709167,
-0.2878051698207855,
-0.34173694252967834,
-0.1547384411096573,
-0.020222071558237076,
0.19363537430763245,
0.8766262531280518,
0.9208502769470215,
0.3940832316875458,
-0.0817045345902443,
0.228910431265831,
0.6867046356201172,
-0.16799694299697876,
0.5826258659362793,
0.2283734381198883,
0.11787234991788864,
0.019467297941446304,
0.7088831663131714,
-0.7464873194694519,
0.5630605220794678,
-0.24267880618572235,
0.3311488926410675,
-0.024276122450828552,
-0.3843482434749603,
0.008160022087395191,
-0.7784268856048584,
-0.046919532120227814,
0.4090918004512787,
0.13684073090553284,
0.7552615404129028,
0.029998544603586197,
0.6227550506591797,
0.1753334403038025,
0.03656667843461037,
-0.4886825978755951,
-0.05823182314634323,
0.5236213207244873,
-0.19626088440418243,
0.2872258126735687,
0.7068008184432983,
-0.250842809677124,
-0.34048566222190857,
0.07805253565311432,
0.5888475775718689,
0.4157712459564209,
-0.01829410530626774,
-0.9085226058959961,
-0.19920973479747772,
-0.14185692369937897,
0.6408255100250244,
0.005648999009281397,
0.5315935611724854,
-0.08082490414381027,
-0.010265549644827843,
0.44555795192718506,
-0.21491388976573944,
0.21659988164901733,
-0.02344542369246483,
0.1328338235616684,
0.7512784600257874,
-0.4500894546508789,
-0.0997917577624321,
0.46209025382995605,
-0.647787868976593,
-0.10637997090816498,
0.340409517288208,
-1.379551649093628,
-0.022081077098846436,
-0.26408857107162476,
-0.001083045732229948,
-0.350509911775589,
-0.014514542184770107,
-0.5001171231269836,
0.7489807605743408,
-0.5713027715682983,
-0.29232853651046753,
-0.24862107634544373,
-0.2313733994960785,
-0.11711762100458145,
0.8761374950408936,
-0.008106381632387638,
-0.2853330969810486,
-0.3303375840187073,
-0.38602423667907715,
0.24638217687606812,
-0.9959778189659119,
0.36343416571617126,
-0.0640457347035408,
-0.4180434048175812,
0.5104683041572571,
0.7246550917625427,
0.48323923349380493,
0.2976100742816925,
-0.4243506193161011,
0.043350424617528915,
0.44334352016448975,
-0.42612239718437195,
0.006577926222234964,
0.3391173481941223,
0.4476318955421448,
0.01641245000064373,
-0.42672690749168396,
-0.6493425965309143,
0.01329498365521431,
0.05439480021595955,
0.8065674901008606,
0.1274540275335312,
0.23981040716171265,
-0.3225908875465393,
0.14228463172912598,
-0.42407625913619995,
0.05861823260784149,
-0.6278260946273804,
0.3529062569141388,
-0.2824033796787262,
-0.5834058523178101,
-0.43645429611206055,
0.2351580411195755,
-0.9654877781867981,
-0.05004086717963219,
-1.5083783864974976,
0.6729233264923096,
0.5259037017822266,
0.3549644649028778,
-0.4445294737815857,
0.3223113417625427,
0.16946491599082947,
-0.0862046331167221,
0.6016067266464233,
-0.1760953813791275,
-0.5294911861419678,
-0.04695511236786842,
-0.10291610658168793,
0.3831254541873932,
0.6454837322235107,
0.15662355720996857,
1.3687169551849365,
-0.0688442513346672,
-0.7867489457130432,
0.5230005383491516,
0.14622360467910767,
-0.5580455660820007,
0.3463418781757355,
0.5168349146842957,
0.1282375007867813,
-0.438289999961853,
-0.3558792769908905,
1.0325959920883179,
-0.301887571811676,
0.485609769821167,
0.7949190139770508,
0.8425331711769104,
0.13692744076251984,
0.9695045948028564,
0.312640905380249,
0.015108992345631123,
0.4642622172832489,
-0.29111382365226746,
0.6968204975128174,
0.4643966257572174,
-0.4970304071903229,
0.6325456500053406,
-0.4163374900817871,
-0.0517737977206707,
-0.49017056822776794,
0.09487283229827881,
-0.6919511556625366,
0.8895977139472961,
0.10656999796628952,
0.01918763481080532,
-0.8939418792724609,
0.019939107820391655,
0.39782050251960754,
0.6335428953170776,
-0.3934895396232605,
-0.18105371296405792,
0.2072248011827469,
0.18440929055213928,
-0.09185565263032913,
-0.5861712098121643,
0.166676327586174,
0.8339217901229858,
-0.13400636613368988,
0.04396957904100418,
0.08451882004737854,
-0.5162330269813538,
-0.8927830457687378,
-0.6742826700210571,
-1.031967043876648,
0.023453321307897568,
-0.3600720465183258,
-0.21160875260829926,
0.7065920233726501,
-0.3975408673286438,
0.3060803711414337,
0.1632300317287445,
0.05463072657585144,
-0.21334417164325714,
-0.3681178092956543,
0.3492956757545471,
0.42325103282928467,
-0.03350450098514557,
-0.7114644050598145,
0.027157893404364586,
-0.536681592464447,
-0.16411373019218445,
-0.19189466536045074,
-0.7133755683898926,
0.27689650654792786,
-0.10038110613822937,
-0.022089814767241478,
0.10483778268098831,
-0.41663140058517456,
0.04885048791766167,
0.005037202499806881,
-0.7400438189506531,
0.031280744820833206,
0.008514327928423882,
-0.46665385365486145,
-0.6620886921882629,
-1.2248477935791016,
0.4370233714580536,
-0.20704591274261475,
-0.8377984762191772,
1.2839713096618652,
0.25290775299072266,
-0.7649684548377991,
0.5460895299911499,
-0.5418112277984619,
0.24392548203468323,
0.2564517557621002,
0.7826108932495117,
1.003670334815979,
0.04597092792391777,
0.03261939436197281,
-0.7895894646644592,
-0.4033813774585724,
0.34462985396385193,
0.09302050620317459,
-1.2157059907913208,
-0.21101367473602295,
0.27939823269844055,
0.5512943863868713,
-0.36190927028656006,
0.6948405504226685,
-1.1492875814437866,
-0.2642901539802551,
-0.43467822670936584,
-0.30122676491737366,
0.2095271646976471,
0.179486483335495,
-0.3507530391216278,
-0.5706807971000671,
0.31824734807014465,
0.46107620000839233,
0.3664219081401825,
0.07302771508693695,
-0.5442742705345154,
0.5931575298309326,
0.4094618558883667,
0.3574839234352112,
-0.42373716831207275,
0.9560460448265076,
-0.7482609748840332,
-0.6225167512893677,
0.4188854992389679,
-0.7567062973976135,
-0.6922757029533386,
0.666214644908905,
0.1760774403810501,
0.06949391216039658,
0.41415727138519287,
-0.3603036403656006,
-0.15452980995178223,
-0.32575446367263794,
0.026003878563642502,
0.46236860752105713,
0.17252275347709656,
0.20849427580833435,
0.08388065546751022,
-0.803368330001831,
-0.5063574314117432,
0.5496658682823181,
-0.4396611750125885,
0.7546086311340332,
-1.2317851781845093,
0.2699083387851715,
-0.8643489480018616,
-0.46875306963920593,
0.2964753210544586,
-0.1091441884636879,
0.9160319566726685,
0.3506661057472229,
-0.01809662953019142,
0.6808980703353882,
-1.0556102991104126,
-0.7948564887046814,
-0.37779510021209717,
0.7377821803092957,
1.0210007429122925,
0.6837592720985413,
0.4182303249835968,
0.16766084730625153,
-0.13321931660175323,
-0.6672296524047852,
-1.1394654512405396,
-0.10432662069797516,
-0.10984794050455093,
-0.10590967535972595,
-0.8751419186592102,
-0.6551297903060913,
-0.4204862415790558,
0.6143674254417419,
-0.1731071174144745,
-0.25242745876312256,
0.06851711124181747,
0.6123445630073547,
0.24870377779006958,
0.3501303493976593,
0.9676729440689087,
0.19327673316001892,
-0.7541443109512329,
-0.6501919031143188,
0.7845305800437927,
0.16461221873760223,
-0.037995461374521255,
-0.03661578521132469,
-0.9691230654716492,
-0.6846293210983276,
-0.6389718055725098,
0.67191082239151,
0.37648624181747437,
-0.12177810072898865,
0.6237467527389526,
0.4125753343105316,
-0.5179855823516846,
-0.25598791241645813,
-0.44402456283569336,
0.4960533082485199,
-0.15322251617908478,
0.15219998359680176,
-0.719458281993866,
0.25650754570961,
-0.4856829047203064,
0.25795677304267883,
0.6238744854927063,
0.4458181858062744,
-0.6567023992538452,
-0.05220906063914299,
0.9382286071777344,
-0.6739695072174072,
0.11211257427930832,
1.1983760595321655,
-0.07514190673828125,
-0.10918989777565002,
0.06128047779202461,
0.6421758532524109,
0.06497549265623093,
-0.4841110408306122,
-0.11967083811759949,
0.051099956035614014,
0.479814738035202,
-0.43292585015296936,
1.0581432580947876,
-0.36608314514160156,
-0.13871800899505615,
-0.06954449415206909,
-0.25282979011535645,
0.9366034269332886,
0.08248303085565567,
-0.9882001280784607,
0.08620510250329971,
-0.7126272916793823,
-0.08125906437635422,
0.48933860659599304,
0.6454121470451355,
-0.3336188495159149,
0.2352907359600067,
-0.3314916491508484,
-0.12391163408756256,
-1.162447452545166,
-0.03465016186237335,
0.06646271795034409,
0.8100634813308716,
0.6848903298377991,
0.6390202045440674,
-0.10841427743434906,
0.02734450064599514,
-0.14743773639202118,
-0.417412132024765,
0.4993056058883667,
-0.047741182148456573,
-0.23206181824207306,
-0.5914961695671082,
-0.362045556306839,
-0.7387491464614868,
-0.6133631467819214,
0.9566118717193604,
-0.06893835961818695,
1.1172130107879639,
0.3680802583694458,
-0.827359676361084,
-0.44651931524276733,
-0.6586155295372009,
-0.28101909160614014,
0.2316838949918747,
-0.22326423227787018,
-0.7362893223762512,
-0.1114068329334259,
0.030754329636693,
-0.27956151962280273,
0.19328735768795013,
-0.2210075557231903,
-0.6589956283569336,
0.28782689571380615,
-0.1355331838130951,
-0.7584158182144165,
0.3182506561279297,
-0.4675252139568329,
1.0312851667404175,
-0.5019460320472717,
0.28809645771980286,
0.11531998217105865,
-0.3582601845264435,
-0.3357047736644745,
-0.17312827706336975,
0.24203817546367645,
-0.5477131009101868,
0.4376848042011261,
-0.029959140345454216,
0.7527943849563599,
0.3313160240650177,
0.015588494017720222,
0.37227582931518555,
-0.42078718543052673,
1.0219248533248901,
-0.030762741342186928,
-0.6097145080566406,
-0.09912972897291183,
0.9294494390487671,
0.26353442668914795,
0.4964841604232788,
-0.20114636421203613,
-1.4975357055664062,
0.044129692018032074,
0.3806932866573334,
0.8535807728767395,
-1.104317307472229,
-0.06920285522937775,
-0.13693328201770782,
-0.23252524435520172,
-0.5924426913261414,
0.6788228750228882,
-0.12930652499198914,
0.20826779305934906,
-0.2925386130809784,
-0.6497806906700134,
0.17779900133609772,
-0.71171635389328,
0.1730692982673645,
-0.37383049726486206,
-0.5119863152503967,
-0.7556367516517639,
1.090790867805481,
-0.5188784003257751,
0.3620092570781708,
0.23741702735424042,
0.12678684294223785,
0.0027091584634035826,
0.15189321339130402,
0.09913552552461624,
-0.4014509618282318,
0.36732837557792664,
0.5669501423835754,
0.06345420330762863,
0.2641400098800659,
-0.8677305579185486,
0.495981901884079,
-0.9153560400009155,
1.2009862661361694,
-0.2868936061859131,
0.06908246129751205,
-0.02664519101381302,
0.022462354972958565,
0.6795365214347839,
-0.682869017124176,
0.5241539478302002,
0.447735995054245,
0.6182865500450134,
1.000533103942871,
0.4186834692955017,
-1.203078031539917,
-0.20104430615901947,
-1.0191535949707031,
-0.8206079006195068,
0.4788629710674286,
0.0256014596670866,
0.21356181800365448,
-0.7111412882804871,
-0.5796613693237305,
0.026727203279733658,
-0.2714999318122864,
0.3580651581287384,
0.4841863512992859,
-0.160241037607193,
-0.1390647441148758,
-0.24855633080005646,
0.29890450835227966,
-0.12107153981924057,
0.015164682641625404,
0.4839145243167877,
0.2615574300289154,
-0.1817234456539154,
-0.01817534677684307,
-0.2803025245666504,
-0.6879136562347412,
-0.8498921990394592,
0.3914172649383545,
0.3553406000137329,
-0.563357949256897,
1.074353575706482,
-0.738330602645874,
-0.8483824133872986,
-1.0123882293701172,
-0.16149623692035675,
0.39831748604774475,
-0.16601310670375824,
0.559985876083374,
-0.03582756966352463,
-0.4771142899990082,
-0.36774978041648865,
-0.06855273991823196,
-0.8402630686759949,
-0.49341484904289246,
0.9818156957626343,
-0.322818398475647,
-0.5069003701210022,
0.2772926986217499,
-0.10753609985113144,
-0.7347220182418823,
-0.8912742137908936,
-0.8411255478858948,
-0.6785717010498047,
0.17443238198757172,
-0.6300749778747559,
0.05912398919463158,
-0.2575618326663971,
-0.10903502255678177,
0.08064413070678711,
1.030181646347046,
-0.22026240825653076,
0.2994631230831146,
0.667415976524353,
-0.5236057043075562,
-1.1545625925064087,
-0.42487549781799316,
0.9367146492004395,
-0.005859526805579662,
-0.2358401119709015,
-0.45278480648994446,
-0.5123789310455322,
-0.11587011069059372,
-0.2304646521806717,
0.770011842250824,
-0.1461571604013443,
0.22504618763923645,
0.5024996399879456,
-0.11664813756942749,
0.17815817892551422,
0.4889622926712036,
0.38138720393180847,
-0.11657538264989853,
0.1731446087360382,
-0.5185908079147339,
-0.2902660667896271,
-0.168068990111351,
0.2079075425863266,
0.5642871856689453,
-0.1776888072490692,
-0.01460118219256401,
-0.09039083868265152,
-0.3726873993873596,
-0.5856386423110962,
-0.6750324368476868,
-0.3341667354106903,
-1.5571945905685425,
-0.9137332439422607,
-1.0286543369293213,
-0.4379611611366272,
-0.4138193726539612,
-0.009398235939443111,
0.04649975150823593,
-0.31728842854499817,
-0.6475216746330261,
-0.02080792933702469,
0.5479392409324646,
0.24792246520519257,
-0.6912614107131958,
-0.35051241517066956,
-0.9479537010192871,
-0.38731226325035095,
-0.7756011486053467,
0.2909594774246216,
0.02636444941163063,
0.3935639560222626,
-0.20599700510501862,
0.08929817378520966,
-0.5824040174484253,
0.5641580820083618,
-0.6222526431083679,
-0.13583482801914215,
0.34000927209854126,
0.5493538975715637,
-1.0566784143447876,
0.7288609147071838,
-0.014744555577635765,
0.17652401328086853,
0.7906849384307861,
-0.36522606015205383,
0.002499052556231618,
0.09070052206516266,
-1.0583127737045288,
-0.270989328622818,
-0.06533994525671005,
0.7249420285224915,
0.16782185435295105,
-0.5043084025382996,
0.8979057669639587,
0.10910918563604355,
-0.9501115679740906,
-0.1097589060664177,
-0.7936429977416992,
0.28232860565185547,
-0.2962518334388733,
0.05701548606157303,
-0.09982327371835709,
0.16677303612232208,
0.2784300148487091,
0.26879242062568665,
-0.07853000611066818,
-0.25786688923835754,
0.18839770555496216,
0.13053829967975616,
-0.39436930418014526,
0.15451180934906006,
0.3408146798610687,
-0.6248645782470703,
0.3454778790473938,
-0.20959703624248505,
-0.7688093185424805,
0.15069079399108887,
0.27450916171073914,
-0.536467969417572,
-0.5763881802558899,
-0.06576970964670181,
-0.9877487421035767,
0.2839951515197754,
0.6761616468429565,
-0.48687466979026794,
0.21026258170604706,
-0.8951030373573303,
-0.596058189868927,
-0.3577998876571655,
-0.9980993866920471,
-0.12058088183403015,
-0.9921894669532776,
-0.03305177018046379,
-0.6873626708984375,
0.22054097056388855,
0.007052527740597725,
0.3206386864185333,
-0.47734934091567993,
0.19778811931610107,
-0.28748151659965515,
-0.5149644613265991,
0.2974885404109955,
0.3557163178920746,
-0.6402683854103088,
-0.14794889092445374,
-0.6626973152160645,
0.2991895377635956,
-0.3818151652812958,
-0.5137024521827698,
-0.8777030110359192,
-0.2105567306280136,
-0.294903427362442,
-0.20823541283607483,
-0.33286893367767334,
0.3191899061203003,
0.2906729280948639,
0.23020604252815247,
-0.025437742471694946,
0.49111899733543396,
0.164023756980896,
0.7187055945396423,
0.20033922791481018,
-0.17136909067630768,
-0.10776777565479279,
0.32485994696617126,
-0.001993348589166999,
-0.12686055898666382,
0.6690436005592346,
0.4692249298095703,
-0.22751441597938538,
-0.40177127718925476,
1.1618154048919678,
-0.29428529739379883,
0.9491249918937683,
0.4226405620574951,
-0.3372032344341278,
-0.18504978716373444,
-0.10801670700311661,
0.45564699172973633,
0.542104959487915,
0.15154992043972015,
0.2728191614151001,
0.39061209559440613,
-0.008030376397073269,
0.18234995007514954,
0.12116765975952148,
0.30737003684043884,
0.09593357890844345,
1.1254959106445312,
0.06662753969430923,
0.983485996723175,
-0.11835712194442749,
-0.025339867919683456,
0.07360425591468811,
-0.3394955098628998,
-0.34511756896972656,
-0.30090901255607605,
-0.05801594257354736,
0.48063984513282776,
-0.5681290030479431,
-0.5361258387565613,
-0.4954981803894043,
-0.547630250453949,
-0.0015120251337066293,
0.019117776304483414,
-0.12807902693748474,
0.27473360300064087,
0.9632258415222168,
0.2817734181880951,
-0.5951963067054749,
0.2703530490398407,
0.27986013889312744,
0.5019334554672241,
-0.049151383340358734,
0.8757996559143066,
0.800897479057312,
0.48762375116348267,
0.22769683599472046,
-0.6409411430358887,
-0.02075861394405365,
0.4159109592437744,
-1.483141541481018,
0.02633078582584858,
-0.2477937638759613,
-0.14107061922550201,
0.3781030774116516,
-0.624129056930542,
0.5922858715057373,
-0.2461116462945938,
-0.190637469291687,
1.2364312410354614,
-0.10469616949558258,
0.4784861207008362,
0.13041317462921143,
-0.1949116289615631,
0.762466311454773,
0.1207490786910057,
0.3533613383769989,
-0.4696640074253082,
0.32815954089164734,
1.2569061517715454,
-0.23084694147109985,
0.21479098498821259,
0.1504194736480713,
0.03278695046901703,
0.2251613289117813,
0.9612618088722229,
-0.05700834095478058,
0.355598121881485,
-0.34383538365364075,
-0.20514777302742004,
-0.16239427030086517,
0.45965516567230225,
-0.1541595309972763,
-0.07482780516147614,
0.33442986011505127,
0.16726861894130707,
-0.3103397786617279,
-0.3359384536743164,
0.5742362141609192,
1.1457993984222412,
-0.06895853579044342,
-0.2516116797924042,
-0.2301257997751236,
0.1402638703584671,
-0.31606829166412354,
-0.4519309401512146,
0.6364500522613525,
-0.6222093105316162,
0.0836692675948143,
0.21772325038909912,
-0.8471075296401978,
-0.8928349614143372,
-0.894120454788208,
-0.2044902890920639,
-0.4862867593765259,
1.0888183116912842,
0.10514930635690689,
0.8078311681747437,
0.23414307832717896,
-0.2446436583995819,
-0.10702747106552124,
0.557895839214325,
0.9592048525810242,
0.013867933303117752,
-0.07547911256551743,
0.5050307512283325,
-0.2061014473438263,
-0.22203397750854492,
0.6678594946861267,
0.9838399887084961,
-0.4118556082248688,
-0.08185143768787384,
0.14518693089485168,
0.22196096181869507,
-0.023846104741096497,
-0.09553506970405579,
0.4507785439491272,
0.30081117153167725,
0.46715736389160156,
-0.5328940153121948,
-0.4292755722999573,
-0.2747139036655426,
-1.2811570167541504,
0.4768392741680145,
-0.349721759557724,
1.0171226263046265,
0.265434592962265,
-0.24952130019664764,
0.5067927837371826,
-0.5797322392463684,
4.099967956542969,
1.2221853733062744,
0.6948782205581665,
-0.2768145203590393,
0.7509771585464478,
0.6070244312286377,
-0.262563556432724,
-0.07982473820447922,
-0.06535892188549042,
-0.2547718584537506,
0.14867864549160004,
0.49713215231895447,
0.09420224279165268,
-0.23130929470062256,
0.3279598653316498,
0.3369348347187042,
0.32623788714408875,
0.6819522380828857,
-0.07030420750379562,
-1.3287203311920166,
-0.22368070483207703,
0.09172123670578003,
-0.06038929149508476,
-0.48663759231567383,
0.22402265667915344,
0.3464663326740265,
0.6244567036628723,
-0.9129146933555603,
-0.2987891137599945,
-0.4591344892978668,
-0.7097037434577942,
-0.6057435870170593,
0.3874156177043915,
-0.16538117825984955,
-1.0338863134384155,
0.017712781205773354,
-0.01945236511528492,
0.1812608242034912,
0.2759975492954254,
0.37796977162361145,
0.2765759527683258,
-0.46030551195144653,
-0.33314961194992065,
0.09228002279996872,
-0.791564404964447,
0.6944780945777893,
-0.04591836407780647,
1.6540294885635376,
0.5536571741104126,
-0.6352061629295349,
0.19324249029159546,
0.004896935541182756,
0.26276835799217224,
-0.48128271102905273,
-0.9094471335411072,
0.676091194152832,
-0.3789205849170685,
-0.21825549006462097,
0.11086077243089676,
0.03229241818189621,
1.213297724723816,
0.4290185868740082,
-0.5849475264549255,
-0.03671703115105629,
-0.13750362396240234,
0.5470247864723206,
0.5727553963661194,
0.21411831676959991,
-0.5605671405792236,
-0.09275548160076141,
-0.28571632504463196,
-0.15023942291736603,
-0.4319533109664917,
-0.41532188653945923,
0.9785366058349609,
0.2816694974899292,
-0.36766475439071655,
0.41673025488853455,
-0.2937813997268677,
-0.18260031938552856,
-0.29651179909706116,
-0.34288766980171204,
0.22366449236869812,
0.13416321575641632,
-0.1413390040397644,
0.9706169962882996,
-0.0097738616168499,
0.3525257706642151,
0.03545369952917099,
0.9079820513725281,
0.9446448087692261,
0.8374208807945251,
-0.6444916725158691,
-0.36745554208755493,
-0.5630394220352173
] |
Nonperturbative evaluation of the diffusion rate in field theory at high temperatures
|
Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated numerically by solving the Langevin equation in real time. A clear crossover from the semiclassical to the high temperature domain is observed. The temperature behaviour of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. The Kramer's predictions for the dependence on viscosity are qualitatively valid in this multidimensional case. In the limit of vanishing friction the diffusion rate is shown to coincide with the one obtained from the direct measurements of the conventional classical real-time Green function at finite temperature.
|
Alexander Bochkarev and Philippe de Forcrand
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210027
|
hep-lat/9210028
|
[
0.27801764011383057,
-0.8271497488021851,
0.2763620913028717,
-0.1157902255654335,
0.22801019251346588,
-0.3888012170791626,
-0.1558603197336197,
-0.6253172755241394,
-0.879758894443512,
1.6005980968475342,
0.5827713012695312,
-0.0159665048122406,
0.9075336456298828,
-0.7036452889442444,
0.055309876799583435,
0.31932705640792847,
-0.23681703209877014,
-0.20730207860469818,
-1.2382193803787231,
0.46232879161834717,
0.31944215297698975,
-0.46817272901535034,
-1.3947551250457764,
-0.5029149651527405,
-0.15476258099079132,
1.0191940069198608,
0.032684314996004105,
0.3471711277961731,
0.668834924697876,
-0.21430471539497375,
-0.025802478194236755,
-0.7251765131950378,
-0.617529034614563,
-0.38734087347984314,
-0.7186506986618042,
-0.2913805842399597,
-0.3813183307647705,
-0.3991326093673706,
0.48845940828323364,
-0.20747996866703033,
0.7939656972885132,
-0.6416555047035217,
0.016723990440368652,
-0.33195894956588745,
-0.8226878643035889,
0.49029025435447693,
-0.3112199306488037,
0.01413913257420063,
0.3849087059497833,
-1.1696112155914307,
0.2792101800441742,
0.2014274150133133,
0.1840856671333313,
-0.8917819857597351,
-0.3307704031467438,
-0.3445712625980377,
0.44386473298072815,
-0.16527533531188965,
-0.4833349585533142,
0.21099166572093964,
0.34340593218803406,
0.4632183015346527,
0.821990430355072,
-0.829458475112915,
0.46630939841270447,
1.335056185722351,
-0.46229317784309387,
0.8310026526451111,
-0.3242282569408417,
-0.520323634147644,
-0.5770084857940674,
-0.5153550505638123,
-0.4605698883533478,
0.2772403359413147,
-0.8116213083267212,
-0.34150946140289307,
-0.11255376785993576,
-0.8278613090515137,
-1.2622301578521729,
-0.8734270334243774,
-0.2638947069644928,
0.30363357067108154,
-0.13042786717414856,
0.4270632863044739,
0.11465830355882645,
-0.4166027009487152,
-0.18471378087997437,
-0.35490524768829346,
-0.013946383260190487,
0.44598156213760376,
0.2973736822605133,
0.9948333501815796,
-0.125469371676445,
0.08943639695644379,
0.017613932490348816,
0.42393970489501953,
-0.2084968090057373,
0.4076770544052124,
0.2697800099849701,
0.3515457808971405,
0.2659379243850708,
1.1491402387619019,
-0.9034423828125,
-0.08195395022630692,
-0.5689290165901184,
0.5241299271583557,
-0.5507835745811462,
-0.0032033000607043505,
-0.039616990834474564,
-0.7093372344970703,
0.3165983259677887,
-0.19153282046318054,
0.6631726026535034,
0.696336030960083,
0.19821543991565704,
0.4551379680633545,
-0.11195066571235657,
0.16934339702129364,
-0.7536643147468567,
-0.22700686752796173,
0.134998619556427,
-0.158172145485878,
0.07258865237236023,
0.5853978991508484,
0.18910588324069977,
-0.026603074744343758,
0.5711699724197388,
0.4113820791244507,
-0.11397382616996765,
0.5675385594367981,
0.5560079216957092,
-0.07023828476667404,
-0.2978113889694214,
0.4011078178882599,
-0.7763426899909973,
0.07062825560569763,
-0.16482560336589813,
0.5232788920402527,
0.23096171021461487,
-0.1086035743355751,
0.5015665888786316,
-0.9600613713264465,
0.26524218916893005,
1.0912524461746216,
0.6233603358268738,
0.49841591715812683,
0.2986353039741516,
-0.030918294563889503,
0.2292099893093109,
0.05650049448013306,
-0.996096134185791,
0.23847560584545135,
0.15984994173049927,
-0.008428236469626427,
0.1978508085012436,
0.5533071756362915,
-0.6040372252464294,
0.32652750611305237,
-0.6731157898902893,
-0.4316725730895996,
0.5051082968711853,
-0.28044724464416504,
-0.4125586450099945,
0.450370728969574,
-0.5742953419685364,
-0.22484001517295837,
-0.7678896188735962,
-0.751923680305481,
0.05889621749520302,
-0.9751147031784058,
-0.6097753047943115,
0.9563973546028137,
0.1418232023715973,
0.9172282218933105,
0.19534523785114288,
0.5293283462524414,
0.5918198227882385,
-0.6197996139526367,
-0.37407293915748596,
-0.103373683989048,
0.1297399252653122,
-0.7448662519454956,
0.05540359020233154,
0.547660231590271,
-0.25115853548049927,
0.24849733710289001,
-0.066438689827919,
-0.378023624420166,
0.49745112657546997,
0.5209429860115051,
0.12452682852745056,
-0.17297713458538055,
-0.04067681357264519,
0.5675097107887268,
-0.8137683868408203,
0.22067300975322723,
-0.7919476628303528,
-0.08175568282604218,
-0.18259364366531372,
-0.8139054775238037,
0.3114031255245209,
0.3241147994995117,
-1.2837305068969727,
0.0481966957449913,
-1.737263798713684,
0.2953401505947113,
0.751422107219696,
0.3149823546409607,
-0.8219683766365051,
-0.15784788131713867,
0.4557744264602661,
-0.36479413509368896,
0.5405764579772949,
-0.9651599526405334,
0.6443124413490295,
-0.0015832341741770506,
0.034486763179302216,
0.14040693640708923,
0.45823150873184204,
0.4148674011230469,
0.446582168340683,
0.31418928503990173,
-0.4090764820575714,
0.6346633434295654,
-0.6505889892578125,
-0.5421116948127747,
0.6078094244003296,
0.5321059226989746,
0.29765084385871887,
-0.12899760901927948,
0.10737773776054382,
0.4376026690006256,
0.003612075001001358,
0.7600885033607483,
0.12433992326259613,
0.15139342844486237,
0.5905784964561462,
0.7752193808555603,
0.7747700214385986,
0.34868112206459045,
-0.5158147215843201,
0.43634870648384094,
1.02691650390625,
0.5462974309921265,
-0.3588851988315582,
-0.2424497753381729,
-0.3825840651988983,
0.35892271995544434,
-1.000291347503662,
0.5728521943092346,
-0.503960371017456,
0.28487783670425415,
-0.3007067143917084,
0.666023313999176,
-0.9369105696678162,
0.049857497215270996,
-0.24294418096542358,
0.16323287785053253,
0.0643482506275177,
-0.7542207837104797,
0.6091935634613037,
0.18884870409965515,
-0.27133816480636597,
-0.34906500577926636,
0.11180880665779114,
0.930221438407898,
-0.205170676112175,
-0.11474604159593582,
0.5349694490432739,
-0.5563146471977234,
-1.5123356580734253,
0.4179428219795227,
-0.5734366774559021,
0.2146657258272171,
-0.3515002429485321,
0.39815330505371094,
0.3563351333141327,
-0.7897493243217468,
0.6691926121711731,
0.41713860630989075,
-0.10764104872941971,
0.44794395565986633,
-0.5833771228790283,
-0.08768033236265182,
0.8269380927085876,
-0.03905005753040314,
-0.7446570992469788,
0.12653958797454834,
-0.5520066022872925,
-0.23130419850349426,
-0.5523415803909302,
-0.2602517008781433,
0.21670159697532654,
-0.3698135018348694,
0.44565483927726746,
-0.20179951190948486,
-0.47831207513809204,
0.04898316040635109,
0.09052080661058426,
-0.7854673862457275,
0.2285233587026596,
0.4252339005470276,
-0.13490021228790283,
0.1987130045890808,
-0.6427393555641174,
0.6237260699272156,
-0.28217893838882446,
-0.22370116412639618,
0.6776806116104126,
-0.023956822231411934,
-0.5067659020423889,
0.8883483409881592,
0.2792303264141083,
0.1117834523320198,
0.12493010610342026,
0.6455300450325012,
0.7428215146064758,
0.025157250463962555,
-0.15921808779239655,
-0.4356868267059326,
-0.1853068321943283,
-0.25715479254722595,
0.015810804441571236,
-0.5087328553199768,
-0.6649833917617798,
0.3228657841682434,
0.27287575602531433,
-0.751521110534668,
0.9237173795700073,
-1.0301414728164673,
-0.3922366201877594,
-0.11991841346025467,
-0.5996106863021851,
0.23313362896442413,
-0.13428962230682373,
-0.2755488455295563,
-0.9732803702354431,
0.12759363651275635,
0.24194985628128052,
0.24972404539585114,
0.32253211736679077,
-0.3291459381580353,
0.43562138080596924,
0.4174569249153137,
0.6157299280166626,
-0.23156984150409698,
-0.050712522119283676,
-0.32324016094207764,
-0.1668129563331604,
-0.24390703439712524,
-0.6767286062240601,
0.005360086914151907,
0.12971821427345276,
0.5009391903877258,
-0.28088685870170593,
0.03480261564254761,
-0.5851293802261353,
-0.35710608959198,
-0.6278952956199646,
-0.30026015639305115,
0.5166106820106506,
0.5041830539703369,
-0.06505300104618073,
-0.5063319802284241,
-0.7980618476867676,
-0.3503344655036926,
0.07749629765748978,
-0.5771443843841553,
0.9283066987991333,
-0.615554690361023,
0.1003400906920433,
0.15751878917217255,
-0.9514607787132263,
0.23177680373191833,
-0.37904471158981323,
0.616428792476654,
0.9264008402824402,
0.5548330545425415,
1.4535192251205444,
-0.6064723134040833,
-0.6621465682983398,
-0.9907861948013306,
0.8585391044616699,
0.913628876209259,
0.6757031679153442,
0.26091447472572327,
0.3882122039794922,
0.40712377429008484,
-0.6418891549110413,
-0.5163342952728271,
-0.46726861596107483,
0.37094631791114807,
0.35782626271247864,
-0.2643416225910187,
0.450410395860672,
0.3278971016407013,
0.2701573967933655,
0.6133080124855042,
-0.13338935375213623,
0.4429396390914917,
0.30570200085639954,
-0.41907835006713867,
0.5828069448471069,
0.1692115217447281,
0.2584540545940399,
0.14890965819358826,
-0.7438245415687561,
0.0050802272744476795,
0.26283687353134155,
0.5360271334648132,
0.060815200209617615,
-0.6287325024604797,
-0.13641001284122467,
-0.16557255387306213,
0.1450769305229187,
0.3947402238845825,
-0.8809074759483337,
0.19725796580314636,
0.6961143612861633,
0.24422307312488556,
-0.4128757119178772,
0.13750962913036346,
0.7417648434638977,
0.7157979011535645,
0.32292863726615906,
-0.91852867603302,
0.33142340183258057,
-0.4814586341381073,
0.406620591878891,
0.1530461460351944,
-0.4191989600658417,
-0.7888978719711304,
-0.6839379668235779,
0.42781418561935425,
-0.4084261655807495,
0.25451573729515076,
1.1589466333389282,
0.11763840913772583,
-0.0935971662402153,
-0.21538543701171875,
-0.6214907169342041,
1.168574571609497,
0.3738780915737152,
-0.5488473773002625,
-0.13964466750621796,
-0.032676611095666885,
-0.12693718075752258,
0.6287033557891846,
-0.33360809087753296,
-0.5404147505760193,
0.02985527366399765,
-0.4170584976673126,
0.8157086968421936,
-0.24272987246513367,
-0.2496395856142044,
0.025215329602360725,
-0.5861883759498596,
-0.6024755835533142,
0.3346949517726898,
0.3613998293876648,
-0.11894531548023224,
0.345264196395874,
0.18849237263202667,
-0.08069693297147751,
0.13093502819538116,
-0.2450273334980011,
0.02842402458190918,
1.1867061853408813,
0.5182524919509888,
0.5419371128082275,
-0.06566615402698517,
0.6284855008125305,
-0.3296944499015808,
0.3587546944618225,
0.6094509959220886,
0.12906208634376526,
-0.36548274755477905,
-0.49639415740966797,
0.06345006078481674,
-0.8889003396034241,
-0.4196999669075012,
0.5193684101104736,
-0.20759473741054535,
1.0114485025405884,
-0.2610616087913513,
-0.4952630400657654,
-0.19677172601222992,
-0.5526101589202881,
-0.5203315615653992,
0.544300377368927,
0.09635240584611893,
-0.6425393223762512,
0.9784919023513794,
-0.8495516180992126,
-0.22972656786441803,
-0.6934349536895752,
0.8527897000312805,
-0.6317541599273682,
0.04471101984381676,
0.6282132863998413,
0.18478159606456757,
0.7599258422851562,
-0.601249098777771,
0.23410356044769287,
-0.9093479514122009,
0.1718321442604065,
-0.2591961920261383,
-0.05830290913581848,
-0.2260446697473526,
0.007985372096300125,
0.4366414546966553,
0.14203424751758575,
-0.47485652565956116,
0.1379893273115158,
0.8031477332115173,
0.0912543386220932,
-0.4850061535835266,
-0.40553387999534607,
-0.25533223152160645,
0.48383772373199463,
-0.3544910252094269,
-0.31285572052001953,
-0.3110656142234802,
0.5320704579353333,
0.04569663107395172,
0.09607736766338348,
0.03694654256105423,
-0.883489727973938,
0.23964959383010864,
-0.10896362364292145,
0.9842380285263062,
-0.6847501397132874,
-0.3056865632534027,
-0.2348208874464035,
-0.6492982506752014,
0.852780818939209,
0.32314226031303406,
-0.22925986349582672,
0.08534025400876999,
-0.712449848651886,
-0.2200678288936615,
0.32790613174438477,
-0.8297095894813538,
0.06640832871198654,
-0.9172099232673645,
-1.1246604919433594,
-0.49794554710388184,
0.7973685264587402,
0.2807275652885437,
0.6099753975868225,
-0.13850128650665283,
0.09063733369112015,
0.32818183302879333,
0.10009270906448364,
0.2932359576225281,
-0.01847623661160469,
-0.15722143650054932,
-0.07102213054895401,
0.27357280254364014,
0.8335949182510376,
-0.4957027733325958,
0.32654115557670593,
-1.063193678855896,
1.1697022914886475,
-0.5678956508636475,
-0.19988498091697693,
0.22277945280075073,
-0.43808513879776,
0.927280604839325,
-0.8253348469734192,
0.6157208681106567,
0.5022023320198059,
0.0545143224298954,
0.7777019739151001,
0.4030175805091858,
-0.7870156168937683,
-0.15663546323776245,
-0.8532863855361938,
-0.45966899394989014,
0.6441943645477295,
0.1845557987689972,
-0.09370970726013184,
-0.840183436870575,
-0.8528716564178467,
0.37844982743263245,
0.6115940809249878,
0.4838796555995941,
0.4473523199558258,
0.3691118657588959,
-0.02585458941757679,
-0.0016719833947718143,
-0.5270666480064392,
-0.31420671939849854,
0.31248506903648376,
-0.14087525010108948,
-0.40915167331695557,
0.12701891362667084,
0.028616541996598244,
-0.5282697677612305,
-1.3219630718231201,
-0.17769335210323334,
0.5174495577812195,
0.4386068284511566,
-0.43308892846107483,
0.9245705604553223,
-0.41622617840766907,
-0.5442107915878296,
-0.2723182141780853,
-0.3562808036804199,
0.020544540137052536,
0.6694535613059998,
0.5616903305053711,
0.560417652130127,
0.30785733461380005,
-0.17710350453853607,
0.4421853721141815,
-0.8703927397727966,
-0.19477581977844238,
0.011487320065498352,
-0.45789721608161926,
-0.4186559319496155,
-0.05046100914478302,
0.19079901278018951,
-0.5639329552650452,
-0.2565454840660095,
-1.0843470096588135,
-0.049192339181900024,
-0.3741544187068939,
-0.2965535521507263,
-0.0509587824344635,
-0.055343400686979294,
0.075913205742836,
0.5037782192230225,
1.0878524780273438,
0.11424653232097626,
-0.40855133533477783,
-0.3745384216308594,
-0.6959249973297119,
-0.218505859375,
-0.3684768080711365,
1.7312588691711426,
0.17105431854724884,
-0.685462236404419,
0.014251579530537128,
-0.23351186513900757,
-0.3569781482219696,
0.23164226114749908,
0.51494300365448,
-0.30289605259895325,
0.12559641897678375,
0.024291707202792168,
0.017476143315434456,
0.09351135045289993,
0.8271502256393433,
0.48737770318984985,
-0.4540802836418152,
-0.5328196883201599,
-0.6766634583473206,
-0.15339314937591553,
-0.5097581148147583,
0.5148826837539673,
0.21118471026420593,
0.008339785039424896,
0.254230797290802,
-0.01973097026348114,
-0.7370527386665344,
-0.2159615308046341,
-1.0401380062103271,
-0.27400532364845276,
-1.4044642448425293,
0.1413070410490036,
-0.33548593521118164,
-0.22527962923049927,
0.6038287281990051,
0.3080090880393982,
0.17905309796333313,
-0.08157079666852951,
-0.8394326567649841,
0.3516271114349365,
0.4702342450618744,
0.010064526461064816,
-0.10128074884414673,
-1.2409956455230713,
-0.43911105394363403,
-0.6212069988250732,
-0.05320776626467705,
-0.12300819903612137,
-0.30231335759162903,
0.0027450169436633587,
-0.20950713753700256,
0.9962896704673767,
-0.54917973279953,
0.6727625727653503,
-1.1648672819137573,
-1.2401540279388428,
0.028290055692195892,
-0.033089328557252884,
-0.6283220052719116,
0.580184280872345,
0.3572998642921448,
0.6990980505943298,
0.21087077260017395,
-0.33798471093177795,
-0.8171130418777466,
0.3337032198905945,
-1.0414643287658691,
0.1290767639875412,
0.5546150207519531,
0.045968662947416306,
-0.5037967562675476,
-0.826594889163971,
0.10646721720695496,
0.06822187453508377,
-0.756672739982605,
0.5242438316345215,
-0.3306499421596527,
0.5236914157867432,
-0.08682293444871902,
0.7531865239143372,
0.4484104812145233,
0.48870739340782166,
-0.20521800220012665,
0.9077742099761963,
-0.27021265029907227,
-0.3354167342185974,
0.4581069052219391,
0.05732649564743042,
-0.2953762412071228,
-0.21292613446712494,
0.26085180044174194,
-0.796517014503479,
0.1540031135082245,
0.21169734001159668,
0.32262635231018066,
0.08528142422437668,
-0.2829078733921051,
-0.4493093490600586,
-0.8124473094940186,
-0.29752060770988464,
-0.24390017986297607,
0.3889167308807373,
0.724831759929657,
-0.5099974274635315,
0.48095738887786865,
-0.308745414018631,
-0.8809162974357605,
0.624882698059082,
-0.13479821383953094,
-0.29704776406288147,
0.08740949630737305,
-0.2078830599784851,
-0.07378833740949631,
0.10968009382486343,
0.118431955575943,
0.34569069743156433,
-0.2887710630893707,
0.4654434323310852,
-0.2382274866104126,
-0.11402180790901184,
-0.23480096459388733,
0.060326673090457916,
-0.7819855213165283,
-0.10490971803665161,
-0.8308704495429993,
0.561178982257843,
-0.6141905784606934,
-1.257372260093689,
-0.24776659905910492,
-0.6588308215141296,
-0.0608028843998909,
-0.14854182302951813,
-0.04012499749660492,
0.1740017533302307,
-0.2565124034881592,
-0.27332279086112976,
0.010762850753962994,
-0.13405287265777588,
-0.3097810447216034,
0.68419349193573,
0.029665743932127953,
-0.21382471919059753,
0.42685452103614807,
-0.18619441986083984,
0.09046217054128647,
-0.6477282047271729,
0.3206920027732849,
1.2295832633972168,
0.749980092048645,
-0.07471521943807602,
0.4289478659629822,
0.12594789266586304,
0.15304304659366608,
-0.0520273894071579,
-0.9400489330291748,
0.2813207805156708,
-0.12974481284618378,
0.3344877362251282,
0.4263404309749603,
0.5521585941314697,
0.16159670054912567,
0.83847576379776,
-0.14633366465568542,
0.2860359847545624,
-0.16606350243091583,
0.23088693618774414,
0.25887683033943176,
0.34324440360069275,
-0.1674625128507614,
0.4349099099636078,
-0.39459216594696045,
0.10812342166900635,
-0.0470634326338768,
-0.5807645320892334,
-0.35580188035964966,
0.10427824407815933,
-0.16197548806667328,
0.29174578189849854,
-0.39334729313850403,
-0.7272980213165283,
0.018800869584083557,
-0.1889531910419464,
0.2957386076450348,
0.6875475645065308,
0.06535753607749939,
0.21148498356342316,
0.5123153328895569,
0.3418732285499573,
-0.09155689179897308,
0.8208143711090088,
0.02479460835456848,
0.9346928000450134,
0.7555726170539856,
0.5853469371795654,
0.3971922993659973,
-0.02638680301606655,
0.49970006942749023,
-0.6193614602088928,
0.22470158338546753,
0.4961434602737427,
-0.8320940732955933,
0.31862133741378784,
-0.38135993480682373,
0.18217571079730988,
0.040213558822870255,
-0.2536317706108093,
0.5260348916053772,
-0.6577726006507874,
0.11185548454523087,
1.0125982761383057,
-0.3312964141368866,
0.1341339349746704,
0.734511137008667,
0.12849141657352448,
0.01890329271554947,
0.3542388677597046,
-0.04524396359920502,
0.2001834660768509,
1.0443636178970337,
1.5193116664886475,
0.3566097617149353,
0.8684552311897278,
0.6823375821113586,
-0.8200501203536987,
0.6789215207099915,
0.8291640281677246,
-0.7176252007484436,
0.6599088907241821,
-0.952046811580658,
-0.3549341559410095,
0.21464084088802338,
0.06733996421098709,
0.17795725166797638,
0.017773842439055443,
0.08948834985494614,
0.10601537674665451,
-0.08501969277858734,
-0.5160487294197083,
1.8656436204910278,
0.07751890271902084,
-0.5600098371505737,
-0.35772526264190674,
0.0720716342329979,
-0.18763235211372375,
-0.10091957449913025,
-0.7098644971847534,
0.20792873203754425,
-0.7720127105712891,
0.443783700466156,
-0.43293991684913635,
-1.0058178901672363,
-0.7424051761627197,
-0.9416996240615845,
0.12513823807239532,
-0.10222095996141434,
0.5311554074287415,
0.22526857256889343,
0.5733373761177063,
-0.3620167374610901,
-0.0056933388113975525,
-0.8272908926010132,
0.17218253016471863,
0.4077114164829254,
0.017314843833446503,
-0.04407854378223419,
0.5573851466178894,
0.21202559769153595,
-0.5825124979019165,
0.32042136788368225,
0.41241025924682617,
-0.9984933137893677,
0.7163905501365662,
-0.2203354686498642,
0.14239422976970673,
0.6066475510597229,
-0.36668989062309265,
-0.06174725666642189,
0.1481216996908188,
0.4724067747592926,
0.2707994282245636,
-0.4445172846317291,
0.0017058462835848331,
-0.5721883177757263,
0.08155550062656403,
-0.2627726197242737,
0.15012916922569275,
-0.07558806985616684,
0.12755398452281952,
0.04732337221503258,
-0.5721728801727295,
4.089040279388428,
0.3011283278465271,
-0.2612537145614624,
0.5369249582290649,
0.7818825244903564,
1.0812064409255981,
0.03169812262058258,
-0.8812775015830994,
0.697961151599884,
-0.3856112062931061,
-0.2631663680076599,
0.20552754402160645,
0.5629494786262512,
0.16746953129768372,
0.07648772746324539,
0.8124505281448364,
-0.4379514455795288,
-0.3719024956226349,
0.06750502437353134,
-0.8707137703895569,
-0.23425757884979248,
-0.04565591365098953,
0.2115069478750229,
0.3466223180294037,
0.30618754029273987,
-0.17405198514461517,
0.40982314944267273,
-0.5208151936531067,
-1.4153748750686646,
-0.6203066110610962,
-0.7375405430793762,
-0.7096952199935913,
0.5199362635612488,
-0.18520112335681915,
-0.9407901763916016,
0.3293275237083435,
0.41989389061927795,
-0.5801123976707458,
-0.10737059265375137,
0.07323833554983139,
-0.23038750886917114,
-0.6544231176376343,
0.2576551139354706,
-0.2025156468153,
-0.18123210966587067,
0.9294933676719666,
-0.6264675259590149,
0.9145261645317078,
0.49903228878974915,
-0.34371939301490784,
0.6042619347572327,
0.4342803955078125,
0.48952504992485046,
0.06021931767463684,
-0.7960899472236633,
0.08804351836442947,
-0.5194203853607178,
-0.048700056970119476,
0.16679099202156067,
0.10524936020374298,
0.37580394744873047,
-0.34021198749542236,
-0.18609166145324707,
0.40755563974380493,
-0.028285879641771317,
0.8047541379928589,
0.502875030040741,
0.076323963701725,
-0.483275830745697,
-0.10543372482061386,
-0.044632840901613235,
-0.7252000570297241,
-0.29334089159965515,
0.6479211449623108,
0.26636189222335815,
0.12254372984170914,
0.11956516653299332,
0.46529966592788696,
0.15063366293907166,
0.031380545347929,
0.28668534755706787,
-0.5696418285369873,
-0.6405720114707947,
-0.17381830513477325,
-0.041458483785390854,
0.23154176771640778,
-0.14594300091266632,
-0.16400089859962463,
-0.5418741703033447,
0.6731061339378357,
0.5772241353988647,
1.3234277963638306,
-0.09732431918382645,
-0.3956681787967682,
-0.7112400531768799
] |
The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory
|
The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.
|
Howard D. Trottier and R. M. Woloshyn
|
hep-lat hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210028
|
hep-lat/9210029
|
[
0.4287835657596588,
-0.0842948630452156,
-0.2369910627603531,
-0.0683063194155693,
-0.5323802828788757,
-0.30952075123786926,
0.19819818437099457,
-0.11621030420064926,
-0.765834391117096,
1.0595510005950928,
0.6505888104438782,
0.022261224687099457,
0.08644013106822968,
-0.739983856678009,
-0.1421358287334442,
0.1658274531364441,
-0.2962872087955475,
-0.852712094783783,
-1.4373635053634644,
1.0386569499969482,
0.5750724077224731,
0.02547500468790531,
-0.8866540789604187,
-0.7068361639976501,
-0.0008703781059011817,
0.9753109812736511,
-0.4514651298522949,
0.020195461809635162,
0.9959790706634521,
1.036941409111023,
0.561704158782959,
-0.9288724064826965,
-0.37604963779449463,
-0.40132108330726624,
-0.14864559471607208,
-0.25295108556747437,
0.11636227369308472,
-0.00029144927975721657,
0.8805072903633118,
-0.3410283625125885,
0.8579862117767334,
-0.5263833999633789,
0.21097010374069214,
0.027823394164443016,
-0.16039182245731354,
-0.5240768790245056,
-0.265176922082901,
-0.5324264764785767,
-0.1312648057937622,
-0.8319684863090515,
0.011605682782828808,
0.3129787743091583,
0.49332138895988464,
-1.0839924812316895,
-0.6391560435295105,
0.08401212841272354,
0.34882476925849915,
-0.33309754729270935,
-0.845888614654541,
0.14752934873104095,
0.5150912404060364,
0.2858363091945648,
0.4112442433834076,
-1.0160081386566162,
0.10364852100610733,
0.7715232968330383,
-0.5791549682617188,
0.2999471426010132,
0.04331852123141289,
-0.5975120067596436,
0.5414963364601135,
-0.3418560326099396,
-0.7326225638389587,
-0.28122520446777344,
-1.2312936782836914,
-0.09480166435241699,
-0.30054715275764465,
-0.08168163895606995,
-1.1727980375289917,
-0.4937385320663452,
0.032871875911951065,
-0.22171393036842346,
-0.07108519971370697,
0.3078567385673523,
-0.49235910177230835,
-0.5072464346885681,
-0.04101772606372833,
-0.038762014359235764,
0.44063717126846313,
0.2686014473438263,
0.2811605930328369,
1.0278578996658325,
0.04933561384677887,
-0.23770487308502197,
0.2525099813938141,
0.93952876329422,
-0.03994732350111008,
0.4163379669189453,
-0.27732089161872864,
0.2970750629901886,
0.23777276277542114,
0.6405671834945679,
-0.8870018124580383,
0.10968571901321411,
-0.5892165899276733,
0.8666464686393738,
0.33226174116134644,
-0.5244935154914856,
0.0704275518655777,
-0.4914373457431793,
0.49869728088378906,
0.11480553448200226,
0.17902794480323792,
0.9538003206253052,
0.3585638403892517,
0.28572753071784973,
-0.38664862513542175,
0.27819162607192993,
-0.4529666006565094,
-0.06548885256052017,
0.3032006621360779,
0.840036928653717,
0.21764019131660461,
0.1326599270105362,
0.17720618844032288,
0.06389312446117401,
0.4292927086353302,
0.3658628761768341,
-0.29982152581214905,
0.13924947381019592,
-0.5110103487968445,
-0.6472952365875244,
-0.3707074820995331,
0.9499114751815796,
-0.39546844363212585,
0.37702590227127075,
-0.187098428606987,
0.8259811997413635,
-0.08572737127542496,
-0.5646587014198303,
0.5344460010528564,
-0.7547168731689453,
0.4222699999809265,
1.2179694175720215,
-0.8577497005462646,
-0.17822304368019104,
0.30419501662254333,
-0.13752178847789764,
-0.493696928024292,
0.12646366655826569,
-0.286834180355072,
-0.2502419054508209,
-0.5367780923843384,
0.47650381922721863,
0.15974372625350952,
-0.04126599058508873,
-0.5820026993751526,
0.12593497335910797,
-0.573057234287262,
-0.5426437854766846,
0.14120909571647644,
-0.9874889850616455,
-0.06832237541675568,
0.30092164874076843,
-0.8145608305931091,
0.024782303720712662,
-0.546846330165863,
-0.09904034435749054,
0.2224186658859253,
-0.9191840887069702,
0.3668098747730255,
0.505118727684021,
-0.016495224088430405,
0.5832816362380981,
0.4305765628814697,
0.9051153063774109,
0.499812513589859,
-0.5396807193756104,
0.6794846057891846,
0.1753203123807907,
-0.17973385751247406,
0.07224518060684204,
0.6518696546554565,
-0.28781044483184814,
0.035928335040807724,
-0.2738243639469147,
0.09035845845937729,
-0.21108733117580414,
0.13120703399181366,
0.10963158309459686,
-0.2805424630641937,
0.025464899837970734,
-0.15282636880874634,
0.7562223672866821,
-0.7251914143562317,
-0.6860446929931641,
-0.3561634421348572,
-0.26241397857666016,
-0.5354546308517456,
-0.6286697387695312,
-0.37015536427497864,
0.17816559970378876,
-0.45157966017723083,
0.7181874513626099,
-1.0700448751449585,
0.3557962477207184,
1.1841686964035034,
0.1052670106291771,
-0.5264461636543274,
0.37116506695747375,
0.05375192314386368,
-0.41837432980537415,
-0.12855106592178345,
-0.28077322244644165,
0.1899818480014801,
0.8298699855804443,
-0.2841838300228119,
0.8394293785095215,
0.4372004270553589,
0.3989133834838867,
0.22169522941112518,
0.17457261681556702,
0.1638057380914688,
0.7803909182548523,
-0.17412224411964417,
-0.6677317023277283,
-0.3310890197753906,
0.509335458278656,
0.4394588768482208,
-0.16633298993110657,
-0.546869695186615,
0.07688803970813751,
-0.3116875886917114,
0.8616628646850586,
0.48897168040275574,
0.398680180311203,
0.5925617218017578,
0.33570727705955505,
0.5968856811523438,
0.22984464466571808,
-0.08269477635622025,
-0.5044124126434326,
0.008000575937330723,
0.17780956625938416,
0.08327268064022064,
0.4229786694049835,
-0.34336501359939575,
0.18112263083457947,
-0.3883676528930664,
0.3603023886680603,
0.3299681544303894,
0.9487569332122803,
0.3743837773799896,
0.18980672955513,
-1.0909531116485596,
-0.36867809295654297,
-0.2687320113182068,
0.5314448475837708,
-0.2288520187139511,
-0.12752044200897217,
0.34481996297836304,
0.27706992626190186,
-0.5391130447387695,
-0.4891253411769867,
0.4104754328727722,
1.1133394241333008,
-0.05892238765954971,
0.7564067244529724,
0.8553906083106995,
-0.37231582403182983,
-0.6751787066459656,
-0.19217287003993988,
-0.9028605222702026,
-0.13720639050006866,
-0.811568558216095,
-0.025012895464897156,
0.7199898958206177,
-0.7830851674079895,
0.573724627494812,
0.025399252772331238,
-0.10036741197109222,
0.38862350583076477,
-0.292340487241745,
0.459359347820282,
0.2904585599899292,
0.12118058651685715,
-0.19649498164653778,
0.21362565457820892,
-0.7027256488800049,
-0.6484166383743286,
0.21015505492687225,
0.1458614617586136,
0.3672226369380951,
-0.49486541748046875,
0.1145424097776413,
0.2767880856990814,
-0.768123984336853,
0.16090808808803558,
-0.16176466643810272,
-0.4918956160545349,
-0.3081548810005188,
0.34543362259864807,
0.017483720555901527,
-0.18932366371154785,
-0.9544046521186829,
0.47788649797439575,
-0.14169470965862274,
-0.27552518248558044,
0.18245281279087067,
0.15837591886520386,
-0.8057156205177307,
0.45264744758605957,
-0.03839898854494095,
0.14035950601100922,
-0.021635623648762703,
0.9047348499298096,
0.7408075332641602,
-0.03946072235703468,
-0.8205108046531677,
-0.6823379397392273,
0.04775894805788994,
-0.11923389136791229,
-0.00671731261536479,
-0.17095883190631866,
-0.320254385471344,
0.687159538269043,
0.017049696296453476,
-0.438965767621994,
0.4079091548919678,
-0.07862278819084167,
-1.1367038488388062,
0.1614551991224289,
-0.6428605914115906,
0.4186004102230072,
-0.3799242079257965,
0.19477787613868713,
-0.6274104118347168,
0.5382010340690613,
0.1326642632484436,
-0.339387446641922,
0.44962432980537415,
0.017666911706328392,
0.43893516063690186,
0.38403618335723877,
0.34751662611961365,
-0.001132239936850965,
0.04773860052227974,
-0.2495591789484024,
-0.9310889840126038,
0.5456024408340454,
-0.5193071961402893,
0.5954723358154297,
-0.011303791776299477,
0.726969301700592,
-0.017237063497304916,
0.32902640104293823,
-0.04671766236424446,
0.006499416194856167,
-0.1693425476551056,
0.09795510768890381,
1.1653330326080322,
0.2636343240737915,
-0.21076752245426178,
-0.19059236347675323,
-0.8324670195579529,
-0.19771134853363037,
-0.12102328985929489,
-0.38649848103523254,
0.6390148997306824,
-0.47948992252349854,
0.5788528323173523,
-0.34922295808792114,
-0.39818117022514343,
-0.5256054401397705,
0.2836161255836487,
0.8518823385238647,
0.5447597503662109,
0.3328322172164917,
0.8203234076499939,
-0.6595004796981812,
-0.6636768579483032,
0.2517712116241455,
0.4392821192741394,
0.9602929949760437,
0.3004676103591919,
0.46963977813720703,
-0.21708446741104126,
-0.16373766958713531,
-0.6311911344528198,
-1.0627251863479614,
-0.8863979578018188,
0.21535387635231018,
-0.0887569934129715,
-0.7224715948104858,
-0.26634863018989563,
-0.30137550830841064,
0.5764226913452148,
0.4916497766971588,
0.3345659375190735,
0.41651099920272827,
0.31992045044898987,
-0.04641636461019516,
0.5102431774139404,
0.4499123990535736,
0.2499346137046814,
-0.018758177757263184,
-1.1106058359146118,
0.0869673565030098,
-0.1778239607810974,
0.693983793258667,
-0.20838437974452972,
0.25118181109428406,
-0.24953746795654297,
-0.5920287370681763,
0.2300957441329956,
0.04682040587067604,
-0.6314129829406738,
0.2880377471446991,
0.10902643948793411,
0.5819122195243835,
0.5599448680877686,
0.2518431842327118,
1.112781047821045,
0.06276557594537735,
-0.01800689846277237,
-0.7398258447647095,
0.1813904345035553,
-0.9582710862159729,
0.13933256268501282,
0.7920578718185425,
-0.9198952913284302,
-0.38148802518844604,
-0.6054654717445374,
-0.4238491356372833,
-0.14080524444580078,
-0.11388704180717468,
1.2069300413131714,
0.5576740503311157,
-0.23062679171562195,
-0.5325719118118286,
0.141072079539299,
0.48114416003227234,
-0.09797359257936478,
-0.6551992297172546,
0.3907351791858673,
-0.007979621179401875,
-0.45994290709495544,
0.3452056348323822,
0.7697573304176331,
-0.7823872566223145,
0.5775396227836609,
-0.8409774899482727,
-0.05324983596801758,
-0.5850965976715088,
-0.9308664202690125,
-0.4562815725803375,
-0.40675780177116394,
-0.1879839152097702,
0.37065577507019043,
0.7746219635009766,
-0.1034817323088646,
-0.893791913986206,
-0.5516658425331116,
-0.45346423983573914,
-0.4918873906135559,
-0.1465863436460495,
0.12430389970541,
0.5901449918746948,
1.0239958763122559,
0.03600615635514259,
0.37075698375701904,
0.4313686490058899,
0.6841141581535339,
-0.34815648198127747,
-0.0855109840631485,
0.19914497435092926,
0.03355764225125313,
-0.34869384765625,
-0.3548074960708618,
-0.5120333433151245,
-0.6214148998260498,
0.19999457895755768,
-0.4836077392101288,
0.28111979365348816,
-0.026419030502438545,
-0.8747974634170532,
-0.1716099977493286,
-0.24315646290779114,
-1.1391013860702515,
1.2175374031066895,
-0.19222243130207062,
-0.23502780497074127,
0.8074566125869751,
-0.6233259439468384,
-0.16000871360301971,
0.2635164260864258,
-0.6163908243179321,
-0.3517002761363983,
0.683644711971283,
0.27833032608032227,
0.6183344721794128,
0.49861639738082886,
-0.8334975242614746,
0.17521725594997406,
-0.2138570100069046,
-0.008837726898491383,
-0.5659117698669434,
-0.39872586727142334,
-0.09662947058677673,
-0.2916383743286133,
0.5224582552909851,
0.1276666522026062,
0.21231749653816223,
-0.1644269973039627,
-0.6909664273262024,
-0.23987944424152374,
0.43453481793403625,
-0.4772244095802307,
-0.05444081127643585,
1.2319960594177246,
0.6191257238388062,
-0.9126110076904297,
-0.3550949692726135,
0.7428374290466309,
-0.35163015127182007,
0.42200109362602234,
-0.1166079193353653,
-0.2701672911643982,
-0.19975177943706512,
-0.7074012160301208,
0.3436668813228607,
-0.6459400057792664,
-0.3844524323940277,
-0.6657409071922302,
-1.021066427230835,
-0.17751745879650116,
0.0023929611779749393,
0.14405448734760284,
0.010159637778997421,
-1.058519959449768,
-0.45447006821632385,
0.5886816382408142,
-0.39988943934440613,
0.08333905786275864,
-0.6541860103607178,
-0.16235458850860596,
0.0059423791244626045,
0.7188718318939209,
-0.6952236294746399,
0.12314385920763016,
0.08292221277952194,
0.1009068638086319,
0.010192761197686195,
0.918621301651001,
-0.038420047610998154,
-0.6034426689147949,
0.2185790091753006,
0.2956904470920563,
0.0177775789052248,
-0.12454712390899658,
-0.792661726474762,
0.7709765434265137,
-0.7417864799499512,
1.3332300186157227,
-0.31570863723754883,
-0.47247642278671265,
-0.29860594868659973,
-0.22565044462680817,
0.41681164503097534,
-0.8686980605125427,
0.7748974561691284,
0.8892390131950378,
-0.13422296941280365,
0.3912558853626251,
0.7654306888580322,
-0.1111290380358696,
-0.06690656393766403,
-1.175857663154602,
-1.3382694721221924,
0.5690170526504517,
-0.21482796967029572,
0.49769526720046997,
-0.7046695351600647,
-0.8867256045341492,
0.0028708819299936295,
0.03721483796834946,
0.5948498249053955,
0.20874716341495514,
0.10350754112005234,
0.681519627571106,
-0.24187062680721283,
0.22008264064788818,
-0.35638704895973206,
-0.02037251926958561,
-0.03834467753767967,
-0.6241708993911743,
0.39787501096725464,
0.3539753258228302,
-0.5410535931587219,
-1.159661889076233,
-0.23867282271385193,
0.7383406162261963,
0.2315872609615326,
-0.26197299361228943,
0.30854544043540955,
-0.532325029373169,
-0.7027904391288757,
-0.5793757438659668,
0.34768348932266235,
0.5678000450134277,
0.35552531480789185,
0.09413312375545502,
-0.0037570965941995382,
0.5057222247123718,
0.1978473663330078,
0.6334699988365173,
0.13022223114967346,
0.3798990249633789,
0.6081349849700928,
-0.9033406972885132,
-0.22133338451385498,
0.5093891024589539,
-0.7489020228385925,
-1.1431623697280884,
-0.24151849746704102,
-0.6274513006210327,
0.24765846133232117,
-1.1354072093963623,
-0.47586482763290405,
-0.06249476596713066,
0.025682462379336357,
-0.13581182062625885,
0.613400399684906,
0.7454907894134521,
-0.15953417122364044,
-0.03002016618847847,
-0.30846527218818665,
-0.7439475655555725,
-0.6393288969993591,
-0.4545890986919403,
1.4135347604751587,
-0.254866361618042,
-0.21713963150978088,
0.4589961767196655,
0.2565094530582428,
-0.34244897961616516,
0.19550952315330505,
0.40492159128189087,
-0.5610193014144897,
0.9003621935844421,
0.601426362991333,
0.13786427676677704,
0.2941786050796509,
0.6544034481048584,
0.5463608503341675,
0.4781522750854492,
0.06575644761323929,
-1.1243654489517212,
-0.6054674386978149,
-0.31536951661109924,
-0.10777975618839264,
0.8052064180374146,
0.27294570207595825,
0.2930673658847809,
0.16864557564258575,
0.04986240714788437,
-0.2199944257736206,
-0.40026867389678955,
-0.1606084406375885,
-0.5229306817054749,
-0.5531529784202576,
-0.4094482958316803,
-0.2990262508392334,
0.18599455058574677,
1.0129433870315552,
0.17452576756477356,
-0.5167062282562256,
-0.3773869574069977,
-0.020963652059435844,
0.449911504983902,
0.28692030906677246,
-0.045894406735897064,
-0.6297752857208252,
-0.23210741579532623,
-0.5621163845062256,
0.09484384953975677,
-0.904158890247345,
0.20009692013263702,
0.16273155808448792,
0.3273867070674896,
0.6256145238876343,
0.17038565874099731,
0.10042224079370499,
-0.717906653881073,
-0.8915098309516907,
0.1873786896467209,
0.15346002578735352,
-0.28474748134613037,
0.6110554337501526,
0.14388282597064972,
0.8804678320884705,
-0.28895947337150574,
0.5280734896659851,
-0.2633816599845886,
-0.34547489881515503,
-0.3818535804748535,
0.24513070285320282,
0.4102398753166199,
0.8042335510253906,
-0.037204284220933914,
-1.0131680965423584,
0.20036514103412628,
0.5480824708938599,
-1.3066893815994263,
0.4091969430446625,
-0.9340154528617859,
-0.24051688611507416,
-0.39367765188217163,
0.21936865150928497,
0.3040175139904022,
0.6000235676765442,
0.29993194341659546,
0.12831254303455353,
0.13108208775520325,
-0.5801809430122375,
-0.12558740377426147,
-0.2253730446100235,
0.09356104582548141,
0.23996780812740326,
0.27739837765693665,
-0.6376214623451233,
-0.33650803565979004,
0.12786512076854706,
-0.5131086707115173,
0.1819176971912384,
-0.28786981105804443,
-0.3992663621902466,
0.23002837598323822,
-0.2821180522441864,
-0.6767181754112244,
0.7622170448303223,
0.5305354595184326,
-0.7995712757110596,
-0.509800374507904,
-0.43443170189857483,
-0.3625888228416443,
0.7794209718704224,
-1.2132408618927002,
-0.24492290616035461,
0.7626569867134094,
-0.6837069392204285,
-0.14066845178604126,
-0.3829510509967804,
-0.4079563617706299,
0.4476560652256012,
-0.28422385454177856,
0.08345475047826767,
0.24587658047676086,
0.07346225529909134,
0.039472997188568115,
0.21900832653045654,
-1.0937293767929077,
0.06882794201374054,
-0.625511884689331,
0.801061749458313,
-1.1639564037322998,
-1.1468896865844727,
-0.7727417945861816,
0.7602353096008301,
0.40903836488723755,
0.2850436270236969,
-0.4545542001724243,
-0.6023281216621399,
-0.06903056800365448,
0.04653787612915039,
0.13063335418701172,
-0.31577667593955994,
-0.18219661712646484,
0.7007133960723877,
-0.24166549742221832,
-0.5704021453857422,
0.038096748292446136,
-0.01510764192789793,
0.2549610435962677,
-0.031628310680389404,
-0.12592901289463043,
1.1164947748184204,
0.5343864560127258,
-0.7664684653282166,
1.2324602603912354,
-0.054318808019161224,
0.4979374408721924,
0.11369261145591736,
-0.552629828453064,
0.14349035918712616,
0.8182210922241211,
0.3221665620803833,
0.1126810684800148,
0.2308289259672165,
0.5317185521125793,
-0.01895507052540779,
0.2049209475517273,
0.3030775785446167,
-0.5631510019302368,
1.0855932235717773,
0.1864665001630783,
0.469097375869751,
-0.6928128600120544,
-0.2067725956439972,
-0.15395964682102203,
0.2875537574291229,
-0.08941546827554703,
-0.32091572880744934,
0.08379208296537399,
-0.3751400411128998,
-0.2433915138244629,
0.30081871151924133,
-0.2829098105430603,
-0.2710375189781189,
-0.09130965918302536,
0.12449817359447479,
0.8745806813240051,
0.25434568524360657,
0.2507101595401764,
-0.11037931591272354,
0.950228214263916,
0.2902846336364746,
-0.12366881221532822,
0.586567759513855,
0.031123576685786247,
1.0240410566329956,
0.7150672674179077,
0.9535682201385498,
0.24388881027698517,
0.3599609136581421,
-0.09876041114330292,
-1.1098740100860596,
0.3393944501876831,
0.19918277859687805,
-0.8786923289299011,
-0.25461387634277344,
-0.23787672817707062,
-0.16444893181324005,
0.08939474076032639,
-0.5095927715301514,
0.2848121225833893,
-1.1607811450958252,
-0.17364870011806488,
0.49308210611343384,
-0.4024604260921478,
-0.09174079447984695,
1.0524933338165283,
0.5247023701667786,
0.1788637936115265,
0.2830480933189392,
0.23975001275539398,
-0.2974949777126312,
1.2009902000427246,
0.86285001039505,
0.23928187787532806,
-0.42466476559638977,
0.29031112790107727,
-0.5844680666923523,
-0.09882646799087524,
0.22395630180835724,
-0.5540680289268494,
0.5481706261634827,
-0.3556591868400574,
-0.2184872180223465,
-0.2702888250350952,
0.023619400337338448,
-0.03895885869860649,
-0.6282515525817871,
0.6439428925514221,
-0.27016475796699524,
-0.35607582330703735,
-0.7227763533592224,
0.8845633268356323,
1.16578209400177,
-0.8010157346725464,
-0.08556097000837326,
0.7033540606498718,
-0.3862804174423218,
-0.5357387661933899,
-0.7969996929168701,
-0.1707598716020584,
-0.23656107485294342,
-0.036846138536930084,
-0.5423480272293091,
-0.37284475564956665,
-0.3670567274093628,
-0.11982594430446625,
0.24579107761383057,
-0.3449332118034363,
0.6888464093208313,
0.48335161805152893,
0.5042082071304321,
0.22052575647830963,
-0.4688098728656769,
0.1479397714138031,
0.5175172686576843,
1.03095543384552,
-0.4225742220878601,
0.2691231071949005,
0.1452324092388153,
0.9057056903839111,
-0.3589220345020294,
0.5565136671066284,
0.8960937857627869,
-0.6637066006660461,
0.6109696626663208,
-0.14469827711582184,
0.2554697096347809,
0.6901910901069641,
0.18234670162200928,
0.4389580190181732,
0.0984172597527504,
-0.24568812549114227,
0.3785419762134552,
-0.6203076839447021,
-0.14825281500816345,
-0.6703316569328308,
0.24366188049316406,
-0.828398585319519,
0.6682136058807373,
0.3627557158470154,
0.1387786865234375,
0.46741926670074463,
-1.0318728685379028,
4.11529016494751,
0.6787574291229248,
0.6375410556793213,
-0.08429180085659027,
0.6453166604042053,
0.738336980342865,
-0.3759927749633789,
-0.8262128829956055,
-0.01958346739411354,
-0.8495550155639648,
-0.1913733333349228,
-0.03258276358246803,
-0.00335224368609488,
-0.45264992117881775,
0.11785642057657242,
1.1430758237838745,
-0.06963019073009491,
-0.39629191160202026,
0.6179549694061279,
-0.9429724812507629,
-0.9226131439208984,
0.18407194316387177,
-0.0098330182954669,
0.36191612482070923,
0.6627482175827026,
0.31584709882736206,
0.46151453256607056,
-0.12179486453533173,
0.21993041038513184,
0.02598448097705841,
-0.35185477137565613,
-1.1202901601791382,
0.07310540229082108,
0.07470542937517166,
-0.5942975282669067,
1.015660285949707,
-0.5616366267204285,
-0.6429843306541443,
-0.13321521878242493,
-0.16610197722911835,
0.0074767302721738815,
-0.3189390003681183,
-0.06475861370563507,
-0.16116802394390106,
-0.6702022552490234,
1.05396568775177,
-0.5166462659835815,
0.723301112651825,
0.36645227670669556,
-1.2179597616195679,
0.7115333080291748,
-0.3432563245296478,
0.52191162109375,
-0.32508400082588196,
-0.9974719882011414,
0.4242084324359894,
-0.2595060467720032,
-0.1367480307817459,
0.5932269096374512,
0.36388227343559265,
0.038142718374729156,
-0.3550061285495758,
0.07287926226854324,
0.4960562288761139,
-0.01836717315018177,
0.26006022095680237,
0.07145586609840393,
0.2944166362285614,
-0.4723682105541229,
0.1096322312951088,
-0.21389833092689514,
-0.19189584255218506,
-0.6307858824729919,
0.43805089592933655,
0.7433691024780273,
0.0665116012096405,
-0.01983848214149475,
0.3417041301727295,
-0.21880684792995453,
0.2743843197822571,
0.3848223388195038,
-0.8020788431167603,
0.20256517827510834,
-0.34465494751930237,
0.6684773564338684,
0.6801841855049133,
-0.5702280402183533,
0.032500430941581726,
0.04491247236728668,
0.8382527232170105,
0.5076636075973511,
1.0224276781082153,
0.22058533132076263,
-0.21676284074783325,
-0.9351116418838501
] |
Renormalisation of lattice currents and the calculation of decay constants for dynamical staggered fermions
|
A numerical calculation of the lattice staggered renormalisation constants at $\beta = 5.35$, $m = 0.01$ is presented. It is seen that there are considerable non-perturbative effects present. As an application the vector decay constant $f_\rho$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript figures appended.)
|
R. Altmeyer, K. D. Born, M. Goeckeler, R. Horsley, E. Laermann and G. Schierholz
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210029
|
hep-lat/9210030
|
[
-0.27440106868743896,
-0.5530270338058472,
0.09992563724517822,
0.7692707777023315,
-0.5360197424888611,
-0.40586817264556885,
-0.477640837430954,
-0.6449121832847595,
-0.5661486983299255,
1.5577458143234253,
0.3680691421031952,
-0.007798200938850641,
0.5163062810897827,
-0.7338343858718872,
-0.08063464611768723,
0.15853606164455414,
0.0912122055888176,
-0.2923748791217804,
-1.6009944677352905,
1.1189817190170288,
0.4451070725917816,
-0.08853352069854736,
-0.5431693196296692,
-0.8023316860198975,
0.15924952924251556,
0.7810201644897461,
-0.17110800743103027,
0.14612986147403717,
0.8084215521812439,
0.5150020122528076,
0.1881096065044403,
0.09473671019077301,
-0.05743103101849556,
-0.7011113166809082,
-0.5106310248374939,
-0.05235984921455383,
-0.338714063167572,
-0.22883863747119904,
0.8049470782279968,
-0.1859433799982071,
1.0286840200424194,
-0.14175434410572052,
-0.36341071128845215,
-0.5079628825187683,
-0.45088014006614685,
0.4144626557826996,
-0.2140296995639801,
-0.1472001075744629,
-0.25788360834121704,
-1.3463921546936035,
0.012270381674170494,
0.05273144692182541,
0.3907557427883148,
-0.48947563767433167,
-0.11247143894433975,
-0.3612480163574219,
-0.05640058591961861,
-0.03375094011425972,
-0.851071834564209,
-0.011269117705523968,
0.30542078614234924,
-0.2964784801006317,
0.3267177641391754,
-0.7356564402580261,
0.48917874693870544,
0.8911401629447937,
-0.09617535024881363,
0.5319380760192871,
0.13682620227336884,
-0.06323295831680298,
0.12176543474197388,
0.3474198877811432,
-0.4165361821651459,
-0.20769305527210236,
-0.40397998690605164,
0.1274997591972351,
0.08949071168899536,
-0.5326992869377136,
-0.23828144371509552,
-0.7980177402496338,
-0.00478177098557353,
0.14116962254047394,
-0.24957843124866486,
-0.21539467573165894,
-0.6895113587379456,
-0.31628385186195374,
-0.4354580044746399,
-0.7128686904907227,
0.1896682232618332,
0.7119249701499939,
0.6875125765800476,
0.9047815203666687,
-0.8165127038955688,
-0.10652973502874374,
0.7138151526451111,
0.6997818946838379,
0.15794390439987183,
0.351241797208786,
0.16010236740112305,
-0.009370752610266209,
0.6307188868522644,
0.6065042614936829,
-0.4091337025165558,
0.4969326853752136,
-0.7012378573417664,
0.6507986783981323,
-0.6760311722755432,
0.3879368305206299,
-0.07727764546871185,
-0.5893406271934509,
0.5642092823982239,
-0.111504927277565,
0.7466798424720764,
0.5205073952674866,
0.12259431928396225,
0.4031811058521271,
-0.18316924571990967,
0.14894552528858185,
-1.0080461502075195,
-0.07924937456846237,
0.5764262080192566,
0.43862348794937134,
0.4170842170715332,
0.5785577297210693,
-0.5346739292144775,
-0.01938551664352417,
0.6804832220077515,
0.13899247348308563,
-0.21073375642299652,
-0.00015757244545966387,
0.5615363717079163,
0.14711792767047882,
-0.20964697003364563,
0.9385479688644409,
-0.9036627411842346,
0.16676528751850128,
-0.417221337556839,
0.6946867108345032,
0.15835674107074738,
0.05750027671456337,
0.5788285136222839,
-1.0179433822631836,
-0.0831507220864296,
0.5221995711326599,
0.36390674114227295,
0.24985972046852112,
0.08892790228128433,
0.21699395775794983,
-0.25839686393737793,
0.22385577857494354,
-0.1422688513994217,
-0.1539139598608017,
-0.12735401093959808,
-0.006893833167850971,
0.15434212982654572,
0.4007984399795532,
-0.46890756487846375,
0.5029641389846802,
-0.5978598594665527,
-0.36463662981987,
-0.10921332240104675,
0.7619770765304565,
-0.4435737133026123,
0.7529268860816956,
-0.522254228591919,
-0.2693079113960266,
-0.3372442126274109,
-0.9186913371086121,
0.48859497904777527,
-0.446685254573822,
-0.40954580903053284,
0.09893467277288437,
-0.3125450015068054,
1.0051008462905884,
0.7256908416748047,
0.8435403108596802,
0.23359178006649017,
-0.18711863458156586,
-0.15751947462558746,
0.23189416527748108,
0.2783135175704956,
-0.6541208028793335,
0.274922639131546,
0.4336452782154083,
-0.16237540543079376,
0.10874922573566437,
-0.268574059009552,
-0.7092514634132385,
0.5915300846099854,
0.40093326568603516,
0.017583368346095085,
-0.30139756202697754,
0.19729790091514587,
0.6097684502601624,
-0.6095778942108154,
0.41023895144462585,
-0.9680478572845459,
0.08929020166397095,
-0.5716909766197205,
-0.5061500668525696,
0.48761314153671265,
0.5117487907409668,
-1.5920072793960571,
0.6579506993293762,
-1.2807368040084839,
-0.026871221140027046,
1.2842622995376587,
0.5688343644142151,
-0.6252238154411316,
-0.265022873878479,
-0.0279480442404747,
-0.19002488255500793,
0.6986714601516724,
-0.5083247423171997,
1.0579606294631958,
0.3115489184856415,
-0.1264203041791916,
0.18465915322303772,
0.1728554219007492,
0.6612908244132996,
0.2673516273498535,
0.20188894867897034,
-0.11210229247808456,
0.23614653944969177,
-0.9167901873588562,
-0.6361467838287354,
0.16107875108718872,
0.5661190152168274,
0.49672868847846985,
-0.05853370577096939,
0.054179597645998,
0.28721553087234497,
-0.31183120608329773,
0.467171847820282,
0.6183245182037354,
-0.245822936296463,
-0.021648667752742767,
0.391067236661911,
0.31521186232566833,
0.665181577205658,
-0.275188684463501,
-0.0796651765704155,
0.74421226978302,
-0.036641910672187805,
-0.4337867498397827,
-0.22659701108932495,
-0.6041586399078369,
0.26154041290283203,
-1.5455037355422974,
0.03426775336265564,
-0.34218063950538635,
0.10861944407224655,
-0.6137387156486511,
0.6361079216003418,
-1.1636216640472412,
0.04295993968844414,
-0.22771507501602173,
-0.010213680565357208,
-0.21825772523880005,
-0.48834630846977234,
-0.08769479393959045,
0.04814229533076286,
0.09332955628633499,
-0.9568496942520142,
0.12896019220352173,
0.6780177354812622,
-0.2075585424900055,
0.05595353990793228,
0.18993982672691345,
-0.5116448998451233,
-1.4545224905014038,
-0.27600786089897156,
-1.1411614418029785,
-0.18236353993415833,
-0.6842069029808044,
0.13596053421497345,
0.623386561870575,
-0.1775212287902832,
0.775158703327179,
-0.5241933465003967,
0.01437619049102068,
0.38899698853492737,
-1.083937168121338,
-0.04247474670410156,
0.6322034001350403,
-0.09649176150560379,
-0.9474278688430786,
0.7538533210754395,
-1.243875503540039,
0.07934039831161499,
-0.17415983974933624,
-0.5200322270393372,
0.7132222056388855,
-0.5501542091369629,
0.5093069076538086,
-0.2026122361421585,
0.13369084894657135,
-0.013286939822137356,
-0.3632061779499054,
-0.6193860173225403,
0.34316486120224,
0.071933314204216,
0.049530040472745895,
-0.05107128247618675,
-1.0537183284759521,
0.5002651214599609,
-0.06715722382068634,
-0.03557511046528816,
0.6443818211555481,
0.1959543228149414,
-1.0754436254501343,
0.3766310513019562,
0.11687811464071274,
-0.14537371695041656,
-0.2745305001735687,
0.9156383275985718,
0.7605442404747009,
-0.03134503960609436,
0.0035201285500079393,
-0.4433895945549011,
-0.3350433111190796,
0.5531512498855591,
-0.20896710455417633,
-0.9871889352798462,
-0.2836906313896179,
0.906599760055542,
0.08547817170619965,
-0.43258193135261536,
0.25732940435409546,
-0.9111279845237732,
-0.8591204285621643,
0.5391354560852051,
-0.33710119128227234,
0.20665378868579865,
-0.1595846563577652,
0.020876990631222725,
-0.7406865954399109,
0.03890405595302582,
0.9918361902236938,
-0.015652529895305634,
0.1312621533870697,
0.17432579398155212,
0.5277007222175598,
0.2446509450674057,
0.40087753534317017,
-0.2837704122066498,
0.1503828465938568,
0.011862516403198242,
-0.6312664747238159,
-0.1363556683063507,
-0.7332132458686829,
0.30453231930732727,
-0.06199533864855766,
0.011517667211592197,
-0.025966910645365715,
0.6837027668952942,
-0.6165043115615845,
-0.6889488101005554,
-0.05642290413379669,
-0.49086350202560425,
0.22314627468585968,
0.6956709623336792,
0.16446790099143982,
-0.3203001320362091,
-1.1446187496185303,
-0.6679973602294922,
0.05889483541250229,
0.4185117185115814,
0.5393574833869934,
-0.5139884352684021,
0.15410736203193665,
0.3815818727016449,
-0.737551748752594,
0.5493265986442566,
-0.26666024327278137,
0.30753424763679504,
0.46098634600639343,
0.1893223077058792,
0.6596524715423584,
-0.624153733253479,
-0.569124162197113,
0.07964987307786942,
1.1593393087387085,
0.5784347653388977,
0.7894439101219177,
0.313724547624588,
0.2030358910560608,
0.061451349407434464,
-0.15708598494529724,
-0.6863363981246948,
-0.14541640877723694,
-0.5273478627204895,
0.20025968551635742,
0.3815041184425354,
-0.09471849352121353,
0.10637295991182327,
-0.04081712290644646,
-0.03853708878159523,
-0.0051015992648899555,
-0.0034706899896264076,
0.19447368383407593,
0.430673211812973,
0.5353768467903137,
0.44401490688323975,
-0.5555472373962402,
-0.37823426723480225,
-0.2640611529350281,
0.26822805404663086,
0.41916629672050476,
-0.16886532306671143,
-0.4001411497592926,
-0.7895901799201965,
-0.4564932584762573,
-0.36381617188453674,
0.5565537214279175,
0.16177396476268768,
-1.0702906847000122,
-0.31568795442581177,
0.2768345773220062,
0.8796591758728027,
0.10599551349878311,
-0.21374793350696564,
1.025688886642456,
0.11016415804624557,
0.3697795867919922,
-0.7569244503974915,
0.7380250692367554,
-0.9318879246711731,
0.6226187348365784,
0.24747659265995026,
-0.9160869121551514,
-0.44048407673835754,
-0.887799084186554,
0.10495323687791824,
-0.13865302503108978,
0.4303761124610901,
1.0895872116088867,
0.4915132224559784,
0.3158400356769562,
-0.4565739929676056,
0.08137571066617966,
0.9789844155311584,
-0.9698345065116882,
-0.1430586278438568,
-0.061069000512361526,
0.10455263406038284,
0.07111680507659912,
0.49689605832099915,
-0.5178478956222534,
-0.3293516933917999,
0.11749929189682007,
-0.7617598176002502,
1.0066298246383667,
-0.13505353033542633,
-0.4950541853904724,
-0.206393763422966,
-0.7274372577667236,
0.3363332748413086,
0.922828197479248,
0.569588303565979,
-0.6331354379653931,
0.18560200929641724,
0.0026524171698838472,
-0.3384600281715393,
-0.3319460451602936,
-0.07434765249490738,
0.21003176271915436,
0.7339128255844116,
0.3932127058506012,
0.16331413388252258,
0.47300851345062256,
0.003911531530320644,
-0.10584159195423126,
-0.22718989849090576,
0.3695532977581024,
0.4373396933078766,
-0.9074330925941467,
-0.19211986660957336,
-0.477038711309433,
-1.058506965637207,
-0.25331565737724304,
0.4273677468299866,
-0.2440890520811081,
0.900346040725708,
0.17533819377422333,
-0.3753223121166229,
-0.5443093180656433,
-0.44975724816322327,
-0.5552221536636353,
0.3582269847393036,
0.1003357544541359,
-0.269702672958374,
0.43533846735954285,
-0.6033173203468323,
0.2194935530424118,
-0.7261732220649719,
-0.014628535136580467,
-0.8085810542106628,
0.023508943617343903,
0.5887230038642883,
0.18838690221309662,
0.35074904561042786,
-0.9262887239456177,
0.5157126188278198,
0.017562182620167732,
0.021637016907334328,
-0.1181894987821579,
-0.05504414066672325,
-0.2798653542995453,
-0.3472004234790802,
0.700645923614502,
0.22552144527435303,
-0.3973088264465332,
0.1388675570487976,
0.08690405637025833,
0.25288403034210205,
-0.04080286622047424,
-0.05763344466686249,
-0.140522301197052,
0.5939257740974426,
0.17364473640918732,
-0.3385148346424103,
0.36737820506095886,
0.5094801783561707,
0.07076884061098099,
0.23765477538108826,
0.3676337003707886,
-0.9434738755226135,
0.1340676248073578,
0.034862928092479706,
0.815345048904419,
-0.8819916844367981,
-0.5496199727058411,
-0.2475299835205078,
-0.45552584528923035,
0.692406952381134,
1.0186481475830078,
-0.8465896844863892,
-0.0062380158342421055,
-0.5175812244415283,
0.06082722544670105,
-0.1410587579011917,
-0.02947663515806198,
-0.037602316588163376,
-0.7794492840766907,
-0.9860907793045044,
-0.01574311964213848,
0.504757821559906,
-0.44517040252685547,
0.567672610282898,
0.3583083748817444,
-0.07584942877292633,
0.06639622151851654,
0.48385289311408997,
0.00851281825453043,
-0.7417815923690796,
-0.4423092007637024,
0.43508681654930115,
-0.4606373906135559,
0.33474287390708923,
-0.6676605343818665,
0.005134756676852703,
-1.0172291994094849,
1.0002574920654297,
-0.4638370871543884,
0.03137641027569771,
0.3026324510574341,
0.5351349711418152,
0.43715402483940125,
-0.2805507779121399,
0.9870892763137817,
0.6367491483688354,
-0.1868220567703247,
0.5007789134979248,
0.7620407342910767,
-0.8339129090309143,
-0.2915498614311218,
-0.2854359745979309,
-0.6711240410804749,
0.5824736952781677,
-0.12034090608358383,
-0.23149225115776062,
-0.6639952063560486,
-0.9061523079872131,
-0.03193521127104759,
0.49525362253189087,
0.26634567975997925,
0.8040693998336792,
-0.027424484491348267,
-0.1611659675836563,
0.23237425088882446,
-0.2742151916027069,
-0.24564456939697266,
0.2921525239944458,
0.4355994164943695,
-0.10383021086454391,
0.6099230051040649,
0.22766128182411194,
-0.6404069662094116,
-0.693318247795105,
-0.10721053183078766,
0.3284755349159241,
0.02727106399834156,
-0.7556489109992981,
0.49627935886383057,
-0.1897379755973816,
-0.4659784436225891,
-0.2434135377407074,
0.16235117614269257,
0.23279517889022827,
0.45015910267829895,
0.9064146876335144,
0.455625981092453,
0.0816497802734375,
-0.028727490454912186,
0.22497007250785828,
-0.8511790037155151,
-0.3847196400165558,
0.19763313233852386,
-0.37124601006507874,
-0.04602249339222908,
0.5580916404724121,
0.22845132648944855,
-0.4511112570762634,
-0.5042706727981567,
-1.1924521923065186,
-0.2553883194923401,
-0.21557047963142395,
-0.6039976477622986,
-0.17641186714172363,
-0.01678248681128025,
-0.17573700845241547,
0.4819090664386749,
0.6116928458213806,
0.6733000874519348,
0.32927998900413513,
0.28761026263237,
-0.7885980606079102,
-0.34444642066955566,
-0.07342630624771118,
0.8875591158866882,
0.05776723846793175,
-1.0541512966156006,
0.01224300917237997,
-0.2287781685590744,
-0.5984284281730652,
0.12132914364337921,
0.5323722958564758,
0.3288988471031189,
0.3610110282897949,
-0.2967008948326111,
0.21793051064014435,
0.5853012800216675,
0.9007107615470886,
0.6392742991447449,
0.0031702141277492046,
-0.5868688821792603,
-1.030415654182434,
0.08362212777137756,
-0.7834546566009521,
0.1082935631275177,
0.35484248399734497,
0.10351897776126862,
0.31690192222595215,
0.2015770524740219,
-0.5560057163238525,
-0.31691256165504456,
-0.6911157369613647,
-0.2723456025123596,
-1.1380689144134521,
-0.23647642135620117,
-0.6493481397628784,
-0.0034650363959372044,
0.15283827483654022,
0.5490162968635559,
-0.28062930703163147,
0.1332000195980072,
-0.4300566017627716,
0.46210139989852905,
0.42605265974998474,
0.09569506347179413,
0.10674768686294556,
-1.0707893371582031,
-0.5455625057220459,
-0.3039402961730957,
0.03828360512852669,
0.3250076174736023,
-0.4090319871902466,
-0.4674796462059021,
-0.31261909008026123,
0.0015439684502780437,
-0.060987260192632675,
0.8597090840339661,
-0.8046714663505554,
-0.7621443867683411,
0.10849740356206894,
-0.6258179545402527,
-0.9774088859558105,
0.8190408945083618,
0.665961503982544,
0.2997951805591583,
0.6882808208465576,
-0.05809732899069786,
-0.7293339967727661,
0.5886397361755371,
-0.6638039946556091,
0.4408456087112427,
0.6722222566604614,
0.3395633101463318,
-0.03926297649741173,
-0.1759004145860672,
0.07152614742517471,
0.39130523800849915,
-0.5743950605392456,
0.35122862458229065,
-0.6625564098358154,
0.19305849075317383,
0.04373745247721672,
0.11382818967103958,
-0.3058646619319916,
0.19987541437149048,
-0.13327330350875854,
0.535197377204895,
0.1485544741153717,
0.3520471751689911,
0.28748834133148193,
0.33566775918006897,
-0.8133149743080139,
0.04427682235836983,
0.4645458459854126,
-0.20560258626937866,
0.04083247110247612,
0.49051886796951294,
-0.5322664380073547,
0.519806444644928,
0.5889261364936829,
-0.6392165422439575,
-0.8697798848152161,
-0.48868265748023987,
-0.3638826310634613,
0.5299118757247925,
0.3645913004875183,
-0.3249601423740387,
0.2885381877422333,
-0.3420901596546173,
-0.7063028812408447,
-0.08362013846635818,
-0.4513935148715973,
-0.039160557091236115,
-0.1997593343257904,
-0.05404192581772804,
-0.13462190330028534,
0.12815193831920624,
-0.23137763142585754,
0.8843594789505005,
-0.21244847774505615,
0.42435500025749207,
-0.38734951615333557,
-0.47090598940849304,
-0.22281377017498016,
-0.33383747935295105,
-0.5884909629821777,
0.18483079969882965,
-0.4183898866176605,
0.37435469031333923,
-0.2918163537979126,
-0.8381607532501221,
-0.06000838428735733,
0.6964789032936096,
-0.15317371487617493,
-0.3016664981842041,
-0.6388388872146606,
0.06356531381607056,
-0.3001415431499481,
0.19871816039085388,
-0.2006392776966095,
-0.2563524544239044,
-0.8526358008384705,
0.22589415311813354,
0.054077327251434326,
-0.5236788988113403,
0.15715332329273224,
0.22944526374340057,
0.06375457346439362,
-0.6784156560897827,
-0.21598687767982483,
1.1358015537261963,
0.888769268989563,
-0.6172859072685242,
0.1598903089761734,
-0.28854262828826904,
0.1974780261516571,
0.11991245299577713,
-0.790494978427887,
-0.22265152633190155,
0.7152875065803528,
0.40093082189559937,
0.9823205471038818,
0.14536230266094208,
0.31141531467437744,
0.6959722638130188,
0.9158636927604675,
0.3483031094074249,
-0.11632140725851059,
0.07168968766927719,
-0.16422773897647858,
0.8895675539970398,
-0.033573321998119354,
0.16879279911518097,
0.14122457802295685,
-0.13131211698055267,
0.09556426852941513,
-0.27758732438087463,
-0.5111112594604492,
0.06858058273792267,
-0.059924960136413574,
0.35421639680862427,
-0.44065147638320923,
0.10350451618432999,
-0.4757412374019623,
-0.19236603379249573,
0.6554844975471497,
-0.10588257759809494,
-0.36456844210624695,
0.12241847813129425,
0.8251295685768127,
0.1292533427476883,
0.030672110617160797,
0.2737303376197815,
0.028759201988577843,
1.1852689981460571,
0.6553319096565247,
0.4783685505390167,
0.6441776156425476,
0.6316251754760742,
0.21088388562202454,
-1.1556950807571411,
0.3669146001338959,
0.48740217089653015,
-0.8576802611351013,
0.5749309062957764,
-0.5132898688316345,
0.23688198626041412,
-0.20933771133422852,
-0.24971909821033478,
0.543973445892334,
-0.564697265625,
-0.31405109167099,
1.2577564716339111,
-0.20123876631259918,
-0.37298479676246643,
0.4240444600582123,
-0.11404526978731155,
0.04602519050240517,
0.43825119733810425,
-0.2388591468334198,
0.28826117515563965,
0.5834627747535706,
0.7448148131370544,
0.06320617347955704,
0.4431236982345581,
0.14607520401477814,
-0.44830331206321716,
0.26394209265708923,
0.8026667237281799,
-0.5931497812271118,
0.14105543494224548,
-0.3753713369369507,
-0.5709851980209351,
0.19612838327884674,
0.24402737617492676,
0.16112203896045685,
0.4189789295196533,
0.26672425866127014,
0.12639816105365753,
-0.9119959473609924,
-0.5237460732460022,
1.328025460243225,
0.5550051927566528,
-0.548232913017273,
-0.6622700691223145,
-0.27502861618995667,
0.09745375066995621,
-0.31679221987724304,
-0.6040889620780945,
0.500356137752533,
-0.12189462780952454,
0.3739570379257202,
-0.23831745982170105,
-0.10858720541000366,
-0.4997790455818176,
-0.7046610116958618,
0.4057433307170868,
-0.9396389722824097,
0.5130077600479126,
0.33900150656700134,
0.46685776114463806,
0.19943749904632568,
0.2210831344127655,
-0.7720483541488647,
-0.591339111328125,
0.48344671726226807,
0.07909704744815826,
0.866589367389679,
1.0684418678283691,
-0.009086494334042072,
-0.39751195907592773,
0.36192888021469116,
0.7120606303215027,
-0.5134497880935669,
0.7326657772064209,
-0.2699439227581024,
0.05242868885397911,
0.5905276536941528,
0.1821860671043396,
-0.14335490763187408,
-0.35385382175445557,
0.5675487518310547,
0.4390466511249542,
0.05706736072897911,
0.18338775634765625,
-0.7866830229759216,
-0.10947594046592712,
-0.41614624857902527,
0.4027354121208191,
0.21202713251113892,
0.44135501980781555,
0.32875335216522217,
-0.9149392247200012,
4.232786655426025,
0.36565840244293213,
0.3017948865890503,
0.4097272455692291,
0.5737956762313843,
1.0719754695892334,
-0.32057324051856995,
-0.3357870876789093,
0.20916607975959778,
-0.5439848899841309,
-0.12927892804145813,
-0.3318401277065277,
-0.0742962509393692,
-0.173262819647789,
-0.449457049369812,
0.7374565005302429,
-0.009520184248685837,
-0.05946776643395424,
-0.3840036690235138,
-0.7551549673080444,
-0.6433409452438354,
-0.08251402527093887,
0.6937457919120789,
0.12417838722467422,
0.20598764717578888,
0.23606200516223907,
-0.02623528055846691,
-0.7776833772659302,
-0.8040654063224792,
-0.492924302816391,
-0.6324302554130554,
-0.667245626449585,
0.34676504135131836,
-0.22236117720603943,
-1.087022066116333,
0.5647702813148499,
0.4959937632083893,
0.1230379045009613,
-0.17275205254554749,
0.019948601722717285,
-0.19859491288661957,
-0.6366058588027954,
-0.0038924061227589846,
-0.40585535764694214,
-0.5628527998924255,
0.6905616521835327,
0.2715243995189667,
0.7749689817428589,
0.13230641186237335,
-0.7309978008270264,
0.1738705039024353,
-0.04716050624847412,
0.00822767149657011,
-0.7004519104957581,
-0.661880373954773,
0.20905163884162903,
-0.6156824231147766,
0.03031853213906288,
0.5138786435127258,
0.00020740058971568942,
0.18932944536209106,
-0.13270314037799835,
-0.3601408898830414,
-0.4296717643737793,
0.20210103690624237,
0.472812682390213,
0.151091068983078,
0.10340654850006104,
-0.03661758080124855,
0.34149280190467834,
-0.09272243827581406,
-0.6079483032226562,
-0.11904465407133102,
0.23787850141525269,
0.016565196216106415,
0.27643704414367676,
0.12949469685554504,
0.530089259147644,
0.3815741240978241,
0.1532844454050064,
-0.32602450251579285,
-0.18947121500968933,
-0.41910988092422485,
-0.3023656904697418,
0.24568714201450348,
0.6746424436569214,
-0.14047794044017792,
-0.7561159133911133,
-0.3964817225933075,
0.44180828332901,
0.7465752363204956,
1.2773758172988892,
0.2211751788854599,
-0.2052697241306305,
-0.7245824337005615
] |
Dual Superconductor Mechanism of Confinement on the Lattice
|
We investigate the dual superconductor mechanism of confinement for pure SU(2) lattice gauge theory in the maximally abelian gauge. We focus on the the dual Meissner effect. We find that the transverse distribution of the longitudinal chromoelectric field due to a static quark-antiquark pair satisfies the dual London equation. Moreover we show that the size of the flux tube scales according to asymptotic freedom.
|
P. Cea and L. Cosmai
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210030
|
hep-lat/9210031
|
[
0.08798862993717194,
-0.5698568224906921,
0.013832190074026585,
0.24327248334884644,
0.22238872945308685,
-0.388490229845047,
-0.22463403642177582,
-0.7057536840438843,
-0.6062798500061035,
1.2058563232421875,
0.6915474534034729,
0.01593788154423237,
0.34720656275749207,
-0.7531693577766418,
-0.014824924059212208,
0.7522515654563904,
0.1932213455438614,
-0.6944412589073181,
-1.4682464599609375,
0.8126625418663025,
0.04387611523270607,
-0.035468731075525284,
-1.1697813272476196,
-0.43226686120033264,
-0.17613433301448822,
0.9171359539031982,
0.1550188958644867,
0.7148413062095642,
1.027593731880188,
0.389263391494751,
0.5721780061721802,
-0.1891549676656723,
-0.48373374342918396,
-0.24166689813137054,
-0.32931143045425415,
-0.2930019199848175,
-0.03126484528183937,
-0.5246855020523071,
0.6903780698776245,
-0.18349608778953552,
0.7112420797348022,
-0.5311238765716553,
-0.061828047037124634,
-0.5492953658103943,
-0.5472288131713867,
0.5536274313926697,
-0.18275251984596252,
0.11073115468025208,
0.15422852337360382,
-1.5635956525802612,
0.040956560522317886,
0.15561920404434204,
0.9253027439117432,
-1.0044822692871094,
-0.42906653881073,
-0.270658940076828,
-0.0594242624938488,
0.21037067472934723,
-0.9083553552627563,
-0.6722837090492249,
0.19895309209823608,
-0.12276343256235123,
0.4202903211116791,
-0.475999116897583,
-0.10446231067180634,
0.9287273287773132,
-0.24760358035564423,
0.2629866600036621,
-0.18719375133514404,
-0.678447425365448,
-0.5130031704902649,
0.055174682289361954,
-1.0911060571670532,
0.11411992460489273,
-0.7419984936714172,
0.13633817434310913,
0.052424244582653046,
-0.24310286343097687,
-0.5954814553260803,
-0.1934429109096527,
-0.01727462001144886,
0.48446014523506165,
-0.440468966960907,
0.41553622484207153,
-0.4431155025959015,
-0.7457728385925293,
0.0011474209604784846,
-0.1326051652431488,
0.0024693876039236784,
0.47405219078063965,
-0.029616542160511017,
0.4774104058742523,
-0.8474015593528748,
-0.4219513535499573,
0.6003723740577698,
0.508672297000885,
0.0452805794775486,
0.7554991841316223,
-0.000875177385751158,
0.2216891348361969,
0.06771907210350037,
1.2902277708053589,
-0.9521660804748535,
0.22821734845638275,
-0.571169376373291,
0.26198503375053406,
-0.04340290278196335,
-0.22293993830680847,
-0.5740146636962891,
-0.851326048374176,
0.134557843208313,
-0.38201311230659485,
1.0001442432403564,
0.730205237865448,
0.42913806438446045,
0.8394901752471924,
-0.26984503865242004,
0.3164454698562622,
-0.6464666128158569,
-0.349039763212204,
0.10092572122812271,
-0.17137789726257324,
0.32359233498573303,
0.30655592679977417,
-0.42890986800193787,
-0.5060561895370483,
0.44857144355773926,
0.35328543186187744,
-0.43350401520729065,
0.49869784712791443,
0.14196498692035675,
-0.5589250326156616,
-0.46392083168029785,
0.8351292014122009,
-0.3707948327064514,
0.3607959449291229,
-0.235343798995018,
0.23438552021980286,
0.3508555591106415,
-0.06354259699583054,
0.8038409948348999,
-0.2774304449558258,
-0.06595154851675034,
1.178035020828247,
0.7777425050735474,
-0.2834060490131378,
0.814452052116394,
0.24029254913330078,
-0.505592405796051,
0.7399763464927673,
-0.7892846465110779,
0.22158357501029968,
0.2989310622215271,
0.0667852908372879,
0.5148202776908875,
0.40595951676368713,
-0.8509706258773804,
0.5659208297729492,
-0.4540500044822693,
-0.5261002779006958,
0.29843154549598694,
-0.028866572305560112,
-0.5639342665672302,
0.5847401022911072,
-0.2063944786787033,
0.4245329797267914,
-0.5749625563621521,
-0.22192874550819397,
0.7974954843521118,
-0.2984156012535095,
-0.22370128333568573,
0.5693356394767761,
0.1167503371834755,
1.305017352104187,
1.0897084474563599,
0.6942287087440491,
0.28308922052383423,
-0.1083339974284172,
0.07276951521635056,
0.8249033689498901,
-0.24408626556396484,
-0.3444415032863617,
0.30192044377326965,
0.27875351905822754,
-0.9412928223609924,
0.15691357851028442,
-0.1714411973953247,
-0.6038767099380493,
0.23296354711055756,
0.018232952803373337,
-0.5958067774772644,
0.6637243628501892,
-0.48195886611938477,
0.3387838900089264,
-0.4911462366580963,
-0.06073848903179169,
-0.9205164313316345,
0.44551947712898254,
-0.6431438326835632,
-0.6663109064102173,
0.3177698254585266,
0.09442655742168427,
-0.944612979888916,
-0.11569035053253174,
-0.6617094278335571,
0.015949085354804993,
0.9865623712539673,
0.24788255989551544,
-0.29691168665885925,
-0.11344251036643982,
0.5160315632820129,
-0.3808254897594452,
0.16193240880966187,
-0.14615802466869354,
0.6938462257385254,
-0.28885766863822937,
-0.28288617730140686,
0.33017978072166443,
0.6034720540046692,
0.2700793743133545,
0.3749963343143463,
0.5634306073188782,
-0.32000455260276794,
0.7867801785469055,
-0.9322106242179871,
-0.3713628947734833,
-0.024480123072862625,
0.3970819115638733,
0.11656828969717026,
0.029301563277840614,
0.19451656937599182,
0.6237950325012207,
0.6343931555747986,
0.004351663403213024,
0.653522789478302,
0.36390915513038635,
0.5367187261581421,
0.5220003128051758,
0.5803972482681274,
0.1764063537120819,
-0.1771135777235031,
0.2983745336532593,
0.09511499851942062,
0.02907085418701172,
-0.6074356436729431,
0.2558978497982025,
-0.43065404891967773,
0.14892567694187164,
-0.990964412689209,
-0.008863169699907303,
-0.5379717350006104,
0.8180088996887207,
0.14476117491722107,
0.05823118984699249,
-1.5272270441055298,
-0.22700011730194092,
-0.5769413113594055,
-0.01688109152019024,
-0.2875249683856964,
-0.037794627249240875,
0.5593725442886353,
0.02409442700445652,
0.010300934314727783,
-0.3719944953918457,
-0.20348159968852997,
0.6921554803848267,
-0.13605773448944092,
0.162156343460083,
0.8487470746040344,
0.21050171554088593,
-1.3163611888885498,
-0.04306068271398544,
-0.9108290076255798,
-0.005091932602226734,
-0.6198749542236328,
0.21905437111854553,
0.8347232937812805,
-0.6117974519729614,
0.6113345623016357,
0.33742281794548035,
-0.027443084865808487,
0.6380764842033386,
-0.9837102293968201,
-0.12839658558368683,
0.36651724576950073,
-0.3103640079498291,
-0.9188440442085266,
0.203384131193161,
-0.7008945941925049,
-0.36467665433883667,
-0.22738848626613617,
0.3806326985359192,
0.5786484479904175,
-0.1542922407388687,
0.26720598340034485,
-0.00018968203221447766,
-0.29439958930015564,
-0.11095576733350754,
0.2953418791294098,
-0.8444538712501526,
0.08480136096477509,
0.02233804203569889,
-0.46369558572769165,
-0.6446660757064819,
-1.0977513790130615,
0.8586415648460388,
0.4681280851364136,
-0.39587071537971497,
0.4838995933532715,
-0.21043850481510162,
-0.2803628742694855,
-0.001347845303826034,
0.4361880123615265,
0.21561749279499054,
-0.3939738869667053,
1.0762431621551514,
0.8366860151290894,
0.0059214201755821705,
0.06595327705144882,
-0.2897548973560333,
-0.36802124977111816,
0.1767626851797104,
0.5090713500976562,
-0.6598323583602905,
-0.278937965631485,
0.890731692314148,
-0.25763168931007385,
-0.6620943546295166,
0.7013628482818604,
-0.9698639512062073,
-0.3980812132358551,
0.10705940425395966,
-0.5451345443725586,
0.1490904688835144,
0.3688683807849884,
0.11955317854881287,
-0.8419252038002014,
-0.2159770429134369,
-0.35522302985191345,
0.032144512981176376,
0.22951985895633698,
0.12203362584114075,
0.4948920011520386,
0.3941923975944519,
0.5068660974502563,
-0.43919315934181213,
0.1872166246175766,
-0.37662607431411743,
-0.1133631244301796,
-0.15847185254096985,
-0.20574353635311127,
0.06971628963947296,
0.14021772146224976,
0.039810601621866226,
-0.3071781098842621,
0.2489309012889862,
-0.7738195061683655,
-0.31689828634262085,
-0.9819449782371521,
-0.5838846564292908,
0.02960709109902382,
0.6192750930786133,
0.29805636405944824,
-0.17981642484664917,
-0.7134515047073364,
-0.7590964436531067,
0.015580466948449612,
-0.1969243735074997,
0.8320967555046082,
-1.066017508506775,
0.32031288743019104,
-0.012632101774215698,
-0.29916203022003174,
0.15331554412841797,
-0.09315488487482071,
0.27654802799224854,
0.5821019411087036,
-0.436806321144104,
0.8697382211685181,
-0.1799793243408203,
-0.8311213850975037,
0.4482700824737549,
1.06600022315979,
0.9542039632797241,
1.0581083297729492,
-0.0858977660536766,
0.2967274487018585,
-0.08263181895017624,
-0.18696191906929016,
-0.07634197920560837,
-0.24503518640995026,
-0.4224871098995209,
0.06186477094888687,
-0.016113614663481712,
0.11932431906461716,
0.07374227046966553,
0.4045318365097046,
0.9923847317695618,
0.27468201518058777,
0.1801060289144516,
0.5471331477165222,
0.27385154366493225,
0.6140342354774475,
0.36727964878082275,
-0.1271953135728836,
0.16559791564941406,
-0.748141348361969,
0.048814862966537476,
0.43041402101516724,
0.03444840759038925,
-0.08188536018133163,
-0.6675670742988586,
-0.14865641295909882,
-0.21293175220489502,
0.19668613374233246,
-0.0123018529266119,
-0.9237844944000244,
0.03746290132403374,
0.09879337251186371,
0.11323448270559311,
-0.3236820101737976,
0.06340303272008896,
0.6391571760177612,
0.41805869340896606,
-0.07769506424665451,
-0.9648920297622681,
0.24269293248653412,
-0.12133677303791046,
0.2509104907512665,
0.27741125226020813,
-0.5239181518554688,
-0.5872431993484497,
-0.8085653185844421,
0.0018637168686836958,
-0.24415694177150726,
0.15582014620304108,
1.0154359340667725,
-0.07631061226129532,
0.19820250570774078,
-1.1959036588668823,
-0.03785575553774834,
0.6997138857841492,
-0.1525406688451767,
-0.2808299958705902,
-0.11309552937746048,
0.15715688467025757,
-0.49532103538513184,
1.176076054573059,
-0.44218987226486206,
-0.42483803629875183,
-0.23022374510765076,
-0.5164399743080139,
-0.20939983427524567,
-0.3069746792316437,
-0.4510667622089386,
0.21684369444847107,
-0.5457835793495178,
-0.18070971965789795,
0.5162190794944763,
-0.10405437648296356,
0.09498871117830276,
0.2699586749076843,
0.4180334806442261,
-0.08357612043619156,
0.19811281561851501,
-0.1294327974319458,
0.31074222922325134,
0.14893749356269836,
0.879275381565094,
0.8774741888046265,
0.38931599259376526,
0.04279307276010513,
0.13660971820354462,
-0.06991725414991379,
0.1972934752702713,
-0.1938631385564804,
-0.06524108350276947,
-0.704047441482544,
-0.469426691532135,
-0.8840899467468262,
-0.5501288175582886,
0.737737774848938,
-0.1923881322145462,
0.6116546392440796,
0.29665133357048035,
-0.35085880756378174,
-0.45016252994537354,
-0.8049973249435425,
-0.7227217555046082,
0.6026326417922974,
0.09406881034374237,
-0.5689675211906433,
0.6305252313613892,
-0.8239887952804565,
-0.009885701350867748,
-0.18318507075309753,
0.15500971674919128,
-0.15567328035831451,
0.10340728610754013,
0.8335176110267639,
0.2649785280227661,
0.5189549326896667,
-0.6962619423866272,
0.6468517780303955,
-0.5807254314422607,
0.23060016334056854,
-0.4998082220554352,
-0.22152972221374512,
-0.6339380741119385,
-0.3470825254917145,
0.8514405488967896,
-0.5759671330451965,
0.06916403770446777,
0.10273408144712448,
-0.011061517521739006,
0.3891403079032898,
-0.3091854155063629,
-0.5402273535728455,
-0.09900002926588058,
0.27895694971084595,
-0.040447693318128586,
-0.14317092299461365,
-0.04592018201947212,
1.03233003616333,
0.5001901388168335,
0.07739699631929398,
-0.08860506117343903,
-0.09792907536029816,
0.06210236996412277,
-0.594201922416687,
0.2367466390132904,
-0.795707106590271,
-0.282307505607605,
-0.21676421165466309,
-0.11664755642414093,
0.5232321619987488,
0.2734856605529785,
-0.3108363151550293,
-0.7235181331634521,
-0.5412948131561279,
-0.5359222888946533,
0.7575361728668213,
-0.0166932400316,
-0.2579185664653778,
-0.5758368968963623,
-0.4864979684352875,
-0.22412636876106262,
1.279739260673523,
-0.36492404341697693,
0.46869343519210815,
0.3848283588886261,
0.12867799401283264,
0.3129218816757202,
0.2216825783252716,
0.0549563430249691,
-0.02412540465593338,
-0.3464529514312744,
0.48703160881996155,
0.2848825752735138,
0.6360370516777039,
-0.7217798233032227,
0.38505762815475464,
-1.0432698726654053,
0.9372273087501526,
-0.5789145827293396,
0.4607018232345581,
0.21245622634887695,
0.2604638636112213,
0.7075809836387634,
-1.0678101778030396,
0.6637610197067261,
0.7292255163192749,
0.0037238853983581066,
0.4306604266166687,
-0.08939781039953232,
-0.03583793714642525,
-0.46270689368247986,
-0.6856182813644409,
-0.20548082888126373,
0.20569565892219543,
-0.19487573206424713,
-0.32814663648605347,
-0.7978817224502563,
-0.9754667282104492,
0.7420206665992737,
-0.09098052978515625,
0.7609262466430664,
0.46212998032569885,
0.16716086864471436,
-0.08150933682918549,
0.32112759351730347,
-0.4801839590072632,
-0.4168508052825928,
-0.19456475973129272,
0.03706187754869461,
0.007271093782037497,
-0.14936351776123047,
0.5247278213500977,
-0.7821406722068787,
-0.5741065144538879,
-0.5467922687530518,
0.25344744324684143,
0.2692457437515259,
-0.8786899447441101,
0.7373559474945068,
-0.010495126247406006,
-0.7183763980865479,
-0.6378650069236755,
-0.162011981010437,
-0.07501506060361862,
-0.020144548267126083,
0.2707918584346771,
0.2880971431732178,
0.170608788728714,
0.18689240515232086,
0.4922575354576111,
-0.22501248121261597,
-0.7256056070327759,
1.0125130414962769,
-0.8948655128479004,
-0.0958087146282196,
0.34465494751930237,
-0.19729618728160858,
-0.6470996737480164,
-0.46494829654693604,
-1.3394438028335571,
-0.18483354151248932,
-0.4084983766078949,
-0.8299344182014465,
-0.22731982171535492,
-0.599251389503479,
-0.1940891444683075,
0.32153886556625366,
1.0166178941726685,
-0.0508732870221138,
0.2622401714324951,
-0.031241891905665398,
-0.39608803391456604,
0.17538991570472717,
0.16522954404354095,
1.0211738348007202,
0.32539623975753784,
-0.6837701201438904,
0.10485654324293137,
0.158985897898674,
-0.13653641939163208,
0.03715392202138901,
0.5719466209411621,
-0.5291941165924072,
0.2639971971511841,
-0.07312410324811935,
-0.036166559904813766,
0.43714720010757446,
0.7857961058616638,
0.1343184858560562,
-0.3675788640975952,
-0.513727068901062,
-0.47336071729660034,
-0.1493527591228485,
-0.32005539536476135,
-0.0020340147893875837,
1.2221482992172241,
0.4826321303844452,
0.1313881278038025,
-0.1977212280035019,
-0.3252468705177307,
-0.31118449568748474,
-1.4396519660949707,
-0.5010311007499695,
-1.05695641040802,
-0.15074296295642853,
-0.41565823554992676,
-0.4722293019294739,
0.25483042001724243,
0.11192643642425537,
-0.2388293296098709,
-0.17146004736423492,
-0.8824716210365295,
0.3057674765586853,
0.1610538810491562,
0.8299040198326111,
-0.5180685520172119,
-0.5161983370780945,
-0.16976948082447052,
0.040446843951940536,
-0.022485965862870216,
-0.18306788802146912,
-0.3013452887535095,
-0.5271679162979126,
0.09372157603502274,
0.543067991733551,
-0.6687095761299133,
0.9254492521286011,
-0.8165494799613953,
-0.4410163462162018,
-0.057512253522872925,
-0.20059622824192047,
-1.3364143371582031,
1.0015921592712402,
0.07475539296865463,
1.0245543718338013,
0.4735614061355591,
-0.18296891450881958,
-0.6741982698440552,
0.6048998236656189,
-0.9704898595809937,
0.2889282703399658,
0.3059365749359131,
0.611661970615387,
-0.1000203788280487,
-0.7912061810493469,
0.0772877112030983,
0.45001843571662903,
-0.9378931522369385,
0.4300643503665924,
-0.6831890940666199,
0.15901242196559906,
-0.4875734746456146,
0.39157021045684814,
0.8116668462753296,
-0.024564890190958977,
-0.4469462037086487,
0.5327866673469543,
-0.22652624547481537,
-0.16035498678684235,
-0.19964466989040375,
0.26789727807044983,
-0.3645460903644562,
-0.1836484968662262,
0.6663327217102051,
-0.5005769729614258,
0.14255380630493164,
0.44167134165763855,
-0.34220877289772034,
0.44320401549339294,
-0.1866036057472229,
-0.5170803070068359,
-0.22740836441516876,
-0.016564859077334404,
-0.6059412956237793,
0.6091777682304382,
0.5308806300163269,
-0.2180149406194687,
-0.3869321942329407,
-0.6760141253471375,
-0.5098058581352234,
0.4141777753829956,
-0.5529019236564636,
0.14793340861797333,
0.07547122985124588,
0.2792086899280548,
0.3969615399837494,
0.5365667939186096,
-0.26370304822921753,
0.28433364629745483,
-0.3508560061454773,
0.4734492897987366,
-0.00841271597892046,
0.2964124083518982,
-0.3504959046840668,
0.21915152668952942,
-0.742122232913971,
0.06797737628221512,
-0.6122555136680603,
0.5427165031433105,
-1.0510058403015137,
-0.8310748934745789,
0.009598171338438988,
0.23623543977737427,
0.1619989424943924,
-0.010562431067228317,
0.2612760663032532,
-0.1699967235326767,
-0.1210806667804718,
-0.2230832725763321,
-0.05737684294581413,
0.022069178521633148,
-0.46341684460639954,
0.6018049120903015,
0.32419896125793457,
-0.6356679797172546,
0.34966275095939636,
-0.08878263831138611,
-0.06930986791849136,
-0.28432801365852356,
-0.08017885684967041,
1.2946175336837769,
0.5122658014297485,
0.17276149988174438,
0.34372416138648987,
-0.348967969417572,
0.34927019476890564,
0.03945014998316765,
-0.6771581768989563,
0.17987298965454102,
-0.11876758188009262,
0.1971190869808197,
0.8764030933380127,
0.11796162277460098,
0.6814659833908081,
0.8268206715583801,
0.08519894629716873,
0.0056258561089634895,
-0.18833647668361664,
-0.08794212341308594,
0.5921077132225037,
0.43902119994163513,
-0.21758657693862915,
0.16008538007736206,
0.24831850826740265,
-0.3750326335430145,
0.18118169903755188,
-0.39325419068336487,
-0.589767336845398,
-0.6128387451171875,
0.34985798597335815,
-0.0945984274148941,
-0.6202536821365356,
-0.5359787940979004,
0.5473026633262634,
0.028302060440182686,
0.22312022745609283,
0.0971352681517601,
-0.13339932262897491,
0.2836368978023529,
0.6264561414718628,
-0.010110772214829922,
0.014409482479095459,
0.533855140209198,
-0.10271593928337097,
1.1656887531280518,
0.704797089099884,
0.668494701385498,
0.7013492584228516,
0.24084366858005524,
0.15624099969863892,
-0.8065955638885498,
-0.004317684564739466,
0.6223723292350769,
-1.1193650960922241,
0.4652765989303589,
-0.16503089666366577,
-0.24412675201892853,
-0.6403161883354187,
-0.6742859482765198,
0.24413202702999115,
-0.5348703861236572,
0.2522232234477997,
0.5942092537879944,
-0.1868894100189209,
0.24259720742702484,
0.8786575794219971,
-0.1652170866727829,
0.5513904690742493,
0.5773722529411316,
0.027455629780888557,
0.23888911306858063,
1.319617748260498,
1.2775777578353882,
0.01906045898795128,
0.12758484482765198,
-0.04373999685049057,
-0.06054010987281799,
0.6910687685012817,
0.518784761428833,
-0.055202070623636246,
0.32050880789756775,
-1.2398518323898315,
-0.4035266935825348,
0.002430480672046542,
0.36403053998947144,
-0.033390115946531296,
-0.2422514408826828,
-0.014767365530133247,
0.014045532792806625,
-1.0191991329193115,
-1.1165976524353027,
1.448632001876831,
0.2839701175689697,
-0.3430905044078827,
-0.4046873152256012,
-0.06481829285621643,
-0.7227042317390442,
-0.2650785744190216,
-0.6090078353881836,
0.12249057739973068,
-0.6519508957862854,
-0.020357508212327957,
0.1402924507856369,
-0.8117371797561646,
-1.0660094022750854,
-0.9806976914405823,
0.4400634765625,
-0.6912146806716919,
0.8133004903793335,
0.3004009425640106,
0.3155457675457001,
-0.042456258088350296,
-0.9503545165061951,
-0.3971324563026428,
0.022375909611582756,
0.7116832733154297,
0.0496671088039875,
-0.14979200065135956,
0.7523712515830994,
0.09366858005523682,
-0.7769908905029297,
0.4896667003631592,
0.931459367275238,
-0.4662683308124542,
0.6489169597625732,
-0.38889598846435547,
0.10969766974449158,
0.4501499533653259,
0.15953485667705536,
0.06528940051794052,
-0.22572141885757446,
0.6381400227546692,
0.3941133916378021,
-0.7060838341712952,
-0.13417114317417145,
-0.7300816774368286,
0.3468325138092041,
-0.3753614127635956,
0.1593780219554901,
0.6193007826805115,
0.4427371621131897,
0.1425272822380066,
-0.6609137058258057,
4.187039852142334,
0.5460979342460632,
0.3029732406139374,
0.13073837757110596,
0.38878804445266724,
0.7239765524864197,
-0.019098378717899323,
-0.5405104160308838,
0.13265660405158997,
-0.5049046874046326,
-0.086087167263031,
0.4754257798194885,
0.6472966074943542,
0.3176681399345398,
0.25049081444740295,
0.6379532814025879,
-0.09359799325466156,
-0.20948243141174316,
-0.1346183568239212,
-0.3929768204689026,
-0.21195441484451294,
0.35484668612480164,
0.7551677227020264,
0.10323277115821838,
0.49336129426956177,
-0.09524893760681152,
0.0585736408829689,
-0.6812747120857239,
-0.7925635576248169,
-0.6046016812324524,
-0.20793722569942474,
-1.2058402299880981,
0.44725045561790466,
-0.6665254831314087,
-0.8244825005531311,
0.5584447979927063,
0.6223343014717102,
-0.5209910273551941,
0.32709649205207825,
0.3855311870574951,
-0.02988351322710514,
-0.19814202189445496,
0.44221213459968567,
-0.29235634207725525,
-0.3016086220741272,
1.0199975967407227,
-0.08096326887607574,
0.7795290946960449,
0.5594990849494934,
-0.8687296509742737,
-0.03265954926609993,
0.07802315801382065,
0.6839342713356018,
-0.6622809171676636,
-0.9620991945266724,
-0.3012009561061859,
-0.8457558155059814,
-0.07709374278783798,
0.040264565497636795,
0.21150198578834534,
0.096608467400074,
-0.37930259108543396,
-0.15427911281585693,
0.4120003283023834,
-0.004895196296274662,
0.3965855538845062,
0.00297716585919261,
0.49133744835853577,
0.3405214250087738,
-0.4752502143383026,
-0.018851369619369507,
-0.2648153603076935,
-0.5827723741531372,
-0.006250334903597832,
0.2215859442949295,
0.3248977065086365,
0.26119351387023926,
0.8301729559898376,
0.7188490033149719,
0.4631884694099426,
-0.3599607050418854,
-0.48308590054512024,
-0.43543457984924316,
0.29804208874702454,
-0.06981700658798218,
0.40790224075317383,
-0.8815748691558838,
-0.5622942447662354,
-0.4039623439311981,
0.6172493100166321,
0.3042599558830261,
1.635938286781311,
-0.48325997591018677,
0.0657619908452034,
-0.5861167907714844
] |
Some universal features of the effective string picture of pure gauge theories
|
The effective string describing the large distance behaviour of the quark sources of gauge field theories in the confining phase in D=3 or D=4 space-time dimensions can be formulated, in the infrared limit, as a suitable 2D conformal field theory on surfaces with quark loops as boundaries. Recent results on self-avoiding random surfaces allow to fix almost uniquely such a conformal theory. As a consequence, some universal relationships among the string tension , the thickness of the colour flux tube, the deconfinement temperature and a lower bound of the glueball mass spectrum are found. The general agreement with the data extracted from recent lattice simulations with different gauge groups is rather impressive.(Talk held by F.Gliozzi at Lattice'92 , Amsterdam)
|
M.Caselle, F.Gliozzi and S.Vinti
|
hep-lat hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210031
|
hep-lat/9210032
|
[
0.3117801547050476,
0.07634750008583069,
0.3645833432674408,
0.4502909481525421,
0.13110989332199097,
-0.9388639330863953,
0.09845500439405441,
-0.25187942385673523,
-1.4064805507659912,
1.8048994541168213,
1.1423916816711426,
0.27432554960250854,
0.38746559619903564,
-0.5531092882156372,
0.262660950422287,
0.12114183604717255,
-0.6989244818687439,
-0.8141344785690308,
-1.1855922937393188,
0.2885608375072479,
0.6803303956985474,
-0.09399737417697906,
-1.1563115119934082,
-1.0951118469238281,
-0.8258470296859741,
0.7619171142578125,
0.6098833680152893,
0.5490980744361877,
1.6288597583770752,
0.8051973581314087,
0.5001593828201294,
-0.8457903861999512,
-0.7700571417808533,
-0.380532830953598,
-0.2782230079174042,
-0.3227364718914032,
0.04542654752731323,
-0.26391100883483887,
0.2646108865737915,
-0.34799906611442566,
1.1853995323181152,
-0.33695727586746216,
0.7972733378410339,
-0.20261578261852264,
-0.6746042966842651,
0.03899529576301575,
-0.09357517957687378,
0.2270059585571289,
-0.34177806973457336,
-1.7814098596572876,
-0.6465241312980652,
0.6238747835159302,
0.00005744048394262791,
-0.48908331990242004,
-0.2491813749074936,
0.12807172536849976,
0.1675344705581665,
0.07907909154891968,
-0.4580146074295044,
-0.520667314529419,
0.592208743095398,
0.042359575629234314,
1.0311633348464966,
-1.100904107093811,
0.11269614100456238,
0.5844915509223938,
-0.3445768356323242,
0.29409822821617126,
0.15986059606075287,
-0.6254417896270752,
-0.7405955791473389,
-0.9936635494232178,
0.06498683243989944,
-0.00422193668782711,
-0.6721214652061462,
0.5077792406082153,
-0.14863331615924835,
-0.6666823029518127,
-0.915410578250885,
-0.38371309638023376,
0.19815751910209656,
0.10648637264966965,
-0.3637452721595764,
0.04725183546543121,
-0.054427485913038254,
-0.14600083231925964,
0.21021772921085358,
0.2224481999874115,
-0.08799725770950317,
-0.00830466952174902,
0.3852143883705139,
0.8561716079711914,
0.5524871349334717,
-0.033303383737802505,
0.18143750727176666,
1.2489593029022217,
-0.6610684394836426,
0.39716142416000366,
0.39037609100341797,
-0.03473173826932907,
0.1479913592338562,
1.2796440124511719,
-0.6009154915809631,
0.34249547123908997,
-0.5156161785125732,
-0.013100497424602509,
0.492613822221756,
-0.5619572997093201,
-0.7155019044876099,
-0.4344891905784607,
-0.39591461420059204,
0.4860701858997345,
0.235279843211174,
0.25451037287712097,
0.22170589864253998,
0.5146320462226868,
0.5737637877464294,
-0.6431810259819031,
-0.6871328353881836,
-0.13848890364170074,
0.1546918749809265,
-0.025940053164958954,
0.4704979360103607,
0.12666019797325134,
-0.032272908836603165,
-0.3446761667728424,
0.74403315782547,
0.9257463812828064,
-0.5513312816619873,
0.3370305299758911,
-0.1494513899087906,
-0.4415965676307678,
-0.3585585355758667,
0.6692399382591248,
0.06268984824419022,
0.4431930482387543,
-0.8379265666007996,
0.25173094868659973,
0.18947377800941467,
-0.002297614933922887,
0.3261095881462097,
-0.438467800617218,
0.06649880111217499,
0.6805726885795593,
0.32658058404922485,
-0.1592613011598587,
0.9253615140914917,
-0.4577702581882477,
-0.5764613151550293,
0.20870694518089294,
-0.8229467272758484,
0.700059711933136,
0.05967165157198906,
-0.25206685066223145,
-0.16724702715873718,
0.3495963513851166,
-1.2588653564453125,
0.5164834260940552,
-1.134434700012207,
-0.424006849527359,
0.5355762243270874,
-0.6285901069641113,
-0.46990281343460083,
0.5284422636032104,
-1.155624270439148,
0.655531644821167,
-0.39880913496017456,
0.1627596765756607,
0.2044549435377121,
-0.1179412379860878,
0.13553839921951294,
-0.027541764080524445,
-0.22063688933849335,
0.008061232045292854,
0.5926403999328613,
0.6891878843307495,
0.8884446024894714,
-0.16571617126464844,
0.4400690495967865,
0.7094124555587769,
-0.24788571894168854,
-0.6843233704566956,
0.707442581653595,
-0.4484807550907135,
-0.36251261830329895,
0.0014200903242453933,
0.28694528341293335,
0.08880080282688141,
0.5552688837051392,
0.4492368698120117,
-0.3872305452823639,
0.5096454620361328,
-0.8275594115257263,
0.46936798095703125,
-0.13214395940303802,
-0.15818394720554352,
-0.5718811750411987,
0.756674587726593,
-0.5153509974479675,
-0.11006540060043335,
-0.4736451208591461,
-0.07629294693470001,
-1.058303713798523,
0.1248956024646759,
-1.6731376647949219,
0.18043600022792816,
0.11143705248832703,
0.07319571077823639,
-0.8573926687240601,
0.47657880187034607,
0.33939069509506226,
-0.03179747983813286,
-0.24989336729049683,
-0.3350134491920471,
-0.32770106196403503,
0.10667301714420319,
0.16729097068309784,
0.41036972403526306,
0.8701966404914856,
-0.3368290066719055,
0.554904043674469,
0.27026158571243286,
-0.1665392816066742,
0.7919415831565857,
0.44727393984794617,
-0.6639831066131592,
0.16381803154945374,
0.829585611820221,
-0.12855738401412964,
0.10743764042854309,
0.2756139039993286,
0.7506332397460938,
-0.19159960746765137,
0.39644163846969604,
0.8220403790473938,
0.8296942710876465,
0.4738919734954834,
0.9324889779090881,
0.7164819240570068,
-0.18749696016311646,
0.5218199491500854,
0.30927562713623047,
0.809575080871582,
0.2014530897140503,
0.21093936264514923,
0.5798085927963257,
-0.7896421551704407,
-0.24306371808052063,
-0.481158047914505,
1.0804529190063477,
-0.2888680398464203,
1.0785785913467407,
0.8939238786697388,
0.2600056529045105,
-0.6521696448326111,
0.028661783784627914,
0.3793140649795532,
0.18142013251781464,
-0.573935866355896,
-0.43694958090782166,
0.3105517625808716,
0.03995293378829956,
-0.5336694121360779,
-0.7813374400138855,
-0.4843830466270447,
1.2269326448440552,
0.281302809715271,
0.06488122791051865,
0.08054568618535995,
-0.4208601415157318,
-0.9986374378204346,
-0.7969304919242859,
-0.7391998767852783,
-0.05764252319931984,
-0.12786516547203064,
0.7543768882751465,
1.4637646675109863,
-0.5285784006118774,
0.4041353762149811,
0.46957623958587646,
-0.5693346261978149,
0.37661778926849365,
0.6791978478431702,
0.763691782951355,
0.6429209113121033,
0.408062219619751,
-1.4173270463943481,
-0.2646530568599701,
-0.21250741183757782,
0.4045591652393341,
0.8597413897514343,
-0.5320633053779602,
1.0392204523086548,
0.13382484018802643,
0.4435749650001526,
0.09057237207889557,
-0.4618073105812073,
-0.2931971549987793,
-0.3977874517440796,
-0.6158760190010071,
0.16605514287948608,
0.35866180062294006,
-0.03375634923577309,
0.08958455175161362,
-0.7129579782485962,
1.4105693101882935,
-0.02331407740712166,
-0.5434104800224304,
0.7918235659599304,
0.33960410952568054,
-0.2601761221885681,
0.20225028693675995,
-0.727900505065918,
0.31553325057029724,
-0.1066289022564888,
0.8976845741271973,
0.40639573335647583,
-0.07516803592443466,
-0.33761516213417053,
-0.6489994525909424,
-0.33025044202804565,
0.35093289613723755,
0.44643256068229675,
-1.0618444681167603,
0.36239632964134216,
0.7345389723777771,
0.07818785309791565,
-0.9401875734329224,
0.3364274799823761,
-0.7991799712181091,
-0.9800485372543335,
-0.14580710232257843,
-0.4989301860332489,
0.3792203962802887,
0.13971613347530365,
0.5009178519248962,
-0.8413447737693787,
0.09080760180950165,
0.3796244263648987,
0.5993185639381409,
0.22858725488185883,
-0.5356554985046387,
0.45460245013237,
-0.25180020928382874,
0.5696864128112793,
0.3392663598060608,
0.44797924160957336,
0.19311976432800293,
-0.24191893637180328,
0.8779080510139465,
-0.4787992835044861,
0.3429546356201172,
0.7024281620979309,
0.6804803013801575,
-0.3886907398700714,
0.23186883330345154,
-0.5705325603485107,
-0.057130537927150726,
-0.9362519979476929,
-0.1505988985300064,
1.0593750476837158,
0.5319516658782959,
-1.019972324371338,
-0.26622745394706726,
-1.1702312231063843,
-0.28225114941596985,
-0.3825100362300873,
0.4271889925003052,
1.1125441789627075,
-0.036109454929828644,
0.47563436627388,
0.36861664056777954,
0.0877857580780983,
-0.004108027555048466,
-0.6700592041015625,
0.14684483408927917,
0.22812522947788239,
-0.1288505345582962,
1.0075832605361938,
-0.75307297706604,
-1.2146915197372437,
0.20016199350357056,
1.2493643760681152,
0.906518280506134,
1.0749776363372803,
0.9585723876953125,
-0.8568225502967834,
0.16943684220314026,
-0.7728924751281738,
-0.3665044903755188,
0.17827001214027405,
0.1870555728673935,
-0.009975675493478775,
-0.4274081885814667,
-0.08829836547374725,
-0.016373367980122566,
0.11315399408340454,
0.812961220741272,
0.4834741950035095,
0.018634065985679626,
0.3623659014701843,
1.0955336093902588,
0.222463920712471,
0.8528999090194702,
-0.03875545412302017,
-0.47581392526626587,
-0.732100248336792,
0.6640751957893372,
0.12664932012557983,
0.009771700017154217,
0.28587111830711365,
-0.49913454055786133,
-0.008956355042755604,
-0.787341833114624,
0.9445483088493347,
-0.01926904171705246,
-0.1857524812221527,
0.5711941719055176,
0.14308656752109528,
-0.3064465820789337,
-0.599056601524353,
-0.09930276870727539,
0.6496729254722595,
0.37509939074516296,
-0.0033109423238784075,
-1.7894272804260254,
0.3499356508255005,
-0.3172839283943176,
0.20484313368797302,
1.2951017618179321,
0.08587842434644699,
-1.628675103187561,
-0.218460813164711,
0.2484034299850464,
-0.7899439930915833,
-0.028070904314517975,
0.09578099846839905,
-0.062309782952070236,
-0.20331481099128723,
-0.4430142045021057,
-0.4238373935222626,
0.2997998595237732,
-0.4902544617652893,
-0.0773831456899643,
-0.2682962417602539,
0.014068995602428913,
0.28592637181282043,
0.2243761569261551,
0.21447037160396576,
-0.6381231546401978,
-0.15055830776691437,
-0.2386602759361267,
-0.7743211984634399,
-0.2632770538330078,
-0.7819346189498901,
-0.6556335687637329,
-0.2716844081878662,
-0.10983353108167648,
0.17912086844444275,
0.028035691007971764,
0.07177361100912094,
-0.3358244001865387,
0.5479698181152344,
0.06414443254470825,
-0.49581289291381836,
0.16126853227615356,
0.7672540545463562,
0.662363588809967,
1.0590629577636719,
0.1497477889060974,
-0.15251152217388153,
0.03533194586634636,
0.32579511404037476,
0.30859753489494324,
0.12975428998470306,
-0.7580971717834473,
0.16842114925384521,
-0.17954300343990326,
-0.27057361602783203,
-0.13645972311496735,
-0.8753703832626343,
0.8462233543395996,
-0.628300666809082,
0.548170268535614,
-0.25305747985839844,
-0.8281298279762268,
-0.8270667195320129,
-1.0234456062316895,
-0.7647703289985657,
0.8797062039375305,
-0.1826917827129364,
-0.30983296036720276,
0.6602541208267212,
-0.8748888373374939,
0.23339907824993134,
0.2783832252025604,
-0.5537272095680237,
-0.06530387699604034,
0.12346651405096054,
0.4871842861175537,
0.08331519365310669,
0.6398198008537292,
-0.8606875538825989,
-0.042651157826185226,
-0.37178394198417664,
0.28757110238075256,
-0.3071448802947998,
-0.7724803686141968,
0.08028499037027359,
0.02021595649421215,
-0.3551070988178253,
-1.0301562547683716,
0.386371374130249,
0.1906374841928482,
0.26660072803497314,
-0.5626360177993774,
-0.006135919596999884,
-0.23272496461868286,
-0.7410147786140442,
0.9757572412490845,
-0.03764272853732109,
-1.5622608661651611,
-0.3797609806060791,
0.522941529750824,
-0.20583301782608032,
-0.09687794744968414,
-0.2342381328344345,
0.20043490827083588,
0.06460922211408615,
-0.2995198965072632,
0.5162197351455688,
-0.6108996868133545,
0.20458146929740906,
-0.6300862431526184,
0.0718352422118187,
0.36295294761657715,
-0.05500420555472374,
0.9603903889656067,
-0.0372396856546402,
-0.4447225034236908,
-0.7501833438873291,
-0.14391621947288513,
0.18969151377677917,
-0.5743162035942078,
-0.24943584203720093,
-0.17048722505569458,
-0.65754634141922,
0.814541220664978,
-0.05404568091034889,
-0.1965537965297699,
0.5101264715194702,
-0.02639155648648739,
-0.3047242760658264,
0.9459447264671326,
0.5061489939689636,
0.18921659886837006,
-0.2377847582101822,
0.23339451849460602,
0.4144056439399719,
-0.10046675056219101,
-0.5192639827728271,
1.1486529111862183,
-1.1013439893722534,
1.372004747390747,
-0.5489626526832581,
0.19535398483276367,
-0.19151358306407928,
-0.5543847680091858,
1.2531318664550781,
-1.1343436241149902,
0.14883865416049957,
-0.031458523124456406,
-0.13524164259433746,
0.13976140320301056,
0.3690741956233978,
-1.0783610343933105,
-0.34536212682724,
-0.6363131403923035,
-0.8599393367767334,
0.8607667088508606,
-0.044741492718458176,
0.06985670328140259,
-0.6422093510627747,
-1.2263331413269043,
0.31960800290107727,
-0.12728872895240784,
0.002284045796841383,
0.10808994621038437,
0.4029606282711029,
-0.10279784351587296,
-0.15468940138816833,
0.3623727560043335,
-0.49235519766807556,
-0.40133917331695557,
-0.2838295102119446,
-0.2011895626783371,
-0.02646387554705143,
0.044821321964263916,
0.05454882234334946,
-0.6830680966377258,
-0.26530829071998596,
-0.20536787807941437,
0.26377835869789124,
-0.17503008246421814,
0.8120288252830505,
-0.44613367319107056,
-0.8904712796211243,
-1.083168387413025,
-0.09867238998413086,
0.02915669046342373,
-0.3438297510147095,
0.26142746210098267,
-0.21950168907642365,
-0.02529277838766575,
-0.23837251961231232,
0.4445887506008148,
-0.44154036045074463,
0.16538484394550323,
0.38443008065223694,
-0.06599602103233337,
-0.625465452671051,
0.17458027601242065,
-0.1926918923854828,
-0.6637679934501648,
-0.4055855870246887,
-0.3307838439941406,
0.04198590666055679,
-0.45568621158599854,
-0.371124804019928,
0.24811100959777832,
-0.6608838438987732,
0.21547797322273254,
0.2121390849351883,
0.7648391723632812,
0.06899446249008179,
-0.34878748655319214,
0.7313236594200134,
-0.3193686604499817,
-0.5422877073287964,
0.3173266351222992,
1.0759220123291016,
-0.27641722559928894,
-0.5496508479118347,
-0.0808982402086258,
0.30389121174812317,
0.25460660457611084,
0.10444436967372894,
0.2602294981479645,
0.2723751664161682,
0.20814408361911774,
0.0913502499461174,
0.11256002634763718,
-0.07932154089212418,
-0.5284690260887146,
0.3459726870059967,
0.18276816606521606,
0.35257014632225037,
-1.2338905334472656,
-0.09765687584877014,
0.003527026390656829,
0.5996811985969543,
1.377225399017334,
-0.1662554293870926,
0.11279056966304779,
0.08478634804487228,
0.06394416093826294,
-0.9125699400901794,
-1.1653066873550415,
0.1629016399383545,
-1.4113973379135132,
-0.44202476739883423,
-0.550728440284729,
-0.2167682945728302,
0.028150295838713646,
0.013392189517617226,
0.33169859647750854,
-0.2252015620470047,
-0.6386407017707825,
0.10673277080059052,
-0.13537178933620453,
0.564206600189209,
-0.028821643441915512,
-0.8389332294464111,
-0.8227599263191223,
0.08475711196660995,
-0.35624590516090393,
-0.11937820166349411,
0.19664625823497772,
0.14280256628990173,
-0.024331606924533844,
0.4650205373764038,
0.005388178862631321,
0.41608375310897827,
-0.42864716053009033,
-0.7298174500465393,
-0.20078299939632416,
0.41862112283706665,
0.04917726665735245,
-0.12842746078968048,
-0.11529465764760971,
0.11899388581514359,
-0.08554713428020477,
-0.1658872812986374,
0.017588872462511063,
0.29483532905578613,
-1.3150362968444824,
-0.370084285736084,
-0.5694929361343384,
0.2537361979484558,
-0.26308152079582214,
-0.6362645030021667,
0.8252580761909485,
-0.38375964760780334,
-1.0651235580444336,
0.21310900151729584,
-0.555534303188324,
-0.328813374042511,
-0.5252401232719421,
-0.14446063339710236,
0.343586802482605,
0.23184356093406677,
-0.18523703515529633,
0.38921910524368286,
-0.566010057926178,
-0.44144436717033386,
-0.33171600103378296,
-0.1229151263833046,
0.11697050929069519,
0.13255101442337036,
-0.004850917030125856,
-0.9604140520095825,
-0.37441393733024597,
0.03481680527329445,
-0.13588206470012665,
0.2592422664165497,
-1.1881080865859985,
-0.8492559790611267,
-0.3875390291213989,
-0.20511281490325928,
0.20329712331295013,
1.1509954929351807,
0.87354975938797,
-0.20624545216560364,
-0.1999620795249939,
-0.8109440207481384,
-0.43309950828552246,
-0.33261364698410034,
-1.125766634941101,
-0.37100693583488464,
0.1334056407213211,
0.298046350479126,
-0.01698424480855465,
-0.0875014141201973,
0.24361930787563324,
0.6944261193275452,
0.2632502615451813,
0.23295629024505615,
-0.2567434310913086,
0.0748513862490654,
-0.4394851326942444,
0.09753626585006714,
-1.4400312900543213,
0.06617813557386398,
0.26784878969192505,
0.425721675157547,
-0.06132053583860397,
-0.2321561574935913,
-0.2680750787258148,
0.31640225648880005,
-0.27772486209869385,
-0.014966130256652832,
-0.0666583999991417,
-0.11953236907720566,
-0.21740882098674774,
-0.1868542581796646,
0.42995485663414,
0.2501683533191681,
-1.0517206192016602,
0.6777236461639404,
-0.4713027775287628,
-1.0800495147705078,
-0.02815123274922371,
0.15710729360580444,
0.3788725435733795,
0.062324803322553635,
-0.39304429292678833,
0.6960532665252686,
0.5981503129005432,
-1.0171924829483032,
1.156461238861084,
0.19634272158145905,
0.6856949329376221,
0.04150695726275444,
-0.017778998240828514,
0.3062050938606262,
0.1463308185338974,
0.7826808094978333,
-0.16136756539344788,
0.9991816282272339,
0.270973801612854,
0.4121209979057312,
-0.026621952652931213,
0.08278222382068634,
0.0795772522687912,
0.18081849813461304,
0.18327659368515015,
0.5916032791137695,
-0.5553176403045654,
0.1472940891981125,
-0.09697917103767395,
0.11076223105192184,
-0.32995927333831787,
0.07914936542510986,
-0.31177476048469543,
0.21133124828338623,
0.3859878480434418,
0.37391602993011475,
-0.43020910024642944,
-0.3303075134754181,
-0.2511339485645294,
0.20762819051742554,
0.13988184928894043,
0.315335214138031,
0.049305085092782974,
1.0998303890228271,
0.6483309864997864,
0.5232864022254944,
0.12365032732486725,
0.9963248372077942,
0.6399379372596741,
0.17628148198127747,
0.9700113534927368,
0.679823100566864,
0.6885852217674255,
0.06452494859695435,
0.40896257758140564,
-0.7705431580543518,
0.2617471516132355,
0.7407536506652832,
-1.4009722471237183,
-0.08010992407798767,
-0.3276696503162384,
0.2512289583683014,
0.12181656807661057,
-1.0471527576446533,
0.6511920094490051,
-0.3383327126502991,
0.5761255621910095,
0.869411051273346,
-0.6099619269371033,
0.5354747176170349,
0.5051913857460022,
0.3545885384082794,
0.6632273197174072,
0.5241522789001465,
0.49012455344200134,
-0.3793396055698395,
0.4281240999698639,
1.2662873268127441,
0.2917255163192749,
0.10555735230445862,
-0.20130111277103424,
-0.2437630295753479,
0.22614054381847382,
0.14380964636802673,
0.28263095021247864,
0.8946986198425293,
-0.6532434821128845,
-0.13998810946941376,
-0.02718023583292961,
-0.04093709960579872,
-0.30325350165367126,
-0.7588539123535156,
0.2518181800842285,
0.7347694039344788,
-0.4291064441204071,
-0.3385539650917053,
0.8344059586524963,
0.38628846406936646,
-0.46946483850479126,
0.057854168117046356,
0.0742853581905365,
-0.890794575214386,
0.08999057859182358,
-1.048438310623169,
0.832334578037262,
0.22490006685256958,
0.2460608333349228,
-0.6404973268508911,
-0.6638840436935425,
-0.2913934588432312,
-1.5735127925872803,
-0.00837963167577982,
-0.5995122194290161,
0.4211145043373108,
0.3032216727733612,
0.3362659513950348,
0.45511025190353394,
-0.9233241081237793,
0.6681928634643555,
-0.40263453125953674,
0.9550922513008118,
0.010486826300621033,
0.26325666904449463,
0.8616717457771301,
0.45948630571365356,
-0.8874248266220093,
0.5570536255836487,
1.2562503814697266,
-0.15116199851036072,
0.8997274041175842,
-0.17455936968326569,
-0.2366463541984558,
0.2753838300704956,
-0.8738682866096497,
0.19141297042369843,
0.1879318356513977,
0.31838226318359375,
-0.21350879967212677,
-0.3896663784980774,
-0.13651442527770996,
-0.8061733841896057,
0.2919146418571472,
-0.8455029726028442,
0.15046514570713043,
-0.30229896306991577,
0.40680453181266785,
0.3542429506778717,
-0.2586032450199127,
3.7341432571411133,
1.6310075521469116,
0.6274697780609131,
-0.3707424998283386,
1.3275657892227173,
0.9799677729606628,
-0.4344066083431244,
-0.09390155971050262,
0.5039088129997253,
-0.6972438097000122,
-0.2700032591819763,
0.911440372467041,
0.2068776786327362,
-0.7123337984085083,
0.38029173016548157,
0.41474252939224243,
-0.08602655678987503,
0.7462356090545654,
-0.030971979722380638,
-0.8481864333152771,
-0.6987022161483765,
-0.03798605874180794,
0.29344674944877625,
0.1996961086988449,
0.0498659722507,
-0.01772884838283062,
0.30217286944389343,
-0.4200277030467987,
-0.4471015930175781,
-0.7293826341629028,
-0.7938973903656006,
-1.2323622703552246,
-0.10372567921876907,
-0.3811497986316681,
-0.6964417695999146,
1.0482347011566162,
0.05962790921330452,
-0.5733669996261597,
0.47687897086143494,
0.2221563458442688,
0.0043290480971336365,
-0.48144152760505676,
0.3912609815597534,
-0.04569004848599434,
-0.779254138469696,
0.42082148790359497,
-0.07142472267150879,
0.629302978515625,
0.24416810274124146,
-0.085933618247509,
0.12732449173927307,
-0.1596592217683792,
0.1915191411972046,
-0.7750070691108704,
-1.0961731672286987,
-0.2748422622680664,
-0.5067580342292786,
-0.9698784351348877,
0.30389174818992615,
0.31428292393684387,
0.1329609751701355,
0.22344112396240234,
0.001427453593350947,
0.36722132563591003,
-0.34744730591773987,
0.7722377777099609,
0.4933515787124634,
-1.0100833177566528,
-0.41824883222579956,
-0.006262201815843582,
0.26182353496551514,
-0.07495733350515366,
-0.6084399223327637,
-0.07675069570541382,
0.10106027871370316,
-0.3596007227897644,
-0.7028933763504028,
1.1182138919830322,
-0.10137628763914108,
0.4161466956138611,
-0.025892579928040504,
-0.7033717632293701,
0.04051585868000984,
0.0893644392490387,
0.23423075675964355,
0.6721743941307068,
-0.5519506931304932,
0.2627658545970917,
-0.532665491104126,
0.17786651849746704,
0.43965834379196167,
1.1813647747039795,
0.33657220005989075,
0.052784159779548645,
-0.8906521797180176
] |
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
|
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.
|
A.C.D. van Enter, R. Fernandez and A.D. Sokal
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210032
|
hep-lat/9210033
|
[
0.5673434138298035,
-0.17002804577350616,
-0.5192409157752991,
-0.049591533839702606,
-0.43601882457733154,
-0.2947441637516022,
0.1831701695919037,
0.1700795441865921,
-0.5671250820159912,
1.0687648057937622,
1.0169278383255005,
-0.10472261160612106,
0.26077672839164734,
-0.5911327004432678,
-0.41012582182884216,
0.18922975659370422,
0.24567824602127075,
-0.3804425001144409,
-0.873742401599884,
0.6731520295143127,
0.5407755970954895,
0.11037725955247879,
-1.3495234251022339,
-0.19460371136665344,
-0.5329309105873108,
0.6161878705024719,
0.7050852179527283,
0.17059212923049927,
1.0374293327331543,
0.8622462749481201,
0.0881328135728836,
-0.30823367834091187,
0.16215449571609497,
0.10437004268169403,
-0.10571292042732239,
-0.9016454815864563,
-0.5579814910888672,
-0.1877380907535553,
0.48292601108551025,
-0.6606101393699646,
1.0534231662750244,
0.15152111649513245,
0.14620932936668396,
-0.18568558990955353,
-1.2001873254776,
-0.1540248543024063,
-0.5008925795555115,
-0.15927691757678986,
-0.21896180510520935,
-1.3236048221588135,
-0.1401343047618866,
0.4857580065727234,
-0.14332394301891327,
-1.6046136617660522,
-0.022649016231298447,
0.2998032569885254,
0.2723385989665985,
-0.3874271810054779,
-0.7597267031669617,
-0.11200858652591705,
0.4741560220718384,
0.6953540444374084,
0.6390887498855591,
0.01055041141808033,
0.23537887632846832,
1.6457690000534058,
-0.3099156618118286,
0.25412920117378235,
-0.436343789100647,
-0.06762734055519104,
-0.12613604962825775,
-0.04180304706096649,
-0.4067557454109192,
-0.38818350434303284,
-1.2598332166671753,
0.20539134740829468,
-0.15513673424720764,
-0.4418317973613739,
-0.6181355714797974,
-0.027243873104453087,
0.45654812455177307,
0.10828035324811935,
-0.18003393709659576,
0.39364495873451233,
-0.4975523352622986,
0.12330257892608643,
0.5780298113822937,
-0.1908435970544815,
-0.5533732771873474,
0.5456255078315735,
-0.21802081167697906,
0.660540759563446,
-0.08768486231565475,
0.3468615710735321,
0.4286963641643524,
0.722707211971283,
-0.06843473017215729,
-0.054900042712688446,
0.41828033328056335,
0.054578326642513275,
-0.7705164551734924,
0.7651788592338562,
-0.4833846688270569,
-0.6256164312362671,
-0.5613278150558472,
0.704754114151001,
-0.5603078007698059,
-0.2523251175880432,
0.045870956033468246,
-0.8947403430938721,
0.8906121850013733,
0.03149136155843735,
0.43507304787635803,
0.13856704533100128,
-0.03034459613263607,
0.9911947250366211,
0.10925387591123581,
0.2709372341632843,
-0.3878869414329529,
-0.3315567970275879,
0.17201876640319824,
0.5264543294906616,
0.3921756446361542,
0.4321269690990448,
-0.500638484954834,
-0.3498934805393219,
0.36624184250831604,
0.4759458601474762,
-0.1971483826637268,
0.09867484122514725,
-0.5551362633705139,
-0.7337007522583008,
-0.8217507004737854,
0.5878198146820068,
-0.4797843098640442,
0.5953482985496521,
0.3898869454860687,
0.305998295545578,
-0.0030342359095811844,
-0.2929098904132843,
1.0322067737579346,
0.08784753829240799,
0.16667978465557098,
0.9131650924682617,
-1.069318413734436,
0.5454228520393372,
-0.10914759337902069,
-0.2503553628921509,
-0.4229171574115753,
-0.27883049845695496,
-0.5529541969299316,
-0.03133097663521767,
-0.04282284155488014,
0.42384055256843567,
-0.01162370853126049,
0.09398815035820007,
-1.3273017406463623,
-0.48083019256591797,
0.09489824622869492,
-0.24763669073581696,
0.2602716088294983,
0.32859811186790466,
-0.3598899245262146,
0.7783984541893005,
-0.06985203921794891,
-0.07027410715818405,
-0.11659930646419525,
-0.744364857673645,
0.37960973381996155,
-0.4083173871040344,
-0.1895729899406433,
0.21218560636043549,
0.018462125211954117,
0.6854701638221741,
0.8670269250869751,
0.90257728099823,
0.5277407169342041,
-0.6607203483581543,
-0.22121524810791016,
0.18025487661361694,
-0.3395996391773224,
-0.545096755027771,
0.3144916594028473,
0.2928311824798584,
-0.673564076423645,
-0.6706275939941406,
0.332148939371109,
-0.3671322166919708,
0.3143937885761261,
-0.04866555705666542,
-0.4298918545246124,
0.5373296141624451,
-0.36658844351768494,
0.5786688327789307,
-0.5034609436988831,
-0.12461213767528534,
-0.7338248491287231,
0.5174682140350342,
-0.6437963247299194,
-0.3437558710575104,
0.23320694267749786,
0.40921449661254883,
-0.5122150182723999,
0.6099408864974976,
-0.8927054405212402,
-0.45504361391067505,
0.797150194644928,
0.21528638899326324,
-0.4600505828857422,
0.10155171155929565,
0.6673100590705872,
0.09809370338916779,
0.3335990011692047,
-0.4431729316711426,
0.37486517429351807,
0.10928289592266083,
0.42425256967544556,
-0.0011162031441926956,
0.08374904096126556,
0.40379709005355835,
0.08749967068433762,
0.15361468493938446,
-0.22180922329425812,
1.3695600032806396,
-0.10773710906505585,
0.031570110470056534,
0.3055129647254944,
0.434411883354187,
-0.25047218799591064,
-0.12601891160011292,
-0.5080154538154602,
0.3199710547924042,
0.2657678723335266,
0.20121046900749207,
-0.017119232565164566,
0.2780438959598541,
0.046866413205862045,
0.8257066011428833,
0.20864564180374146,
-0.16732686758041382,
0.39753544330596924,
-0.06283755600452423,
0.060875292867422104,
-0.061999496072530746,
-0.9028856158256531,
0.16856083273887634,
-0.08160646259784698,
0.27427488565444946,
-0.12234178185462952,
1.1918288469314575,
-0.020412571728229523,
0.23623165488243103,
-0.04996923357248306,
0.22020845115184784,
-1.1769442558288574,
0.1333989053964615,
-0.12520766258239746,
0.564325213432312,
-0.29416126012802124,
-0.26742222905158997,
0.4079217314720154,
0.017488539218902588,
-0.3155779242515564,
-0.8456196784973145,
-0.1627780795097351,
0.7804400324821472,
-0.5551468133926392,
0.4567103087902069,
0.9892359375953674,
-0.3708226680755615,
-0.6852723360061646,
-0.15600073337554932,
-0.8987249732017517,
0.10471757501363754,
-0.4894760549068451,
0.725976824760437,
0.348416268825531,
-0.6616588830947876,
0.4775618314743042,
-0.1694486439228058,
0.0016889291582629085,
0.2542935907840729,
-0.19724969565868378,
0.181597501039505,
0.5738319158554077,
0.4630589485168457,
-0.3660908341407776,
-0.05724562332034111,
-0.41309505701065063,
-0.4292144775390625,
-0.16772057116031647,
-0.644168496131897,
0.15582294762134552,
-0.44564831256866455,
0.09658578038215637,
0.4317416846752167,
-0.6621046662330627,
0.36933308839797974,
0.06812726706266403,
-0.6951649785041809,
0.1805412769317627,
0.283430814743042,
-0.11884414404630661,
-0.13883787393569946,
-0.7328246235847473,
0.7563973665237427,
0.12095435708761215,
-0.32961955666542053,
0.7180052399635315,
0.1903757005929947,
-0.560600221157074,
0.4336441457271576,
-0.05239049345254898,
0.28478002548217773,
-0.34362873435020447,
0.4984232187271118,
0.11986985057592392,
-0.0023261241149157286,
-0.5842682123184204,
-0.4133293032646179,
0.3902941048145294,
0.03457332402467728,
0.2326706200838089,
-0.4893598258495331,
0.07571596652269363,
1.0192619562149048,
0.28514835238456726,
-0.4404109716415405,
0.9521567225456238,
-0.6390631198883057,
-1.0607211589813232,
-0.06538649648427963,
-0.3943948745727539,
-0.12995542585849762,
-0.07904595136642456,
0.35662728548049927,
-0.6430061459541321,
0.0852099359035492,
-0.5731608867645264,
0.07403575628995895,
0.8111671805381775,
-0.7847490310668945,
0.9399097561836243,
0.6647266149520874,
0.5193233489990234,
-0.11263836920261383,
0.3242822587490082,
-0.3169020414352417,
-0.7548225522041321,
0.17212516069412231,
-0.0006137426244094968,
0.6808665990829468,
0.15728896856307983,
0.7580358982086182,
0.0075507634319365025,
0.046285755932331085,
-0.2993490993976593,
-0.11829251796007156,
-0.8825153112411499,
0.05003588646650314,
-0.029314670711755753,
0.8849624395370483,
-0.22698833048343658,
0.14970065653324127,
-0.6006067991256714,
-0.25798460841178894,
-0.1518428474664688,
-0.3164399266242981,
0.2576253116130829,
-0.8216355443000793,
-0.050646282732486725,
-0.09626566618680954,
-0.44595545530319214,
0.4214082956314087,
0.3387255370616913,
0.7782780528068542,
1.2031307220458984,
0.6455148458480835,
0.3892856240272522,
-0.5367228984832764,
-0.3881979286670685,
-0.07331543415784836,
0.6713640093803406,
0.49883049726486206,
0.3716667890548706,
-0.24063752591609955,
0.04058317095041275,
0.33608245849609375,
-0.9419530034065247,
-0.11033808439970016,
-0.4763209819793701,
-0.6004806160926819,
0.650282084941864,
-0.4404500126838684,
0.21499620378017426,
-0.2767024338245392,
0.16716408729553223,
0.5004443526268005,
0.1074567511677742,
-0.3934248983860016,
0.1366531252861023,
-0.026959002017974854,
-0.047372933477163315,
0.2675037980079651,
0.19393593072891235,
0.08332280069589615,
-0.8058172464370728,
0.7967094779014587,
0.19118022918701172,
0.41262295842170715,
0.08420661091804504,
0.024502186104655266,
-0.2800693213939667,
-0.7081856727600098,
0.33858463168144226,
-0.08698838204145432,
-0.2527918219566345,
0.06585188210010529,
0.15575571358203888,
0.13644208014011383,
-0.12677381932735443,
-0.13516202569007874,
0.22009624540805817,
0.38436159491539,
0.4201587438583374,
-0.9792542457580566,
0.7739821076393127,
-0.8953434228897095,
0.4376908242702484,
0.326641708612442,
0.18491032719612122,
-0.5053991675376892,
-1.1093024015426636,
0.163629949092865,
-0.5010973215103149,
0.019978102296590805,
0.9831908941268921,
0.7641384601593018,
-0.6352326273918152,
-0.719197154045105,
-0.361750066280365,
0.6903315782546997,
-0.4910206198692322,
-0.34532299637794495,
0.08307487517595291,
0.3758734166622162,
-0.00660602655261755,
0.36628925800323486,
-0.5222193002700806,
-0.5659881234169006,
-0.12227588146924973,
-0.7385815382003784,
0.5853435397148132,
-0.27534765005111694,
-0.9186163544654846,
-0.29044249653816223,
0.27575427293777466,
-0.12396810948848724,
0.6502289175987244,
0.6427332162857056,
-0.43764135241508484,
-0.399910569190979,
0.36051586270332336,
-0.7162795066833496,
-0.0653999000787735,
0.08545074611902237,
0.4072541892528534,
0.8753086924552917,
0.6139096617698669,
0.20702669024467468,
0.5664028525352478,
0.0748838558793068,
0.3760431110858917,
-0.1856485903263092,
0.7285774350166321,
0.05557549372315407,
-0.08022773265838623,
-0.07484449446201324,
-0.5166453123092651,
-1.0305194854736328,
0.26856863498687744,
0.4266997277736664,
0.24173912405967712,
0.2557429373264313,
0.031974416226148605,
-0.49763262271881104,
-0.2566409111022949,
-0.23602968454360962,
-0.7604394555091858,
0.8826786279678345,
-0.4327749013900757,
0.4510022699832916,
0.747603714466095,
-0.4911578595638275,
0.40344470739364624,
-0.6822161078453064,
-0.536749541759491,
-0.5329754948616028,
0.5087811350822449,
0.3583259582519531,
0.8373719453811646,
0.5932642817497253,
-0.1744917631149292,
0.20138178765773773,
-0.49106067419052124,
-0.24329358339309692,
-0.7808616757392883,
-0.2605248987674713,
0.07233723998069763,
0.09020423889160156,
0.3535175025463104,
0.4505888819694519,
-0.24373680353164673,
0.23785041272640228,
-0.4610466957092285,
-0.44377803802490234,
0.4258691668510437,
-0.4380407929420471,
0.04222632199525833,
0.8325092196464539,
0.4805789291858673,
-0.9603476524353027,
-0.10417930036783218,
0.0836649239063263,
0.3630595803260803,
0.6141619086265564,
0.06852736324071884,
-0.5482155680656433,
0.3736748695373535,
-1.3296672105789185,
0.007171499542891979,
-0.9605433344841003,
-0.46796998381614685,
-0.23754137754440308,
-0.6978213787078857,
-0.37042126059532166,
-0.15802648663520813,
0.6191455125808716,
0.20279142260551453,
-0.23207072913646698,
-0.5686524510383606,
0.14021413028240204,
-0.5662031769752502,
-0.5042185187339783,
0.18382903933525085,
0.00413195975124836,
-0.03192855790257454,
0.7599474787712097,
-0.553385853767395,
0.3829140365123749,
-0.05296700447797775,
-0.11543368548154831,
0.15241678059101105,
0.6052216291427612,
0.47134676575660706,
-0.19078539311885834,
0.019169876351952553,
0.20450358092784882,
0.5536744594573975,
0.5352476835250854,
-0.6804320812225342,
0.561881422996521,
-0.5567986369132996,
1.2857426404953003,
-0.5300958156585693,
-0.021510155871510506,
0.055074311792850494,
-0.4103671610355377,
0.9529747366905212,
-0.1474771648645401,
-0.01289462111890316,
0.8223384022712708,
-0.1265556663274765,
0.4532068371772766,
0.05854423716664314,
-0.5055066347122192,
0.34488213062286377,
-0.7733950614929199,
-0.4204051196575165,
0.44605639576911926,
0.21319039165973663,
0.32911011576652527,
-0.4736385941505432,
-0.7402539849281311,
0.1665443331003189,
-0.15817368030548096,
-0.11347617208957672,
0.10734385997056961,
-0.03904416412115097,
0.4436264634132385,
0.38055163621902466,
0.0184952225536108,
-0.23810897767543793,
0.011971374973654747,
-0.6513575911521912,
-0.35662969946861267,
0.7104378938674927,
0.01279122568666935,
-0.7449772953987122,
-0.7837044596672058,
-0.27859607338905334,
-0.06364931911230087,
0.6544721126556396,
-0.37158405780792236,
0.6570719480514526,
-0.47505563497543335,
-0.5619636178016663,
-0.45324698090553284,
0.46147626638412476,
0.38230979442596436,
0.18258042633533478,
0.32879358530044556,
-0.03184717148542404,
0.0011926176957786083,
-0.565528929233551,
0.14554277062416077,
-0.235259011387825,
-0.44325941801071167,
0.5767974853515625,
-0.48696544766426086,
0.11795369535684586,
0.4540458023548126,
0.5564007759094238,
-0.4733634293079376,
-0.3847978413105011,
-1.1578843593597412,
-0.07932582497596741,
-0.35414713621139526,
0.28162673115730286,
0.014579778537154198,
-0.7843163013458252,
-0.04107178375124931,
-0.14331543445587158,
0.7958524227142334,
0.3204801678657532,
0.6421036124229431,
-0.17374275624752045,
-0.21853019297122955,
-0.6388509273529053,
0.09641926735639572,
0.8818854093551636,
0.20568139851093292,
-1.0612435340881348,
0.4466725289821625,
0.383991539478302,
-0.00372102577239275,
-0.26654645800590515,
0.8501543998718262,
-0.22573262453079224,
0.49319639801979065,
0.14331591129302979,
-0.21762412786483765,
-0.25197267532348633,
-0.35877546668052673,
0.15539638698101044,
0.6752438545227051,
-0.1523154377937317,
-0.6163311004638672,
0.5566117763519287,
0.18604128062725067,
0.35031387209892273,
0.5582014322280884,
0.2299075871706009,
-0.2630191743373871,
-0.12655101716518402,
0.005020943004637957,
0.04108452424407005,
-0.5679417252540588,
0.12672019004821777,
-0.8697649240493774,
-0.248513862490654,
-0.9722099900245667,
-0.07971559464931488,
0.7022094130516052,
0.503505527973175,
-0.5618923306465149,
0.06742413341999054,
-0.6475571393966675,
0.0163173396140337,
-0.11299276351928711,
0.008225155994296074,
-0.3563557267189026,
-0.5905616879463196,
0.22437827289104462,
-0.4960377514362335,
0.02571098692715168,
-0.7889384031295776,
-0.489007830619812,
0.22008517384529114,
-0.3474327325820923,
0.9973249435424805,
0.37837815284729004,
0.32304662466049194,
-1.0441104173660278,
-0.6378284692764282,
-0.6156241297721863,
-0.023973457515239716,
-0.6622721552848816,
1.0853077173233032,
-0.4246973991394043,
1.570176124572754,
0.12817688286304474,
0.28712689876556396,
-0.45894989371299744,
-0.2839354872703552,
-0.43089520931243896,
0.2975810468196869,
0.05999324843287468,
0.34625259041786194,
-0.36909574270248413,
-0.40071308612823486,
0.23968742787837982,
0.1599075347185135,
-0.9471890330314636,
0.45862632989883423,
-0.6906964182853699,
0.07580728083848953,
-0.50423264503479,
0.4738316535949707,
0.40275371074676514,
0.4115355610847473,
-0.11860447376966476,
0.3273681104183197,
0.3766475021839142,
0.1274224817752838,
0.454408198595047,
0.09768345206975937,
-0.3184744417667389,
-0.40753793716430664,
0.3887750506401062,
-0.7335179448127747,
-0.31506770849227905,
0.6636947393417358,
-0.22107523679733276,
-0.16561102867126465,
-0.1301911175251007,
-0.4201357364654541,
0.04447746276855469,
-0.0417742095887661,
-0.552518367767334,
0.527669370174408,
0.590322732925415,
-0.12437206506729126,
0.0037247012369334698,
-0.34703972935676575,
-0.4175529181957245,
0.618885338306427,
-0.6418197751045227,
-0.5230688452720642,
0.11438670009374619,
-0.4592236280441284,
0.08440884202718735,
0.41666531562805176,
-0.47661444544792175,
0.19614873826503754,
0.13446561992168427,
-0.2826177775859833,
0.7865656018257141,
0.03553337976336479,
-0.2202410101890564,
0.5504155158996582,
-1.0525760650634766,
-0.03869014233350754,
-0.5774831175804138,
0.9806841015815735,
-0.9185967445373535,
-1.3003604412078857,
-0.5675015449523926,
0.8068035840988159,
0.06594207882881165,
0.05804796889424324,
-0.2879650294780731,
0.031119508668780327,
-0.16943301260471344,
-0.474734902381897,
-0.5264731645584106,
-0.09390731155872345,
-0.6603987216949463,
0.8192857503890991,
-0.5887152552604675,
-0.6367806196212769,
0.23641324043273926,
-0.3157765567302704,
1.15776526927948,
-0.5577248334884644,
0.1613193303346634,
0.39732474088668823,
0.4864140748977661,
0.00517310481518507,
0.12955009937286377,
0.010037888772785664,
0.7662392854690552,
0.4379468858242035,
-0.569963276386261,
0.04914326220750809,
1.015568733215332,
0.20186446607112885,
-0.3897857964038849,
0.11883852630853653,
0.1116299033164978,
0.23511463403701782,
-0.2620161771774292,
-0.32275769114494324,
-0.3828538954257965,
0.44174090027809143,
-0.5654512047767639,
0.294094443321228,
-0.11936211585998535,
-0.058222219347953796,
-0.5285517573356628,
0.08710703998804092,
0.4348292052745819,
-0.24804915487766266,
0.23662221431732178,
0.1882389783859253,
0.1122465580701828,
0.14238549768924713,
-0.666437029838562,
-0.1797412633895874,
0.0015920741716399789,
-0.3428964614868164,
0.5479011535644531,
0.5718285441398621,
0.11978596448898315,
0.06628362089395523,
0.4957106411457062,
0.2689729630947113,
-0.1458754986524582,
0.9115484952926636,
0.43724924325942993,
0.8229458928108215,
1.3939464092254639,
0.1999891698360443,
0.1851884126663208,
-0.005890673492103815,
0.2160762995481491,
-0.8405489921569824,
0.3395925462245941,
0.34529075026512146,
-0.46180009841918945,
-0.1467549204826355,
-0.40137606859207153,
-0.5917679667472839,
-0.3733772039413452,
-0.29486170411109924,
0.13130900263786316,
-1.0697754621505737,
0.5519099831581116,
0.5312652587890625,
-0.6259116530418396,
0.2760362923145294,
0.6902605295181274,
0.6355308890342712,
0.2846076190471649,
0.19439131021499634,
0.0979795753955841,
-0.04628244787454605,
0.7234403491020203,
1.304978609085083,
0.6161219477653503,
0.20779190957546234,
0.27971652150154114,
-0.8761265277862549,
0.8712224364280701,
0.01779784820973873,
-0.5915431380271912,
0.2225586622953415,
-0.2488144338130951,
-0.46895477175712585,
-0.10045793652534485,
-0.29793423414230347,
-0.24381785094738007,
-0.7702077627182007,
0.6665146946907043,
0.12350651621818542,
-0.5053946375846863,
-0.6148344278335571,
1.1015671491622925,
0.7218687534332275,
-0.3568330407142639,
-0.35960960388183594,
0.6106178760528564,
-0.5745643377304077,
-0.5016302466392517,
-0.7855166792869568,
0.406893789768219,
-0.21014027297496796,
-0.4166751801967621,
0.03595669940114021,
-0.2761249244213104,
-0.9028087854385376,
-0.4004770815372467,
-0.32033011317253113,
-0.35130029916763306,
0.8118646740913391,
0.3561791479587555,
0.04067564755678177,
-0.036747004836797714,
-0.28021541237831116,
-0.011251415126025677,
-0.001174981240183115,
1.112593650817871,
-0.30509674549102783,
-0.039455197751522064,
0.05618401616811752,
-0.14009800553321838,
-0.3992503881454468,
-0.12052624672651291,
0.8905764222145081,
-1.275722622871399,
0.48839205503463745,
-0.8925929069519043,
0.6898594498634338,
0.2562214732170105,
-0.4007748067378998,
-0.08977065235376358,
0.12191841751337051,
-0.1740168184041977,
-0.5016294717788696,
-0.891843318939209,
-0.0951773002743721,
-1.3396245241165161,
-0.22172348201274872,
0.004290955141186714,
0.34210920333862305,
-0.14469392597675323,
-0.49151748418807983,
0.2457967847585678,
-1.002145767211914,
4.2403178215026855,
0.6352344751358032,
-0.14326980710029602,
-0.05675293877720833,
0.8146207928657532,
0.653467059135437,
-0.2045682817697525,
-0.4287543296813965,
0.2575395703315735,
0.09143298864364624,
-0.7505107522010803,
0.5130061507225037,
0.486530601978302,
-0.34535178542137146,
0.8275713920593262,
0.9920820593833923,
-0.09008793532848358,
-0.43151140213012695,
0.5225599408149719,
-1.1290489435195923,
-0.37386947870254517,
-0.4244421422481537,
-0.12888450920581818,
0.6875163912773132,
0.4253382086753845,
1.0421345233917236,
0.5752198100090027,
-0.1373354196548462,
-0.6515560746192932,
-0.7010826468467712,
-0.7607548832893372,
-0.8447691202163696,
0.3331138789653778,
-0.17415361106395721,
-1.3264273405075073,
0.8933056592941284,
0.13026762008666992,
-0.783577561378479,
0.4828351140022278,
-0.3724851608276367,
0.12054727226495743,
-0.8787133097648621,
0.1855747252702713,
-0.7388390302658081,
-0.12554463744163513,
0.4894412159919739,
-0.47099626064300537,
0.8694730401039124,
0.21475644409656525,
-0.9329129457473755,
0.29632803797721863,
0.249905064702034,
0.5986052751541138,
-0.04217672720551491,
-0.851417601108551,
0.2289370894432068,
-0.5500617027282715,
-0.029989946633577347,
0.4182819128036499,
-0.07346808910369873,
0.3893274664878845,
-0.7492057681083679,
0.0075589921325445175,
0.5768607258796692,
0.34476402401924133,
0.0236407108604908,
0.06718502938747406,
0.10210378468036652,
-0.09381778538227081,
0.46424445509910583,
-0.019235223531723022,
-0.284349262714386,
-0.3362796902656555,
-0.006009140983223915,
0.31822603940963745,
0.4990283250808716,
0.15483158826828003,
0.7084983587265015,
-0.41115882992744446,
-0.1220795214176178,
0.22908808290958405,
0.10431234538555145,
-0.36616989970207214,
0.06632031500339508,
-0.13349100947380066,
0.5407566428184509,
-0.8926039934158325,
-0.059748295694589615,
-0.7476013898849487,
0.9303470849990845,
0.39875131845474243,
0.9790191650390625,
-0.4147489070892334,
-0.05317658185958862,
-0.5670512318611145
] |
The effective potential and the renormalisation group
|
We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.
|
C. Ford, D.R.T. Jones, P.W. Stephenson and M.B. Einhorn
|
hep-lat hep-ph
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210033
|
hep-lat/9210034
|
[
0.35121163725852966,
-0.1017061173915863,
-0.1628051996231079,
0.663962721824646,
-0.3524959683418274,
-0.3230005204677582,
-0.3553105890750885,
-0.29699036478996277,
-0.39873889088630676,
1.6185411214828491,
0.7931379079818726,
-0.005000038538128138,
0.12006362527608871,
-0.6066466569900513,
-0.6848732233047485,
0.4882943630218506,
0.2752428352832794,
-0.5712020397186279,
-1.3626974821090698,
0.7845523953437805,
0.13258132338523865,
-0.5649014711380005,
-1.301119327545166,
-0.28432679176330566,
-0.4690493941307068,
0.6785168051719666,
0.05630464479327202,
0.33081546425819397,
1.0015003681182861,
0.2431727796792984,
0.4668879806995392,
-0.7926235198974609,
0.04041357338428497,
-0.33809950947761536,
-0.1889926940202713,
-0.35801559686660767,
0.43610578775405884,
-0.08828487992286682,
0.6079228520393372,
-0.6820715665817261,
0.6872716546058655,
-0.13082149624824524,
-0.20092633366584778,
-0.21803274750709534,
-0.5179977416992188,
0.06193685904145241,
-0.5407933592796326,
-0.04785165563225746,
0.10809972137212753,
-1.0861741304397583,
0.057388029992580414,
0.22303397953510284,
0.4746362566947937,
-0.32209786772727966,
-0.41006532311439514,
-0.5675484538078308,
-0.00700919097289443,
0.36436617374420166,
-0.5906074643135071,
-0.5634843707084656,
0.539717972278595,
-0.17504343390464783,
-0.06358936429023743,
-0.47208839654922485,
0.12279804050922394,
1.37943696975708,
-0.02593865618109703,
0.7814445495605469,
-0.004341830033808947,
-0.3084266185760498,
-0.06973714381456375,
0.12825319170951843,
-0.812437117099762,
0.1223992332816124,
-0.7692270278930664,
-0.001042304327711463,
0.009601711295545101,
-0.6098076701164246,
-1.2595075368881226,
0.4151376485824585,
-0.015597181394696236,
-0.14779289066791534,
-0.1981685906648636,
0.4790932536125183,
-0.1914444863796234,
-0.34926867485046387,
-0.13467490673065186,
0.15615862607955933,
0.036143671721220016,
0.8401694297790527,
0.29051247239112854,
0.7848861813545227,
-0.04443337395787239,
-0.12418678402900696,
0.09712864458560944,
0.14979076385498047,
0.4261803925037384,
0.25239092111587524,
0.36646491289138794,
0.01107836328446865,
-0.3799576461315155,
0.8166153430938721,
-0.7562123537063599,
-0.3162800371646881,
-0.5433336496353149,
0.05849162116646767,
-0.3123760223388672,
-0.09964476525783539,
0.18981638550758362,
-0.41502466797828674,
0.23725777864456177,
-0.3736947476863861,
0.1365528255701065,
0.8025634288787842,
-0.13208836317062378,
0.6422758102416992,
-0.3714761734008789,
0.18843355774879456,
-0.4893544912338257,
-0.5104966759681702,
0.2988608181476593,
0.40664854645729065,
0.08951989561319351,
0.2685750126838684,
0.4822942614555359,
-0.056841060519218445,
-0.0292985662817955,
0.7189725637435913,
-0.871184229850769,
0.1163753941655159,
-0.21131260693073273,
-0.15968774259090424,
-0.3771412670612335,
0.795464277267456,
-0.5793765783309937,
-0.07392145693302155,
0.13699942827224731,
0.34288251399993896,
0.5142185091972351,
-0.2369152307510376,
0.661581814289093,
-0.673316478729248,
-0.04655073583126068,
1.0887913703918457,
-0.7186146974563599,
0.474192351102829,
0.1751432716846466,
0.5465657114982605,
-0.354873389005661,
0.6087040901184082,
-0.6136784553527832,
-0.5776485204696655,
-0.3212754726409912,
0.9735057353973389,
-0.21679337322711945,
0.6129181385040283,
-0.5015517473220825,
0.10486690700054169,
-0.7208464741706848,
-0.37347108125686646,
0.3243353068828583,
0.13074809312820435,
-0.43710893392562866,
0.44148367643356323,
-0.3063769042491913,
0.3443462550640106,
-0.7625911235809326,
-0.4654805660247803,
0.34355729818344116,
-0.6690173149108887,
0.36336249113082886,
0.3913883566856384,
-0.2352796196937561,
1.1568939685821533,
-0.09294787794351578,
0.03306303173303604,
0.4090290367603302,
-0.7147237062454224,
-0.41802000999450684,
0.44849255681037903,
-0.3678875267505646,
-0.1304309219121933,
0.8285529017448425,
-0.3243321180343628,
0.04124840721487999,
-0.09518980979919434,
-0.7419447302818298,
-0.13708366453647614,
-0.45153698325157166,
0.47812679409980774,
-0.5841951370239258,
0.7273135781288147,
-0.7944723963737488,
0.5544252395629883,
-0.11543960124254227,
-0.251575767993927,
-0.5928279757499695,
0.08750810474157333,
-0.46762728691101074,
-0.715429961681366,
0.1259111911058426,
0.3753355145454407,
-0.8191794753074646,
0.35130247473716736,
-1.1359338760375977,
-0.21206578612327576,
0.36440110206604004,
0.2550807297229767,
-0.8707741498947144,
-0.31933480501174927,
0.4061858654022217,
0.12289886921644211,
0.06169719249010086,
-0.46137821674346924,
-0.09742362797260284,
0.215021550655365,
0.055361583828926086,
0.15764574706554413,
0.3188033401966095,
0.46638795733451843,
0.44529953598976135,
0.5015203356742859,
-0.16367998719215393,
0.974207878112793,
-0.5326789617538452,
-0.7460296154022217,
0.1518978327512741,
0.6082649230957031,
0.17877992987632751,
-0.1345413327217102,
-0.19869866967201233,
0.4117280840873718,
-0.14512813091278076,
0.3652617931365967,
0.2882455587387085,
0.1343267410993576,
0.7600789666175842,
0.7827840447425842,
0.5578030943870544,
0.2696668803691864,
-0.14556343853473663,
0.24267400801181793,
0.2670426070690155,
-0.24511267244815826,
-0.18274159729480743,
0.505843460559845,
-0.255717396736145,
0.2582052946090698,
-0.5735650062561035,
0.7245838046073914,
-0.045752476900815964,
1.005016803741455,
0.34840062260627747,
0.40142950415611267,
-0.9968418478965759,
0.15125663578510284,
0.030398137867450714,
0.09637541323900223,
-0.16855603456497192,
-0.42353737354278564,
-0.33676034212112427,
0.31813567876815796,
-0.31332412362098694,
-0.5750319361686707,
-0.13701112568378448,
0.8537095785140991,
0.1258464902639389,
0.1042589321732521,
1.2124342918395996,
-0.4790079891681671,
-1.1724897623062134,
0.005966385826468468,
-0.919066846370697,
-0.03582916408777237,
-0.07778289914131165,
-0.20025591552257538,
0.8885964155197144,
-0.9354779124259949,
0.29931706190109253,
0.04816354066133499,
-0.5643603801727295,
0.865810751914978,
-0.29408472776412964,
0.5220822691917419,
0.19146549701690674,
0.05474979802966118,
-0.34544822573661804,
-0.001896203146316111,
-0.7117742300033569,
0.12586885690689087,
-0.20929549634456635,
0.07824913412332535,
0.6076087355613708,
-0.31355974078178406,
0.2734721899032593,
-0.018281975761055946,
-0.41065526008605957,
0.28842195868492126,
0.36449795961380005,
-0.45540907979011536,
0.30628687143325806,
0.9485470056533813,
0.13283492624759674,
-0.2806698679924011,
-1.225030541419983,
0.38658928871154785,
0.08747077733278275,
0.030867300927639008,
0.273554265499115,
0.3220463693141937,
-0.4901197552680969,
0.3464657664299011,
-0.2055622786283493,
0.338322252035141,
0.2637661397457123,
0.6668859720230103,
0.5124415159225464,
0.2781391143798828,
0.11360453069210052,
-0.7108128070831299,
-0.022514279931783676,
0.04378591850399971,
0.41367119550704956,
-0.17160826921463013,
-0.014097040519118309,
0.8387858867645264,
-0.02057766541838646,
-0.8586570620536804,
0.5537146329879761,
-1.0496786832809448,
-0.5354803204536438,
0.4974924921989441,
-0.3963816165924072,
0.4697987735271454,
0.04283266142010689,
0.37148773670196533,
-1.15250825881958,
-0.12407569587230682,
-0.5832836627960205,
0.7161988019943237,
0.4753885567188263,
-0.3459535837173462,
0.22408224642276764,
0.7039869427680969,
0.14602412283420563,
-0.29913944005966187,
0.05613803490996361,
0.17187993228435516,
-0.6549756526947021,
0.6408050060272217,
-0.8901579976081848,
0.3527180254459381,
-0.037795115262269974,
0.37675347924232483,
0.18778689205646515,
0.3979424834251404,
-0.32042405009269714,
-0.42365843057632446,
-0.6458998918533325,
-0.5300571918487549,
0.07247749716043472,
0.9163118600845337,
0.09258659929037094,
0.12287915498018265,
-0.5385448932647705,
-0.13991287350654602,
-0.006383456289768219,
-0.03372301161289215,
0.17368462681770325,
-0.7688358426094055,
0.20646938681602478,
-0.11474438011646271,
-0.6911024451255798,
-0.2964012622833252,
0.031163066625595093,
0.19094450771808624,
0.561867356300354,
0.3378414511680603,
0.7012673020362854,
-0.17420659959316254,
-0.2764133810997009,
0.1761852204799652,
0.9907681345939636,
0.6737480163574219,
0.1584961861371994,
0.4030192494392395,
0.43836960196495056,
-0.3253646790981293,
-0.5010349154472351,
-0.7533294558525085,
-0.6256084442138672,
-0.3955656886100769,
0.49304407835006714,
-0.32423681020736694,
0.100569948554039,
-0.21687495708465576,
0.729815661907196,
0.34035906195640564,
0.6572840809822083,
0.46543458104133606,
0.44706040620803833,
0.1933034062385559,
0.9297383427619934,
0.40713217854499817,
0.05564422532916069,
1.0645850896835327,
-0.9183165431022644,
0.3802962005138397,
0.027627956122159958,
0.7562903165817261,
-0.314506471157074,
-0.19197003543376923,
0.1349882185459137,
-0.8004788756370544,
0.2959915101528168,
-0.009185057133436203,
-0.5102767944335938,
0.5788044333457947,
0.020877962931990623,
0.09796794503927231,
-0.5072034001350403,
-0.15069960057735443,
0.9146626591682434,
0.5636980533599854,
0.01116943173110485,
-0.7206793427467346,
0.4474608898162842,
-0.3919012248516083,
0.03254184499382973,
0.2803276777267456,
-0.8080249428749084,
-1.184880256652832,
-0.8899936676025391,
-0.4861825704574585,
-0.7796639204025269,
0.335252970457077,
0.6813768148422241,
0.34869927167892456,
0.14455296099185944,
-0.5710963606834412,
-0.28315791487693787,
0.5009030699729919,
-0.5470986366271973,
-0.5926584601402283,
0.7380877137184143,
-0.13986337184906006,
0.21636399626731873,
0.4269901216030121,
-0.3143206536769867,
-0.3902064859867096,
-0.04683847725391388,
-0.7534330487251282,
0.05635898932814598,
-0.36059898138046265,
-0.32985398173332214,
-0.4681697189807892,
-0.47155842185020447,
-0.5306644439697266,
0.6204228401184082,
-0.06083887070417404,
-0.06061196327209473,
-0.24929530918598175,
-0.30108633637428284,
-0.3725583553314209,
-0.15103159844875336,
0.2497338503599167,
-0.29064276814460754,
0.7068871855735779,
0.6660510897636414,
0.14796289801597595,
0.21042291820049286,
0.5489016771316528,
0.06168263405561447,
0.41862359642982483,
0.14986544847488403,
0.00732067134231329,
-0.024437500163912773,
-0.3813340663909912,
0.14602059125900269,
-0.44960108399391174,
-0.9042599201202393,
0.022174393758177757,
-0.3323025703430176,
0.24890458583831787,
0.21342261135578156,
-0.1147104874253273,
-0.16781529784202576,
-0.3507266640663147,
-0.8513926863670349,
0.31384965777397156,
0.008982231840491295,
-0.4886705279350281,
0.42551591992378235,
-0.6833281517028809,
-0.3879585862159729,
-0.291206955909729,
-0.26638224720954895,
-0.014412554912269115,
0.613178551197052,
0.6432620286941528,
0.08841243386268616,
0.6703765392303467,
-1.2839316129684448,
0.6980775594711304,
-0.5277596116065979,
-0.47228437662124634,
-0.7097946405410767,
-0.27316612005233765,
-0.1682099550962448,
0.012329665943980217,
0.11961587518453598,
0.33679816126823425,
-0.22271718084812164,
0.00899945292621851,
-0.07110800594091415,
-0.39487913250923157,
0.37481340765953064,
-0.46996673941612244,
0.2049098163843155,
0.6348008513450623,
0.24841129779815674,
-0.32653653621673584,
0.0025794056709855795,
0.28176751732826233,
-0.37827423214912415,
0.2357167899608612,
-0.06362394988536835,
-0.7586894631385803,
0.27744248509407043,
-0.730915367603302,
0.3713199496269226,
-1.1157264709472656,
-0.2921562194824219,
-0.10869037359952927,
-0.7318816781044006,
-0.13955378532409668,
0.8319986462593079,
0.34788787364959717,
-0.500399112701416,
-0.40324723720550537,
-0.4820556938648224,
0.20497825741767883,
-0.14224520325660706,
-0.012354091741144657,
-0.6523382663726807,
0.21596193313598633,
-0.6544861793518066,
0.36517056822776794,
-0.18795767426490784,
0.2013838142156601,
0.017084816470742226,
0.07175195962190628,
0.24455894529819489,
0.32209569215774536,
0.5144182443618774,
-0.3469501733779907,
0.23543289303779602,
0.24684597551822662,
-0.19357497990131378,
0.8810499906539917,
-0.9048275947570801,
0.06974844634532928,
-0.6455252766609192,
1.6286119222640991,
-0.750046968460083,
-0.5830091834068298,
0.2895953953266144,
0.3002570569515228,
0.5688586235046387,
-0.45904144644737244,
0.16430728137493134,
0.4967644512653351,
0.18625111877918243,
0.5551154613494873,
0.3540331721305847,
-0.5112008452415466,
-0.32536986470222473,
-0.2912532091140747,
-0.4396352767944336,
0.584109365940094,
0.11523846536874771,
-0.3798049986362457,
-0.9086092710494995,
-0.8587586283683777,
0.12686051428318024,
-0.19873647391796112,
0.07017496973276138,
0.4249721169471741,
-0.11606348305940628,
-0.14466485381126404,
-0.19266195595264435,
0.1783732920885086,
-0.4164341688156128,
0.5953918099403381,
0.34537163376808167,
0.15039953589439392,
-0.06649664789438248,
-0.13631998002529144,
-0.48769649863243103,
-0.580880343914032,
-0.2536507248878479,
0.24595174193382263,
-0.07478231936693192,
-0.08340585976839066,
0.824285089969635,
-0.24090668559074402,
-0.17040449380874634,
-0.23503732681274414,
-0.06907927244901657,
0.2976854741573334,
0.4884771704673767,
0.30490171909332275,
0.46913304924964905,
-0.04331262409687042,
-0.20844094455242157,
0.388817697763443,
0.016716862097382545,
0.16938889026641846,
0.8683226108551025,
-0.6642824411392212,
-0.1790022850036621,
0.389758825302124,
-0.029709486290812492,
-0.9856616854667664,
0.12467020004987717,
-1.0063745975494385,
0.3986324071884155,
-0.2551935613155365,
-0.24431076645851135,
-0.6153520941734314,
0.11733093112707138,
-0.48067402839660645,
1.0023938417434692,
0.4044068455696106,
-0.28132104873657227,
0.06915492564439774,
-0.5147244334220886,
-0.36375105381011963,
-0.9264553785324097,
-0.1436159908771515,
1.3710390329360962,
0.06424126029014587,
-1.182491421699524,
-0.06220764294266701,
-0.04422614723443985,
-0.21771098673343658,
-0.06684648990631104,
0.6296436786651611,
-0.6874074935913086,
0.29707249999046326,
0.7770192623138428,
0.03692745417356491,
0.5113022327423096,
0.5503002405166626,
0.4911107122898102,
0.1421050727367401,
-0.17877276241779327,
-0.7830712795257568,
-0.18058164417743683,
-0.19294919073581696,
0.056318532675504684,
1.1998411417007446,
0.24273201823234558,
0.1462172418832779,
0.09765233099460602,
-0.4331718385219574,
0.19972825050354004,
-0.5195098519325256,
0.13636411726474762,
-0.6937029957771301,
-0.6281642913818359,
-0.21650801599025726,
-0.14544153213500977,
0.40668365359306335,
0.38215136528015137,
-0.3620161712169647,
0.10457539558410645,
-0.21259738504886627,
-0.1445743590593338,
0.07667651027441025,
0.3381507992744446,
-0.07119635492563248,
-0.8336239457130432,
-0.692678689956665,
0.08639934659004211,
-0.11468706279993057,
-0.6709564328193665,
-0.023489458486437798,
-0.054365407675504684,
0.10160798579454422,
0.34193727374076843,
-0.17570963501930237,
1.3706610202789307,
-0.9909921884536743,
-0.574429988861084,
0.3004854917526245,
-0.11299773305654526,
-0.9211314916610718,
0.1842164844274521,
-0.37280455231666565,
0.9219926595687866,
0.299530029296875,
-0.01996580883860588,
0.2161094695329666,
-0.12499050796031952,
-0.5328653454780579,
-0.18491515517234802,
-0.23470669984817505,
0.5916094779968262,
-0.2387784719467163,
-1.054961919784546,
-0.28087475895881653,
0.3052951395511627,
-1.1194674968719482,
0.440864622592926,
-0.17483831942081451,
0.14920192956924438,
0.10900168120861053,
0.1835533082485199,
-0.06749846041202545,
0.3198166489601135,
-0.41779208183288574,
0.812906801700592,
-0.2907089591026306,
-0.05179108306765556,
0.1430720090866089,
0.040434643626213074,
-0.0058899084106087685,
0.32455411553382874,
0.19708038866519928,
-0.16396504640579224,
-0.0920233204960823,
0.5987188220024109,
-0.03169608488678932,
-0.5276323556900024,
0.0446506030857563,
0.05698290467262268,
-0.3377464711666107,
-0.4787728190422058,
-0.7814680933952332,
0.5050266981124878,
0.4029010236263275,
-0.8633168339729309,
-0.43042734265327454,
-0.3558628261089325,
-0.7939175367355347,
0.3157315254211426,
-0.9402511119842529,
-0.7665573358535767,
-0.17094437777996063,
-0.5592417120933533,
0.28624871373176575,
0.309213250875473,
-0.07678253203630447,
-0.34961238503456116,
0.10946551710367203,
-0.016859687864780426,
-0.048692766577005386,
-0.19995611906051636,
-0.5970978140830994,
0.5551465749740601,
-0.7484362125396729,
-0.4014095664024353,
-0.6810543537139893,
0.6351348161697388,
-0.9329152703285217,
-0.7454222440719604,
-0.38056087493896484,
0.7681628465652466,
0.5935790538787842,
-0.1923941820859909,
-0.46407344937324524,
-0.13865962624549866,
-0.32236093282699585,
-0.3024309277534485,
-0.7637847065925598,
-0.4155169427394867,
-0.0005299027543514967,
0.32116663455963135,
-0.19643595814704895,
-0.060478512197732925,
0.46056368947029114,
-0.17168554663658142,
0.19511857628822327,
0.2508957087993622,
-0.0436013787984848,
0.5035622119903564,
-0.1566743105649948,
-0.6491381525993347,
1.0879822969436646,
0.31883636116981506,
0.40893909335136414,
0.3081963062286377,
-0.665494978427887,
0.36766529083251953,
0.2929675281047821,
0.28820815682411194,
0.8131513595581055,
-0.11489345878362656,
-0.04272415488958359,
0.14719067513942719,
-0.05055542290210724,
-0.0347423255443573,
-0.08783626556396484,
0.5390695333480835,
0.501735508441925,
0.1620059609413147,
0.20376762747764587,
-0.14305159449577332,
0.3478780686855316,
0.09051505476236343,
0.19483204185962677,
0.07082634419202805,
-0.2140783667564392,
-0.3582541048526764,
-0.049209482967853546,
0.21723432838916779,
-0.8006609678268433,
-0.24204958975315094,
-0.6215812563896179,
0.20167002081871033,
0.6715540289878845,
0.09754584729671478,
-0.02650298923254013,
0.685211181640625,
0.7746257185935974,
0.14845362305641174,
0.031711846590042114,
0.6339324712753296,
0.5622515082359314,
1.1417824029922485,
0.14096316695213318,
0.8705315589904785,
0.5831308960914612,
0.5291700959205627,
0.3374660909175873,
-0.7027199864387512,
0.23652946949005127,
0.14617440104484558,
-1.0275189876556396,
-0.10154011845588684,
-0.2747923731803894,
-0.4864545166492462,
-0.4386328160762787,
-0.31903019547462463,
0.5921950936317444,
-0.6447423696517944,
0.22338919341564178,
0.7072516083717346,
-0.27051210403442383,
0.11729995161294937,
0.6309487819671631,
0.05786675959825516,
0.4041024446487427,
0.8183508515357971,
0.42287492752075195,
-0.10569244623184204,
0.7824484705924988,
1.0398601293563843,
0.12283793091773987,
-0.12763376533985138,
0.16289182007312775,
-0.778367817401886,
-0.04754812270402908,
0.5294653177261353,
-0.17625930905342102,
0.5228445529937744,
-0.47128039598464966,
-0.20908309519290924,
-0.09933797270059586,
-0.07775802165269852,
-0.7054685950279236,
-0.12201669812202454,
0.20526564121246338,
0.1502445638179779,
-0.5405144095420837,
-0.24048884212970734,
1.4610155820846558,
0.5888291001319885,
-0.12030065804719925,
-0.5383789539337158,
0.05817154794931412,
0.011211046017706394,
-0.551630437374115,
-0.6582525372505188,
0.1108798086643219,
-0.06333018839359283,
-0.12245812267065048,
0.022212406620383263,
-0.5647724270820618,
-0.22267673909664154,
-0.7115461826324463,
0.3259127736091614,
-0.6334542036056519,
0.24968984723091125,
0.4268384277820587,
-0.0266123004257679,
0.433784544467926,
-0.6874499320983887,
0.1386200189590454,
-0.1444988250732422,
1.2976067066192627,
0.10636516660451889,
0.3977953791618347,
0.5881240367889404,
0.44897767901420593,
-0.5751510858535767,
0.5311762094497681,
0.9680392146110535,
-0.8824112415313721,
0.8951088786125183,
-0.12069766223430634,
0.6703656315803528,
-0.14563342928886414,
0.2991317808628082,
0.2666317820549011,
0.03931216523051262,
0.3539036512374878,
-0.37202128767967224,
-0.678677499294281,
-0.3668844997882843,
-0.8834351897239685,
0.08956028521060944,
-0.5799424052238464,
0.5665578246116638,
0.4343968331813812,
0.5097140073776245,
-0.15433169901371002,
-0.7606964111328125,
4.383513927459717,
0.5578557848930359,
0.6960145235061646,
0.3318091034889221,
0.38689330220222473,
0.5344570279121399,
-0.19737732410430908,
-0.6780673265457153,
0.15962012112140656,
-0.8383283615112305,
0.11526221036911011,
-0.043035369366407394,
0.21514461934566498,
0.11892960965633392,
-0.09817806631326675,
0.6467633247375488,
-0.6800820231437683,
-0.34735730290412903,
0.4602685570716858,
-1.1152973175048828,
-0.6566746830940247,
0.10940936952829361,
0.19026947021484375,
-0.17572733759880066,
0.35610076785087585,
0.3494967818260193,
0.20733429491519928,
-0.4704623520374298,
-0.2443322390317917,
-0.11695299297571182,
-0.8129448890686035,
-0.8375898599624634,
-0.0895693376660347,
-0.4409763813018799,
-0.6020798087120056,
0.33312124013900757,
0.2286675125360489,
-0.34890294075012207,
0.11345141381025314,
-0.12846782803535461,
0.0835801437497139,
-0.4377072751522064,
0.12149526178836823,
-0.03005770407617092,
-1.222881555557251,
1.1143085956573486,
-0.01992596499621868,
1.0475488901138306,
0.6381291151046753,
-0.7020293474197388,
0.3537991940975189,
-0.041083380579948425,
0.8940715789794922,
-0.045211125165224075,
-0.9657536745071411,
-0.23926885426044464,
-0.44830939173698425,
-0.06097355857491493,
0.23902446031570435,
0.4196085035800934,
0.3666790723800659,
-0.3696105480194092,
-0.3151884973049164,
0.41057559847831726,
-0.25928518176078796,
0.6409255862236023,
0.041536323726177216,
-0.20067410171031952,
-0.6056485176086426,
0.2098798155784607,
-0.32342737913131714,
-0.24361589550971985,
-0.4680789113044739,
0.09934525191783905,
-0.11173748970031738,
0.4636951982975006,
-0.4578128457069397,
0.4934070408344269,
-0.11382221430540085,
0.08628018200397491,
0.219870463013649,
0.01618785224854946,
-0.5602721571922302,
0.13441230356693268,
-0.07529926300048828,
0.7015157341957092,
-0.195135235786438,
0.4826991558074951,
0.28569889068603516,
0.4613572061061859,
0.49060219526290894,
0.8564654588699341,
0.23281295597553253,
0.03242899104952812,
-0.8891444802284241
] |
The $I=1$, $J=1$ channel of the O(4) $\lambda \phi^4_4$ theory
|
A Monte Carlo simulation of the $O(4)$ $\lambda \phi^4$ theory in the broken phase is performed on a hypercubic lattice in search of an $I=1$, $J=1$ resonance. We investigate the region of the cutoff theory where the interaction is strong as it is there that a resonance would be expected to have a better chance to form. In that region the presence of an $I=1$, $J=1$ resonance with mass below the cutoff is excluded. NOTE: The full ps file is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lat92_proc_rho.ps (to get it type: get lat92_proc_rho.ps)
|
Khalil M. Bitar, Pavlos Vranas
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210034
|
hep-lat/9210035
|
[
0.4595080316066742,
0.06421738862991333,
0.08409357815980911,
0.28735673427581787,
0.04461634159088135,
-0.2595558762550354,
-0.1450675129890442,
-0.4272705912590027,
-0.6819906234741211,
1.310849905014038,
0.40750616788864136,
0.009835785254836082,
0.05211126431822777,
-0.4843422472476959,
-0.24526046216487885,
0.574105441570282,
0.09606513381004333,
-0.7437400817871094,
-1.0720245838165283,
0.5955597758293152,
0.33072924613952637,
0.11533492803573608,
-1.2074885368347168,
-0.34741684794425964,
-0.33640310168266296,
0.8990822434425354,
0.38376104831695557,
0.41654717922210693,
1.1010125875473022,
0.7079653739929199,
-0.2369573563337326,
-0.4510984420776367,
-0.37303587794303894,
-0.2259671837091446,
-0.6326660513877869,
-0.31821706891059875,
-0.5893097519874573,
0.20075780153274536,
0.3640243411064148,
-0.3015221059322357,
0.8525623679161072,
-0.5143341422080994,
0.22084346413612366,
0.19008436799049377,
-0.36390170454978943,
0.14577236771583557,
-0.17755651473999023,
-0.14098787307739258,
0.44244295358657837,
-1.2301088571548462,
-0.006780402269214392,
0.5215073823928833,
-0.16593264043331146,
-0.6020002961158752,
-0.30717113614082336,
0.3513842821121216,
0.39396387338638306,
-0.20455209910869598,
-0.4553123116493225,
-0.4917287230491638,
0.5445566773414612,
-0.08815257996320724,
0.6552331447601318,
-1.082071304321289,
0.03948083519935608,
0.9376598596572876,
-0.051315657794475555,
0.6336578130722046,
0.4234393835067749,
-0.07977155596017838,
-0.15404097735881805,
-0.009054022841155529,
-1.0016510486602783,
-0.23478226363658905,
-0.9143843650817871,
0.0765504464507103,
0.2891587018966675,
0.16459117829799652,
-0.5888202786445618,
0.11725570261478424,
0.14078828692436218,
0.261989027261734,
-0.17037133872509003,
0.2575426995754242,
-0.861192524433136,
-0.00242698285728693,
0.39469650387763977,
-0.32175979018211365,
0.12951813638210297,
0.4731842577457428,
-0.5156967043876648,
0.41546228528022766,
-0.38315045833587646,
0.3144424259662628,
0.006792909931391478,
0.17484426498413086,
-0.15290798246860504,
0.4024337828159332,
0.003279566764831543,
-0.016853811219334602,
0.14720776677131653,
0.38827916979789734,
-0.38525399565696716,
0.09744390845298767,
-1.0301517248153687,
0.42540988326072693,
-0.13538287580013275,
0.26745861768722534,
0.10208965837955475,
-0.8016871213912964,
0.41304126381874084,
-0.5887150764465332,
0.19658219814300537,
0.4084150493144989,
0.5254482626914978,
0.5338716506958008,
-0.698555588722229,
0.20949400961399078,
-1.026341438293457,
-0.46064895391464233,
0.6077705025672913,
0.45220446586608887,
0.6782355904579163,
0.8443241119384766,
0.3136698305606842,
-0.19165924191474915,
0.08414402604103088,
0.7224674224853516,
-0.3153684735298157,
0.8959010243415833,
0.0725708156824112,
-0.23676998913288116,
-0.6177248358726501,
1.0015408992767334,
-0.8329861164093018,
0.21404771506786346,
-0.4802805185317993,
0.5090342164039612,
0.2203182727098465,
-0.15896591544151306,
0.9053404927253723,
-0.35957375168800354,
-0.1143888607621193,
1.128822684288025,
-0.07577336579561234,
0.27214595675468445,
-0.10211143642663956,
-0.28973978757858276,
-0.10079614073038101,
0.31527990102767944,
-0.17544297873973846,
-0.24581295251846313,
-0.34917762875556946,
0.4438669681549072,
-0.4136219620704651,
0.7772087454795837,
-0.45642468333244324,
-0.3749692738056183,
-0.27537575364112854,
-0.25962018966674805,
0.5857524275779724,
-0.09542194753885269,
-0.5031675696372986,
0.3539869487285614,
-0.3539362847805023,
0.4273724853992462,
-0.44990333914756775,
-0.03295936435461044,
-0.07107783854007721,
-0.7430347800254822,
-0.18198800086975098,
0.348923921585083,
-0.27468249201774597,
0.6346035599708557,
0.7546608448028564,
0.3435310423374176,
0.7720798254013062,
-0.7758887410163879,
-0.27740758657455444,
0.41829752922058105,
-0.613204836845398,
-0.05972328409552574,
0.2746587097644806,
-0.0847381204366684,
-0.8403875827789307,
-0.5052140355110168,
0.5399706959724426,
0.00821820367127657,
-0.015550683252513409,
0.2903868556022644,
-0.6568349003791809,
-0.13427473604679108,
-0.17909406125545502,
0.6473660469055176,
-0.9670016765594482,
0.1911011040210724,
-1.041150450706482,
-0.03864511847496033,
-0.8163208961486816,
-0.0198379959911108,
0.08103763312101364,
0.39735543727874756,
-0.8386803269386292,
0.33008792996406555,
-1.4129908084869385,
-0.023140592500567436,
0.5801846981048584,
0.18927505612373352,
-0.575536847114563,
0.3371371328830719,
0.4031226933002472,
-0.4837367832660675,
0.38919997215270996,
-0.7956412434577942,
0.06508422642946243,
-0.19946368038654327,
0.18816888332366943,
0.48046836256980896,
-0.0714958906173706,
0.1489230990409851,
1.0395363569259644,
0.16002075374126434,
0.19483880698680878,
1.0974949598312378,
0.22131125628948212,
-0.2474636286497116,
-0.16971266269683838,
0.13086329400539398,
0.13624228537082672,
-0.37729719281196594,
-0.014017329551279545,
0.40409085154533386,
0.0070107681676745415,
0.8573596477508545,
0.7261502742767334,
0.4781852662563324,
0.2933169901371002,
0.003118781140074134,
0.543006420135498,
-0.022599706426262856,
0.07893282175064087,
-0.5065980553627014,
0.18408788740634918,
-0.6206449270248413,
-0.02302168868482113,
0.27554622292518616,
-0.6232365369796753,
0.09299381822347641,
-0.6011127829551697,
0.5464667677879333,
0.4540444016456604,
0.3122570216655731,
0.1731170415878296,
0.32514461874961853,
-1.1623626947402954,
-0.3449707627296448,
-0.6394971609115601,
0.10850903391838074,
-0.21150529384613037,
-0.5112545490264893,
-0.4268524646759033,
0.18420088291168213,
-0.3591115474700928,
-1.071282982826233,
-0.12826132774353027,
0.6976115107536316,
-0.786827027797699,
0.3788663148880005,
0.4641887843608856,
-0.2254418581724167,
-0.9125964045524597,
0.02772541716694832,
-0.8574710488319397,
-0.022322045639157295,
-0.6191268563270569,
0.37437427043914795,
1.1129049062728882,
-0.8316852450370789,
-0.17124907672405243,
0.006945410277694464,
-0.1333426684141159,
0.3687671422958374,
-0.29681769013404846,
0.3034883439540863,
0.05946141481399536,
0.7081486582756042,
-0.699567973613739,
0.11730005592107773,
-0.2946538031101227,
-0.022113380953669548,
0.03583845868706703,
-0.3169531524181366,
0.6225844621658325,
-0.14513595402240753,
0.33957692980766296,
0.4451937973499298,
-0.8765999674797058,
0.14536063373088837,
0.06872399151325226,
-0.41047438979148865,
0.5199100971221924,
-0.2807384729385376,
-0.058909088373184204,
-0.26306596398353577,
-0.8152467608451843,
0.3762030601501465,
0.1914684772491455,
-0.39642134308815,
0.29079487919807434,
-0.07054933905601501,
-0.3576919138431549,
0.2793481647968292,
-0.22698672115802765,
0.30218103528022766,
-0.07100430130958557,
0.34549880027770996,
0.05690922960639,
-0.03437497466802597,
-0.5831730365753174,
0.017483755946159363,
-0.7767024636268616,
-0.15896138548851013,
0.2339782416820526,
-0.2766016721725464,
-0.2593524158000946,
0.384463906288147,
0.1804112046957016,
-0.6015685200691223,
0.3761604130268097,
-1.0574994087219238,
-0.9890540242195129,
0.08798257261514664,
-0.720816433429718,
0.3883945941925049,
0.25198546051979065,
0.0760393738746643,
-0.3821761906147003,
0.23181331157684326,
-0.21065153181552887,
0.10246269404888153,
0.5405063629150391,
-0.2588980197906494,
0.44279828667640686,
0.3122723400592804,
0.9387169480323792,
-0.6073101758956909,
0.3678954243659973,
-0.03927943482995033,
-0.5797126293182373,
0.5665878653526306,
-0.21729367971420288,
0.4454824924468994,
-0.04760473594069481,
0.573483407497406,
-0.16385120153427124,
0.05361291766166687,
-0.4793883264064789,
-0.470310777425766,
-0.8169702887535095,
-0.5832246541976929,
0.3511805236339569,
0.40534332394599915,
-0.5474036335945129,
-0.06482759118080139,
-0.38932427763938904,
-0.10226722061634064,
0.529941201210022,
0.4508724510669708,
0.5471664071083069,
-0.3070894181728363,
0.2296280562877655,
0.3508404791355133,
-0.5052119493484497,
0.4413505792617798,
0.1042209044098854,
-0.05219485983252525,
0.8954898715019226,
0.6063571572303772,
0.6022968888282776,
-0.45803460478782654,
-0.6345288157463074,
0.10360335558652878,
0.9432517886161804,
0.5653226971626282,
0.10720915347337723,
0.17583118379116058,
0.09179390966892242,
-0.21289560198783875,
-0.5664780139923096,
0.06614196300506592,
-0.216958150267601,
-0.21002978086471558,
0.35300326347351074,
-0.27560701966285706,
-0.41328394412994385,
-0.18114137649536133,
0.13499407470226288,
0.6416265964508057,
-0.056093063205480576,
-0.1361965537071228,
0.45063573122024536,
-0.14534473419189453,
0.2721746861934662,
0.6380347013473511,
-0.11501719057559967,
-0.2106637954711914,
-0.6715258359909058,
0.34758245944976807,
0.18362188339233398,
-0.173887699842453,
-0.3060944080352783,
-0.3346259593963623,
0.08275356143712997,
-1.0253822803497314,
0.5939913988113403,
0.23275797069072723,
-0.14932481944561005,
0.3352828919887543,
0.03205143287777901,
0.2001296728849411,
-0.8222118020057678,
0.44280606508255005,
0.35065266489982605,
0.28965041041374207,
0.5383223295211792,
-0.8643200397491455,
0.21598196029663086,
-0.5429778099060059,
0.16520580649375916,
0.7018440365791321,
0.4914356470108032,
-1.1964174509048462,
-0.24813953042030334,
-0.3618389070034027,
-0.012640339322388172,
0.4886845350265503,
1.2016488313674927,
0.6332943439483643,
-0.33411145210266113,
-0.4545258581638336,
-0.430034875869751,
1.218366026878357,
-0.2955038845539093,
-0.31867942214012146,
0.3702828884124756,
0.07370039820671082,
-0.2835870385169983,
0.6211203932762146,
-0.2955271899700165,
-0.9218344688415527,
-0.2841852903366089,
-1.0342700481414795,
0.43149930238723755,
-0.20033419132232666,
-0.44431236386299133,
-0.1876857578754425,
-0.1266574114561081,
-0.13006511330604553,
0.23662947118282318,
0.3617759644985199,
-0.33428263664245605,
-0.5348361730575562,
0.3043656051158905,
-0.17500929534435272,
-0.30577409267425537,
-0.12034424394369125,
0.4944697618484497,
1.1409772634506226,
1.028835654258728,
0.5503128170967102,
0.1311539113521576,
0.22557395696640015,
0.029596885666251183,
-0.345657616853714,
0.35720565915107727,
-0.00497578177601099,
-0.5498274564743042,
-0.7112058401107788,
0.07187649607658386,
-0.4967465400695801,
-0.3147806227207184,
-0.18984737992286682,
-0.02682930789887905,
0.7492626905441284,
0.49303317070007324,
-0.4490417540073395,
-0.8759053945541382,
-0.17244690656661987,
-0.9333155751228333,
0.8573270440101624,
-0.1268419772386551,
-0.3857400417327881,
0.8513122797012329,
-0.35255318880081177,
0.23114439845085144,
-0.40205714106559753,
-0.2632051110267639,
-0.09385044872760773,
0.19446931779384613,
0.5430363416671753,
0.8046537041664124,
0.38883230090141296,
-0.11517829447984695,
1.0614606142044067,
-0.6133634448051453,
0.20475614070892334,
-0.6263124346733093,
-0.13065625727176666,
-0.42542338371276855,
-0.07190071046352386,
0.34260523319244385,
-0.16121870279312134,
-0.13191282749176025,
-0.3169570565223694,
-0.2674114406108856,
0.13570016622543335,
-0.10780195891857147,
-0.636397659778595,
-0.01130562461912632,
0.19813847541809082,
0.24333325028419495,
-0.5465620756149292,
-0.2706684172153473,
0.32051271200180054,
0.2644367218017578,
-0.3018244206905365,
-0.10880260914564133,
-0.10001379996538162,
0.07539109885692596,
-0.49225810170173645,
0.1720888614654541,
-0.6754028797149658,
-0.009899787604808807,
0.04834944009780884,
-0.23855870962142944,
0.40624484419822693,
-0.0227079838514328,
-0.060659781098365784,
-0.07420371472835541,
-0.5984588861465454,
-0.50127774477005,
0.11824487149715424,
-0.742817223072052,
-0.5910488367080688,
-0.4574844241142273,
-0.10224409401416779,
-0.05212485417723656,
0.5361120700836182,
-0.2827771306037903,
0.4315926432609558,
0.1243356317281723,
-0.3014719784259796,
0.06997185945510864,
0.2826196849346161,
0.5930474996566772,
-0.11205144226551056,
0.13776041567325592,
0.46325433254241943,
-0.2017190158367157,
0.63015216588974,
-0.6572371125221252,
0.8949248194694519,
-0.44453001022338867,
1.0586044788360596,
-0.6021184921264648,
0.20097747445106506,
-0.4038465619087219,
0.1808631867170334,
0.7242411971092224,
-0.7618910670280457,
0.5272976756095886,
0.8809173703193665,
-0.40068209171295166,
0.09994825720787048,
0.5636460781097412,
-0.7513835430145264,
0.09458353370428085,
-0.05895564332604408,
-0.5738705992698669,
0.6977619528770447,
-0.05733415484428406,
0.36562874913215637,
-0.8628759980201721,
-1.0279955863952637,
-0.023644069209694862,
-0.03783656284213066,
-0.14380593597888947,
0.24656477570533752,
0.39679187536239624,
0.2770904302597046,
-0.12465792149305344,
0.16138401627540588,
-0.008841577917337418,
-0.143215611577034,
-0.8922244310379028,
-0.4071216881275177,
-0.004287568852305412,
0.16992762684822083,
-0.32732975482940674,
-1.1461143493652344,
-0.1299128383398056,
0.6076831221580505,
-0.22552873194217682,
-0.15956008434295654,
0.8119840025901794,
-0.5296433568000793,
-0.5981823801994324,
-0.5627748966217041,
0.305825412273407,
0.49709340929985046,
0.2290666699409485,
0.8277747631072998,
-0.07248841226100922,
-0.03716815635561943,
0.6235535740852356,
-0.11287421733140945,
-0.019038720056414604,
-0.4750278890132904,
0.7538543939590454,
-0.465425580739975,
-0.38994792103767395,
0.8289567232131958,
0.07902801036834717,
-0.7125893831253052,
-0.2960282862186432,
-0.9282435178756714,
0.09339200705289841,
-0.5313860774040222,
0.5423884391784668,
-0.17602378129959106,
-0.2660478949546814,
0.06908481568098068,
0.2566803991794586,
1.1076719760894775,
0.21124911308288574,
0.07545962184667587,
0.16073521971702576,
-0.19487841427326202,
-1.0168452262878418,
0.0869060680270195,
0.7576701641082764,
0.16729475557804108,
-0.9750385284423828,
0.6678726077079773,
0.6281480193138123,
-0.5178222060203552,
-0.1294691562652588,
0.620364248752594,
-1.280565619468689,
-0.04962608963251114,
-0.18655015528202057,
-0.6050606966018677,
0.5668538212776184,
0.009153438732028008,
0.13371436297893524,
0.13810575008392334,
-0.2090347856283188,
-0.6928821206092834,
-0.09950485080480576,
-0.30596914887428284,
0.4608202278614044,
0.5492541193962097,
0.5305566787719727,
0.3237179219722748,
-0.15435421466827393,
-0.18344496190547943,
0.10392692685127258,
-0.6108155250549316,
-0.012740271165966988,
-0.6684662103652954,
-0.16861023008823395,
-0.002975990530103445,
-0.3017963469028473,
0.6480069160461426,
0.7331032156944275,
-0.09595463424921036,
-0.19513382017612457,
-0.6103741526603699,
0.0026280772872269154,
0.3260166347026825,
0.3157408535480499,
0.07106737792491913,
-1.0940186977386475,
0.2275586575269699,
-0.041391950100660324,
-0.2468513548374176,
-0.7913026809692383,
0.008873479440808296,
0.32756316661834717,
0.00540511030703783,
0.39988118410110474,
0.04503157362341881,
0.5988855957984924,
-1.0577515363693237,
-0.7301492691040039,
0.18586231768131256,
0.23142269253730774,
-0.373853862285614,
0.7698753476142883,
0.16810771822929382,
0.9776904582977295,
0.5336410999298096,
-0.4282049536705017,
-0.16465631127357483,
-0.06398604810237885,
-0.4921049177646637,
-0.24629274010658264,
0.2570764422416687,
0.023364925757050514,
-0.006850758101791143,
-0.7647168040275574,
-0.47233104705810547,
0.03601185604929924,
-1.364569902420044,
-0.17337310314178467,
-0.12120123207569122,
0.10742160677909851,
-0.4946315288543701,
0.775504469871521,
0.47874900698661804,
-0.06510508805513382,
0.5097348093986511,
1.2759886980056763,
-0.43323197960853577,
0.032845016568899155,
0.7946632504463196,
0.5093693137168884,
-0.3053360879421234,
0.5240896940231323,
0.5906133651733398,
-0.36346787214279175,
-0.18555785715579987,
0.7296124696731567,
-0.11374060809612274,
-0.07337681204080582,
0.017237206920981407,
-0.3020917475223541,
-0.24689380824565887,
-0.31865885853767395,
-0.3147992789745331,
0.6260243058204651,
0.7324708700180054,
-0.7434250712394714,
-0.12556956708431244,
-0.23316237330436707,
-0.8622376918792725,
0.09157638996839523,
-0.6145560145378113,
-0.3800972104072571,
0.29619166254997253,
-0.6240594983100891,
0.1356295943260193,
0.4571067988872528,
0.07849980890750885,
0.5477566719055176,
0.2885812222957611,
0.3584471642971039,
0.5736098885536194,
0.053187835961580276,
-0.3225311040878296,
0.17715737223625183,
-0.8134179711341858,
-0.5415880084037781,
-0.24685801565647125,
0.8787634968757629,
-0.9231067299842834,
-1.385279893875122,
-0.8068520426750183,
0.5902038216590881,
-0.3220299482345581,
0.1455971747636795,
-0.3656994700431824,
-0.156401127576828,
0.055861696600914,
-0.08191566169261932,
-1.120344877243042,
-0.17263951897621155,
-0.7293963432312012,
0.9297781586647034,
-0.22147861123085022,
-0.9194045662879944,
0.07643505185842514,
-0.16709496080875397,
0.8885543346405029,
-0.14791841804981232,
0.30875489115715027,
0.9561886787414551,
0.568485677242279,
-0.2625361979007721,
0.5584872961044312,
0.35389822721481323,
0.6634417176246643,
0.5116475820541382,
-0.3156990110874176,
0.16287685930728912,
0.32950863242149353,
-0.13781620562076569,
0.6162003874778748,
0.5186046361923218,
0.6137827634811401,
0.6622468829154968,
0.24072113633155823,
0.17584821581840515,
0.04320858046412468,
0.2429082691669464,
0.19687803089618683,
0.30263668298721313,
-0.4346614480018616,
-0.3127976357936859,
0.17094628512859344,
0.09444176405668259,
0.054264847189188004,
-0.34239909052848816,
-0.012207778170704842,
-0.04406292736530304,
0.1719335913658142,
0.10528098046779633,
-1.539662480354309,
-0.4654568135738373,
-0.326387494802475,
0.41718897223472595,
-0.09864460676908493,
-0.009715007618069649,
-0.07095251232385635,
0.5465539693832397,
0.278665691614151,
0.34421104192733765,
0.2654014825820923,
1.0378258228302002,
0.09530059248209,
0.6828658580780029,
0.7977422475814819,
-0.09581417590379715,
0.24043495953083038,
-0.2294488549232483,
0.7187159061431885,
-0.49541541934013367,
-0.14864644408226013,
0.37652620673179626,
-0.8263253569602966,
-0.09127993881702423,
-0.18258064985275269,
0.1249547153711319,
-1.0595741271972656,
-0.4374437630176544,
0.15152108669281006,
-0.8992136120796204,
-0.2582119405269623,
0.9610716700553894,
0.20745109021663666,
0.6292677521705627,
0.48971879482269287,
0.12058088928461075,
-0.017861181870102882,
0.2351730614900589,
0.027258675545454025,
-0.4937875270843506,
0.9803652763366699,
1.5120409727096558,
0.22580364346504211,
0.1777334064245224,
0.08075585216283798,
-0.44844475388526917,
0.4309007525444031,
0.6542708277702332,
-0.015573780983686447,
1.0437328815460205,
-0.27697473764419556,
-0.09994947165250778,
0.18996305763721466,
0.02288304828107357,
-0.08777011930942535,
-0.7067634463310242,
0.01745014823973179,
-0.2757234275341034,
-0.03621673956513405,
-0.391364187002182,
1.3100762367248535,
0.36734190583229065,
-0.6055776476860046,
-0.4016655683517456,
0.41398367285728455,
-0.692007303237915,
0.09584897756576538,
-0.8480933308601379,
0.6129871010780334,
-0.4187067747116089,
-0.4404415488243103,
0.01439406257122755,
-0.42033275961875916,
-0.24343810975551605,
-0.5835530757904053,
0.3510431945323944,
-0.35626664757728577,
0.5127200484275818,
0.5378140807151794,
0.09301622211933136,
0.3362811505794525,
-0.31745004653930664,
0.22069577872753143,
0.42063772678375244,
0.7342761158943176,
-0.20123696327209473,
-0.18744875490665436,
0.6342675089836121,
0.4895957112312317,
-0.59160977602005,
0.6007694005966187,
0.24890929460525513,
-0.11659684777259827,
0.23391760885715485,
-0.928402304649353,
0.7307837009429932,
0.32881346344947815,
-0.3846810758113861,
0.145903080701828,
-0.231961190700531,
0.11484137177467346,
-0.27790161967277527,
-0.10607855021953583,
-0.030886534601449966,
-0.8977047801017761,
0.30158767104148865,
-0.4677431881427765,
0.2889591157436371,
-0.19662949442863464,
0.5699572563171387,
0.07934299111366272,
-1.00119149684906,
4.333227157592773,
0.9309471249580383,
0.31471142172813416,
0.35679692029953003,
0.7199026942253113,
1.0239782333374023,
-0.47679874300956726,
-0.44755882024765015,
-0.01700178161263466,
-0.14743296802043915,
-0.8143712282180786,
0.10333473235368729,
0.13703343272209167,
-0.04337334632873535,
-0.14817306399345398,
0.6148097515106201,
-0.2048107087612152,
0.1258852332830429,
-0.0690067857503891,
-0.8337959051132202,
-0.5494614839553833,
0.16636857390403748,
0.11397215723991394,
0.20496149361133575,
-0.07830732315778732,
0.524639368057251,
0.11943911015987396,
-0.07945072650909424,
-0.31220942735671997,
-0.9067175388336182,
-0.5308243036270142,
-0.8496252298355103,
0.7421464323997498,
0.15971961617469788,
-1.1074872016906738,
0.025454288348555565,
0.10487329959869385,
-0.5163624882698059,
0.30818673968315125,
0.03550645709037781,
-0.23131445050239563,
-0.3804949223995209,
0.10910018533468246,
-0.7144745588302612,
-0.12415063381195068,
0.31589117646217346,
-0.21956728398799896,
0.3657299876213074,
0.10998973250389099,
-0.8904523849487305,
0.619800329208374,
0.2500690817832947,
0.12059630453586578,
-1.053869366645813,
-0.8249500393867493,
0.12216673791408539,
-0.8280649185180664,
-0.2608698904514313,
0.2004867047071457,
-0.09036233276128769,
-0.3637799024581909,
-0.21905793249607086,
-0.5530290007591248,
0.5233704447746277,
-0.26035937666893005,
0.5848934650421143,
-0.36734187602996826,
-0.3068602979183197,
-0.7996123433113098,
0.048952557146549225,
0.15706931054592133,
-0.08182895183563232,
-0.23879365622997284,
0.01610032096505165,
0.7577860355377197,
0.253923624753952,
-0.39890530705451965,
0.3522573709487915,
-0.7219633460044861,
0.0008978054393082857,
0.03237534686923027,
-0.33731943368911743,
0.22677448391914368,
0.2104327529668808,
-0.0011840049410238862,
0.5046630501747131,
-0.7424143552780151,
0.6910346746444702,
-0.3187078535556793,
0.6924678683280945,
0.5114086866378784,
1.085354208946228,
0.21110382676124573,
0.5795710682868958,
-1.3500912189483643
] |
A better large $N$ expansion for chiral Yukawa models
|
We consider the most general renormalizable chiral Yukawa model with $SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w )$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c \rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio $\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$ only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. The large $N=\sqrt{N_{c} N_{w}}$ expansion is expected to be no worse quantitatively in this model that in the purely scalar case and the $N=\infty$ limit is soluble even when the model is regularized non--perturbatively. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to $m_t \le 1~TeV$.
|
George Bathas and Herbert Neuberger
|
hep-lat hep-ph hep-th
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210035
|
hep-lat/9210036
|
[
0.40951916575431824,
-0.5126247406005859,
-0.5942455530166626,
-0.10219186544418335,
0.1796359270811081,
-0.3668355941772461,
-0.569631814956665,
-0.2554696500301361,
-0.8228226900100708,
1.5932615995407104,
0.00981934741139412,
0.08789301663637161,
0.4995647370815277,
-0.8352126479148865,
0.10928785055875778,
0.35716384649276733,
-0.5724795460700989,
-0.2083541452884674,
-1.7564815282821655,
0.5092024803161621,
0.054673612117767334,
-0.17114166915416718,
-1.4186753034591675,
-0.23852097988128662,
-0.16056190431118011,
0.8414542078971863,
-0.1040382981300354,
0.16670414805412292,
0.46502766013145447,
0.10503961890935898,
0.1372928023338318,
-0.9240884780883789,
0.22465036809444427,
-0.5260206460952759,
-0.0020468896254897118,
-0.3820432424545288,
0.16569970548152924,
-0.1356576681137085,
0.699455201625824,
-0.35672473907470703,
0.8233399391174316,
-0.42868679761886597,
-0.44260334968566895,
-0.3384537696838379,
-0.5150542259216309,
-0.7154272198677063,
-0.6613336801528931,
-0.5602452158927917,
-0.2629019320011139,
-0.541593074798584,
0.7164502143859863,
0.12454422563314438,
0.03187059238553047,
-0.5088813900947571,
-0.3830200433731079,
-0.26078641414642334,
0.021284235641360283,
-0.27747443318367004,
-0.530737042427063,
-0.2380150854587555,
0.3768458962440491,
-0.6495879292488098,
0.10871315002441406,
-0.6944695115089417,
-0.1724773496389389,
0.9647287130355835,
-0.10607083886861801,
1.1953952312469482,
0.07857272773981094,
-0.6273224949836731,
-0.14408951997756958,
-0.6338205337524414,
-0.4472576081752777,
0.3254586458206177,
-0.3983224332332611,
0.10507999360561371,
0.3428160548210144,
-0.9686528444290161,
-0.9004477858543396,
-0.40069109201431274,
-0.21864630281925201,
-0.5579595565795898,
-0.4745280146598816,
0.4140009582042694,
-0.2691324055194855,
-0.1909845769405365,
-0.2365744411945343,
-0.17319439351558685,
0.5079333186149597,
0.46203818917274475,
0.3922826051712036,
0.8708322048187256,
-0.1763913482427597,
0.03562029451131821,
0.4074665307998657,
0.532116174697876,
0.21583321690559387,
-0.23769250512123108,
0.8954175114631653,
0.00760361785069108,
-0.6484807729721069,
0.5377978086471558,
-0.7184563279151917,
0.7148284912109375,
-0.38245871663093567,
0.38476064801216125,
0.2513534128665924,
-0.18711625039577484,
0.3216240406036377,
-1.0380845069885254,
0.21345369517803192,
-0.5328190326690674,
0.24774646759033203,
1.3286720514297485,
0.4000440239906311,
0.5272839069366455,
-0.1491333246231079,
0.13399970531463623,
-0.023154165595769882,
0.10282951593399048,
0.38241562247276306,
-0.2993510663509369,
0.7378787398338318,
0.8197916150093079,
0.7169426679611206,
-0.3729590177536011,
-0.04948975518345833,
0.3782937824726105,
-0.7271886467933655,
0.7649189829826355,
0.07921724021434784,
-0.4905017912387848,
-0.07771186530590057,
0.5226951241493225,
-0.8513150215148926,
0.3971678614616394,
0.10251868516206741,
0.14269934594631195,
-0.11774329841136932,
-0.6316941976547241,
0.1976165920495987,
-0.7226229906082153,
0.4251078963279724,
1.1451104879379272,
-0.49539801478385925,
0.13681350648403168,
0.14187319576740265,
1.4648572206497192,
-0.10734709352254868,
0.3636030852794647,
-0.8570241928100586,
-0.17737844586372375,
-0.392040491104126,
0.5230662226676941,
0.36151614785194397,
0.28257492184638977,
0.15677304565906525,
0.2158673256635666,
-0.7259286642074585,
-0.890383780002594,
0.2956106662750244,
-0.009386826306581497,
0.12148649990558624,
0.17531301081180573,
0.03384573012590408,
-0.1324363648891449,
-0.5762630105018616,
-1.2766023874282837,
-0.047268178313970566,
-0.25301671028137207,
0.07743135839700699,
0.2024955153465271,
-0.18360567092895508,
0.9706008434295654,
-0.1415693461894989,
0.34825271368026733,
0.9698532819747925,
0.022970564663410187,
-0.2298978716135025,
-0.10152801871299744,
-0.28162112832069397,
-0.6949830055236816,
0.4925665259361267,
-0.07349582016468048,
0.8529670834541321,
-0.4197778105735779,
-0.2532999515533447,
-0.3171437978744507,
-0.4237021505832672,
0.6890503764152527,
0.09133584052324295,
0.4687335789203644,
-0.4497240483760834,
0.705909788608551,
-0.35689395666122437,
0.25685641169548035,
-0.6853696703910828,
-0.39263126254081726,
-0.7647762298583984,
-0.4073638916015625,
0.21666784584522247,
-0.003322433913126588,
-0.8508902192115784,
0.20405064523220062,
-1.0447202920913696,
-0.10425560176372528,
1.0491212606430054,
-0.23612074553966522,
-0.8129234910011292,
-0.4355260133743286,
-0.17262817919254303,
-0.08247344195842743,
-0.10269846022129059,
-0.57582026720047,
0.2359740138053894,
0.5094487071037292,
-0.03737005963921547,
0.9590746164321899,
0.6072986721992493,
0.7893368601799011,
0.06537235528230667,
0.6310880780220032,
0.1413741409778595,
0.6321184635162354,
-1.0132938623428345,
-0.5024070739746094,
0.06058801710605621,
0.5793753862380981,
0.873093843460083,
0.25330787897109985,
0.09426818788051605,
0.37792128324508667,
-0.49705520272254944,
0.5325124263763428,
0.5240087509155273,
0.011248414404690266,
0.3267810642719269,
0.7114238739013672,
0.5033114552497864,
0.16844874620437622,
-0.028258075937628746,
-0.5810661911964417,
0.6774851083755493,
0.23028920590877533,
0.11647146195173264,
-0.0024929551873356104,
0.05649843439459801,
0.26405107975006104,
-0.7191808819770813,
0.9852054715156555,
-0.9144191741943359,
0.6997814774513245,
0.45655882358551025,
0.7180438041687012,
-0.7764932513237,
-0.14592202007770538,
0.4216010272502899,
0.7640840411186218,
-0.13415378332138062,
-0.39813798666000366,
0.3647855818271637,
-0.0004403489292599261,
-0.708549439907074,
-0.6146556735038757,
0.5760369300842285,
0.977774441242218,
0.10930248349905014,
-0.09547131508588791,
0.6973675489425659,
-0.5348532199859619,
-1.3157228231430054,
-0.013929866254329681,
-0.9496762752532959,
0.1104956865310669,
-0.6006711721420288,
-0.7074467539787292,
0.4862882196903229,
-0.8738440275192261,
0.8039320707321167,
0.20100043714046478,
-0.10032627731561661,
-0.47165727615356445,
-0.7911500930786133,
0.31378111243247986,
0.168146014213562,
-0.6029085516929626,
-0.16452853381633759,
0.5452351570129395,
-0.4270211160182953,
0.47622379660606384,
-0.09167822450399399,
0.6637061834335327,
1.0077173709869385,
-1.0601134300231934,
0.5164167881011963,
-0.6682729125022888,
-0.394237220287323,
0.49177008867263794,
0.09916993230581284,
0.12629598379135132,
-0.06508584320545197,
0.9211925268173218,
-0.1676015555858612,
-0.36963826417922974,
-0.8407995104789734,
0.4511594772338867,
0.3315829336643219,
-0.39430227875709534,
0.4734632968902588,
0.36594051122665405,
-0.4247908592224121,
0.15130256116390228,
-0.20651692152023315,
0.10871195048093796,
-0.16076935827732086,
1.393848180770874,
0.8367992043495178,
0.18183761835098267,
0.44952329993247986,
-0.48532816767692566,
-0.48122233152389526,
0.16907145082950592,
0.28421416878700256,
-0.14969977736473083,
-0.09823786467313766,
0.7094503045082092,
0.23448538780212402,
-0.5129495859146118,
0.2690413296222687,
-0.6889594793319702,
-0.6716492772102356,
0.3192233741283417,
-0.06635308265686035,
0.5853447914123535,
-0.18996882438659668,
-0.2189624309539795,
-1.0865496397018433,
0.031594518572092056,
1.2710477113723755,
0.5872003436088562,
0.5202092528343201,
-0.7523167729377747,
0.5027614235877991,
0.17743918299674988,
0.3222084045410156,
0.40040943026542664,
0.032653868198394775,
-0.29785510897636414,
-0.49735909700393677,
0.5539480447769165,
-0.9822128415107727,
-0.21051351726055145,
-0.25934457778930664,
0.05109110102057457,
0.4357560873031616,
0.3863431513309479,
-0.5011544227600098,
-0.7137994766235352,
-0.8719660043716431,
-0.13889387249946594,
0.580945611000061,
0.4601881802082062,
-0.4178113043308258,
0.15891651809215546,
-0.09328088909387589,
-0.4479734003543854,
0.6033414006233215,
0.0838107168674469,
0.4749467372894287,
-0.46784284710884094,
0.29072296619415283,
-0.18820059299468994,
0.25206688046455383,
-0.3602326512336731,
-0.7546429634094238,
0.36358943581581116,
0.16069123148918152,
0.6054798364639282,
1.1600615978240967,
-0.6292158961296082,
-0.4515848755836487,
-0.16650082170963287,
0.5542207360267639,
0.8809443116188049,
0.23278146982192993,
0.39681485295295715,
-0.10654903948307037,
0.3780952990055084,
-0.19704276323318481,
-0.9911417365074158,
-0.26031479239463806,
0.07840457558631897,
-0.1712953895330429,
-0.13780973851680756,
0.29211318492889404,
-0.06472620368003845,
0.33297431468963623,
-0.589941680431366,
0.6716185808181763,
0.16495627164840698,
0.43706002831459045,
0.31538429856300354,
0.6501266956329346,
0.5057726502418518,
0.07628677785396576,
-0.08205421268939972,
-1.0917295217514038,
-0.04644649848341942,
0.2784729301929474,
0.15195125341415405,
-0.1904771625995636,
0.045644573867321014,
-0.22091282904148102,
-0.7434331774711609,
0.45867422223091125,
0.08986422419548035,
-0.716251015663147,
0.048814911395311356,
-0.044288285076618195,
0.8296889066696167,
0.10138969868421555,
0.44529134035110474,
0.6943157315254211,
0.4100858271121979,
0.3843567371368408,
-1.168566346168518,
0.5715157985687256,
-0.8993298411369324,
0.5894737243652344,
0.584547221660614,
-1.5900717973709106,
-0.6225426197052002,
-1.0611960887908936,
-0.2988694906234741,
-0.2167423516511917,
0.22704845666885376,
1.0681707859039307,
0.16036640107631683,
0.28021734952926636,
-0.7222338914871216,
-0.7701150178909302,
0.1695847511291504,
0.1999206691980362,
-0.43495747447013855,
0.07272511720657349,
0.07982809841632843,
0.014369103126227856,
0.38947978615760803,
-0.09697199612855911,
-0.7065231204032898,
0.2511828541755676,
-0.7953004837036133,
0.2530432939529419,
-0.872948944568634,
-0.49241548776626587,
-0.396880179643631,
-0.3318183720111847,
-0.6959381699562073,
1.0292803049087524,
0.017266109585762024,
0.4329243004322052,
-0.18944530189037323,
0.03792600706219673,
-0.35620447993278503,
-0.029908619821071625,
0.30085328221321106,
-0.5100577473640442,
1.1411094665527344,
0.7123613953590393,
0.061313822865486145,
0.12827616930007935,
0.9462671279907227,
-0.215251624584198,
0.5889630913734436,
0.3647581934928894,
-0.15065494179725647,
-0.3266192674636841,
-0.3950381875038147,
-0.07091107219457626,
-0.6138873100280762,
-0.823492705821991,
-0.3399520814418793,
-0.9221557378768921,
-0.2858375608921051,
0.060903649777173996,
-0.40225088596343994,
-0.12722140550613403,
-0.7782866954803467,
-0.6704437136650085,
-0.13062845170497894,
0.17669595777988434,
-0.029237832874059677,
0.752080500125885,
0.05083690211176872,
-0.21129508316516876,
0.06145220249891281,
-0.4346931278705597,
-0.4682544767856598,
0.5115063190460205,
0.3792797923088074,
-0.4828164875507355,
0.41062164306640625,
-0.7110891938209534,
0.4387906789779663,
-0.09234969317913055,
0.36383479833602905,
-0.6750588417053223,
-0.6473761796951294,
-0.12316472083330154,
-0.3003866672515869,
-0.20458613336086273,
-0.03499552980065346,
-0.024464629590511322,
0.2789981961250305,
0.45579084753990173,
0.04684668406844139,
0.009087304584681988,
-0.5889894962310791,
-0.5265157222747803,
0.8844667077064514,
0.2580181658267975,
0.07829660922288895,
0.29602670669555664,
0.43743982911109924,
-0.29985538125038147,
0.7733193635940552,
0.6051270365715027,
-0.9363439679145813,
0.39041951298713684,
0.04605376720428467,
1.0732697248458862,
-0.9182534217834473,
-0.21881401538848877,
-0.5630984306335449,
-0.6345319151878357,
0.09342395514249802,
0.6695931553840637,
0.8552410006523132,
-0.41603347659111023,
-0.4172365963459015,
-0.5878980159759521,
0.6503130197525024,
0.21608833968639374,
-0.3368038833141327,
-0.7889288663864136,
-0.5113953948020935,
-0.2892850935459137,
0.25803035497665405,
0.18467101454734802,
-0.1434324085712433,
0.3042012155056,
-0.3788875639438629,
0.4348274767398834,
0.4960140287876129,
0.4115670919418335,
-0.636478841304779,
0.4173029661178589,
0.42408064007759094,
0.008681082166731358,
0.28013715147972107,
-0.4936051368713379,
0.31116241216659546,
-1.035475730895996,
1.104856014251709,
-0.1319810450077057,
-0.6921647787094116,
-0.15845414996147156,
0.23877663910388947,
-0.03793111816048622,
-0.776491105556488,
0.28173038363456726,
0.37719711661338806,
-0.014201062731444836,
0.539893627166748,
0.8715192079544067,
-0.721615195274353,
-0.6857190132141113,
-1.0928844213485718,
-0.7200847864151001,
0.5353512167930603,
-0.18266724050045013,
-0.06889407336711884,
-0.8121922016143799,
0.255704402923584,
0.1611916869878769,
-0.17229892313480377,
1.2165000438690186,
0.263584166765213,
-0.3249380886554718,
0.18406955897808075,
-0.282108336687088,
-0.46643367409706116,
-0.6624597907066345,
0.8408381342887878,
0.36396992206573486,
0.10095175355672836,
0.0112773347645998,
-0.08278415352106094,
-0.7802492380142212,
-1.066792607307434,
0.045805007219314575,
0.41603484749794006,
0.06181958690285683,
0.30840206146240234,
0.9093868732452393,
0.13435393571853638,
0.028133423998951912,
-0.2498151808977127,
-0.006977603305131197,
0.05037136375904083,
0.20967663824558258,
0.5957083106040955,
0.15931567549705505,
0.6639620065689087,
-0.5438410043716431,
0.734492301940918,
-0.24325965344905853,
-0.07858160138130188,
0.5127882957458496,
-0.5182063579559326,
-0.18042977154254913,
0.04822496697306633,
0.21077655255794525,
-1.3270411491394043,
-0.2178623527288437,
-1.0435923337936401,
0.22196537256240845,
-0.4929125905036926,
-0.24127206206321716,
-0.21386700868606567,
-0.25890952348709106,
-0.2236485779285431,
0.7947747111320496,
0.5354125499725342,
0.12082801014184952,
-0.22700048983097076,
-0.1963057965040207,
-0.9452450275421143,
-0.7020151615142822,
-0.02875697612762451,
1.4450843334197998,
0.06678005307912827,
-0.5487098693847656,
-0.17728674411773682,
-0.14717207849025726,
-0.9203640222549438,
0.1664620339870453,
0.6042618751525879,
-0.30895766615867615,
0.6268956661224365,
0.5088362097740173,
0.38344165682792664,
0.6650677919387817,
1.0042479038238525,
-0.07423563301563263,
0.10769527405500412,
0.5214250683784485,
-1.004567265510559,
-0.5557372570037842,
0.45255598425865173,
0.4655380845069885,
0.40793511271476746,
-0.2986327111721039,
0.009993023239076138,
-0.08894848823547363,
-0.6353121995925903,
0.1915014535188675,
-1.109161376953125,
-0.15179534256458282,
-1.1402122974395752,
-0.24141553044319153,
-0.675885021686554,
0.12469715625047684,
0.05308620259165764,
0.6777634024620056,
-0.23407697677612305,
-0.29642775654792786,
-0.8188717365264893,
-0.23781338334083557,
0.30226606130599976,
0.6060926914215088,
-0.39976608753204346,
-0.7507110834121704,
-0.37442198395729065,
-0.31976884603500366,
0.4870746433734894,
-0.05171408876776695,
-0.515394389629364,
0.24991239607334137,
0.4053614139556885,
0.4385526180267334,
-0.515365481376648,
0.4983696937561035,
-0.6236444711685181,
-0.8555150032043457,
0.31385260820388794,
-0.041219767183065414,
-0.98799729347229,
0.39854058623313904,
0.6002556681632996,
0.7791909575462341,
-0.0872495248913765,
-0.012402853928506374,
-0.24736636877059937,
-0.09990077465772629,
-0.522175133228302,
-0.4400056302547455,
-0.18225742876529694,
1.017817497253418,
-0.1795879751443863,
-1.0323413610458374,
0.3690433204174042,
0.4014838635921478,
-1.0824840068817139,
0.7529863119125366,
-0.07300620526075363,
0.17576657235622406,
-0.10717203468084335,
0.05938074737787247,
-0.048150040209293365,
0.5914070010185242,
0.74233078956604,
1.5327200889587402,
-0.12151257693767548,
-0.5326526761054993,
-0.10488901287317276,
0.2890297472476959,
-0.7119273543357849,
0.48975762724876404,
0.15561524033546448,
-0.2293158620595932,
0.20723703503608704,
0.6522020101547241,
-0.4445857107639313,
0.3044677674770355,
-0.3630310893058777,
-0.6004661321640015,
-0.381644070148468,
0.03834110125899315,
-0.7060472965240479,
0.6918686032295227,
0.4756629467010498,
-0.7894247770309448,
-0.2611623704433441,
-0.30496102571487427,
-0.7243777513504028,
1.0085625648498535,
-0.8093461394309998,
-0.5262528657913208,
0.030500132590532303,
-0.5844520330429077,
0.6340903639793396,
0.14036305248737335,
-0.3109418451786041,
-0.4421612620353699,
-0.021512720733880997,
0.6209746599197388,
-0.2710737884044647,
-0.1119588315486908,
-0.5440418720245361,
0.5535562038421631,
-0.24088893830776215,
0.22597171366214752,
-0.9411409497261047,
0.391824334859848,
-1.284316897392273,
-0.6559233069419861,
-0.297163724899292,
0.7488628029823303,
-0.4386003613471985,
-0.0468037985265255,
-0.2786462604999542,
0.1559382528066635,
-0.5772138237953186,
-0.12090512365102768,
-0.6026235222816467,
-0.4731161594390869,
-0.229836568236351,
-0.16823413968086243,
-0.3711944818496704,
-0.05967414006590843,
0.1494847685098648,
0.25447770953178406,
0.0414736308157444,
0.20457769930362701,
0.15428568422794342,
0.7842632532119751,
-0.12924891710281372,
-0.708770751953125,
0.6241082549095154,
0.07282233983278275,
0.4436655044555664,
0.4934214949607849,
-1.2096315622329712,
0.580537736415863,
0.4023977518081665,
0.708407998085022,
1.0407418012619019,
0.4142448306083679,
0.03609654679894447,
0.22549189627170563,
0.7713647484779358,
0.25500211119651794,
0.5132663249969482,
0.5931934118270874,
0.3325479328632355,
0.32477042078971863,
-0.3165629506111145,
-0.04721285402774811,
-0.051572103053331375,
0.34519606828689575,
0.1275038868188858,
-0.1668306142091751,
-0.32392048835754395,
-0.2803190350532532,
-0.31792452931404114,
0.4508054852485657,
-0.10364218056201935,
-0.5498064160346985,
-0.5811964869499207,
-0.25219008326530457,
0.48651233315467834,
0.4127820134162903,
0.17995421588420868,
0.6189067959785461,
0.7604458928108215,
-0.1758836954832077,
-0.7717978954315186,
0.5791083574295044,
0.012892727740108967,
0.804234504699707,
0.0813441351056099,
1.1966955661773682,
0.05138226971030235,
0.30007657408714294,
-0.21260730922222137,
-0.6610719561576843,
0.6815614700317383,
-0.11123599857091904,
-1.4569592475891113,
0.06180466711521149,
-0.8923028111457825,
-0.5371559262275696,
0.10149512439966202,
-0.43576642870903015,
0.6428682208061218,
-0.5883409380912781,
0.0822545662522316,
0.49317115545272827,
-0.8938959836959839,
-0.05492369458079338,
0.1674472838640213,
0.006020642817020416,
0.40322184562683105,
0.8707787394523621,
-0.15354880690574646,
-0.4618735909461975,
1.177927851676941,
0.9926716089248657,
0.004345693625509739,
0.028829211369156837,
0.2443855255842209,
0.10159711539745331,
0.17773734033107758,
0.15468762814998627,
-0.7805284857749939,
0.6224896311759949,
-0.797828197479248,
-0.8210743069648743,
-0.3622317612171173,
0.12818482518196106,
-0.436871737241745,
-0.5236217379570007,
0.060962215065956116,
0.19501683115959167,
-0.4786084294319153,
0.2144078016281128,
1.1113932132720947,
0.8410228490829468,
-0.5917342901229858,
-0.6748574376106262,
-0.44085487723350525,
-0.18686847388744354,
-0.7547711730003357,
-0.5272419452667236,
0.7851667404174805,
-0.21190790832042694,
-0.0007340045413002372,
-0.2754923105239868,
-0.18474146723747253,
-0.6448348760604858,
-0.5379860997200012,
0.061569638550281525,
-0.538282036781311,
0.4871143698692322,
0.30389511585235596,
0.5335432887077332,
-0.1686066836118698,
-0.4908437430858612,
0.24697798490524292,
-0.3520371615886688,
0.9113886952400208,
-0.07886139303445816,
0.2150503545999527,
1.0252984762191772,
0.3037651479244232,
-0.8186371922492981,
0.5808188915252686,
1.3027549982070923,
-1.1004843711853027,
1.010002851486206,
0.20232686400413513,
0.2336719036102295,
0.3108454644680023,
0.4199291169643402,
0.08098544925451279,
0.04146077111363411,
0.21181635558605194,
0.6470557451248169,
-0.0917070135474205,
-0.44264453649520874,
-0.29036810994148254,
0.09722628444433212,
-0.4466007649898529,
0.5986595153808594,
-0.014204627834260464,
0.15784281492233276,
0.38584253191947937,
-0.2670920789241791,
3.9493408203125,
0.07155817747116089,
0.5504364967346191,
0.2637313902378082,
0.06016889959573746,
0.7711448073387146,
-0.1651953160762787,
-0.6236681938171387,
-0.21977560222148895,
-0.8078270554542542,
0.10684888809919357,
-0.059521857649087906,
-0.03955836594104767,
-0.5406447649002075,
-0.8085746169090271,
0.9675473570823669,
-0.25832682847976685,
-0.16036725044250488,
0.15173393487930298,
-1.6872458457946777,
-0.1162637397646904,
0.3893132507801056,
0.1414078027009964,
-0.6065267324447632,
0.2797102630138397,
-0.19538407027721405,
0.9661371111869812,
-0.8445590734481812,
-0.3654962182044983,
0.11687443405389786,
-1.0800034999847412,
-0.6590943932533264,
0.491585910320282,
-0.6987683773040771,
-0.9085496664047241,
0.34603554010391235,
-0.3553125262260437,
-0.33051133155822754,
0.2064753919839859,
0.5023537874221802,
-0.21136948466300964,
0.16616737842559814,
0.2743026316165924,
-0.18299894034862518,
-0.5929542183876038,
0.9162067174911499,
-0.8913447260856628,
1.2290006875991821,
0.6238120198249817,
-1.1415127515792847,
0.713724672794342,
-0.1188453808426857,
0.7836446762084961,
-0.27023714780807495,
-0.8396072387695312,
0.447889506816864,
-0.049889203161001205,
0.31637901067733765,
0.5431209206581116,
0.31638652086257935,
0.5957838296890259,
0.05678337439894676,
0.011039561592042446,
-0.2697496712207794,
0.11946927756071091,
1.0584018230438232,
0.537861168384552,
0.15123648941516876,
-0.42220279574394226,
0.3411751091480255,
-0.29628175497055054,
-0.258224219083786,
-0.5971028208732605,
0.6924306750297546,
0.02267969772219658,
-0.07448214292526245,
-0.2584826350212097,
0.41210269927978516,
0.2397582232952118,
-0.14379630982875824,
0.2768207788467407,
-0.1933852732181549,
-0.5954970717430115,
0.11093077063560486,
-0.09547848254442215,
1.0422143936157227,
-0.15949007868766785,
0.40964633226394653,
0.0042367433197796345,
0.5749344825744629,
-0.02243509702384472,
1.3597452640533447,
0.6266730427742004,
0.008001587353646755,
-0.5722087025642395
] |
Meson-Meson Scattering in Lattice QED_2+1
|
Scattering phase shifts of a meson-meson system in staggered 3-dimensional lattice QED are computed. The main task of the simulation is to obtain a discrete set of two-body energy levels. These are extracted from a 4-point time correlation matrix and then used to obtain scattering phase shifts. The results for the l=0 and l=2 partial waves are consistent with short- range repulsion and intermediate-range attraction of the residual meson- meson interaction.
|
H. R. Fiebig (Physics Department FIU University Park Miami, Florida 33199, USA) and R. M. Woloshyn (TRIUMF, 4004 Wesbrook ...
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210036
|
hep-lat/9210037
|
[
0.1398504227399826,
-0.03969355672597885,
1.4272947311401367,
0.5337302684783936,
0.2008076012134552,
0.3333175778388977,
-0.032271258533000946,
-0.055645231157541275,
-0.2955859899520874,
1.214173436164856,
0.29728588461875916,
-0.29219818115234375,
0.4394568204879761,
-0.5371094942092896,
-0.2804141342639923,
0.8823237419128418,
0.3843059241771698,
-0.6118901968002319,
-0.807557225227356,
-0.14942550659179688,
-0.4924660325050354,
-0.7465876340866089,
-0.5994035601615906,
-0.1821279674768448,
-0.4666506350040436,
0.5073968172073364,
0.23071302473545074,
0.5466997027397156,
1.5152274370193481,
0.5803766250610352,
0.32804155349731445,
-0.3063543140888214,
0.1583075225353241,
-0.9536566734313965,
-0.08653748780488968,
-0.5060268044471741,
0.6873278617858887,
-0.0545184500515461,
0.47973906993865967,
-0.3748895525932312,
1.7824288606643677,
-0.012534466572105885,
0.9496833086013794,
0.03746912628412247,
-0.3779710531234741,
-0.2583087980747223,
0.04687243327498436,
0.41923028230667114,
-0.6052277088165283,
-0.7089536786079407,
0.30638158321380615,
0.3636930286884308,
0.34039103984832764,
-0.3233907222747803,
-0.3778461813926697,
-0.37736472487449646,
-0.040269918739795685,
0.04148714616894722,
-0.18538960814476013,
0.36404260993003845,
-0.3313210606575012,
0.5509227514266968,
0.42752158641815186,
-0.4882071912288666,
0.022509586066007614,
1.0176329612731934,
-0.7618677616119385,
0.3735728859901428,
0.44062697887420654,
-0.7479611039161682,
-0.2518438696861267,
-0.18687941133975983,
0.09680633991956711,
-0.3089087903499603,
-0.928515613079071,
0.11975365877151489,
-0.16040697693824768,
-0.19649048149585724,
0.07344602793455124,
0.029958277940750122,
-0.47978517413139343,
0.04658836871385574,
-0.05906841531395912,
0.7168078422546387,
-0.2742004692554474,
-0.30016249418258667,
-0.5215176939964294,
0.39206433296203613,
0.5124531984329224,
0.7759049534797668,
0.055519454181194305,
0.6457521915435791,
-0.06847435981035233,
-0.45409348607063293,
-0.5204715132713318,
0.2860252261161804,
0.08317452669143677,
0.08100907504558563,
0.23574703931808472,
0.31162822246551514,
0.28209608793258667,
0.16639728844165802,
-0.21168223023414612,
0.3697991967201233,
-0.40910041332244873,
0.8730904459953308,
0.5835340023040771,
0.30805760622024536,
-0.7928359508514404,
-0.5602284073829651,
-0.41935107111930847,
0.22029364109039307,
0.2159559279680252,
-0.09831079095602036,
0.5722226500511169,
0.08423811197280884,
0.40306994318962097,
0.022457795217633247,
-0.8682263493537903,
-0.7019891142845154,
-0.5588613748550415,
0.20994187891483307,
-0.29674920439720154,
0.3446062207221985,
-0.07155027985572815,
-0.11860832571983337,
0.7769126296043396,
0.6764107346534729,
-0.06291249394416809,
0.2144809365272522,
0.08471707254648209,
-0.3682910203933716,
0.09962008148431778,
0.3088293969631195,
0.15112489461898804,
0.3819916844367981,
-0.10182392597198486,
1.1114821434020996,
0.549812376499176,
-0.4135963022708893,
0.16506406664848328,
-0.39870569109916687,
0.01750779338181019,
0.9386067390441895,
-0.33659735321998596,
0.15483538806438446,
0.23704932630062103,
-0.7915343046188354,
-0.3060418665409088,
0.24147644639015198,
-0.07777827978134155,
0.37226468324661255,
-0.13074341416358948,
0.06314736604690552,
0.06706581264734268,
0.952418863773346,
-1.5795313119888306,
0.7877230644226074,
-0.2593112885951996,
-0.16034413874149323,
0.17438849806785583,
-0.7611511945724487,
-0.825645387172699,
0.3280015289783478,
-0.5841353535652161,
0.4469339847564697,
-0.979780375957489,
0.00570716243237257,
-0.2083483636379242,
-0.4172022044658661,
0.2613472044467926,
0.10543296486139297,
-0.14257219433784485,
0.4283740520477295,
0.6331729292869568,
0.016376473009586334,
0.6661072373390198,
-0.047270458191633224,
-0.3093843460083008,
0.3036733865737915,
-0.24151219427585602,
-0.47033607959747314,
0.38029348850250244,
0.6358948945999146,
0.17212586104869843,
0.0034041462931782007,
-0.7502164244651794,
0.5195649266242981,
0.7530624270439148,
-0.6257531642913818,
-0.46778613328933716,
0.9555514454841614,
-1.02244234085083,
-0.1482628881931305,
-1.1887513399124146,
-0.8047192096710205,
-0.7715697884559631,
0.6374134421348572,
-0.6015095710754395,
-0.39243149757385254,
-0.4539625942707062,
0.26244327425956726,
-0.9857449531555176,
-0.052223265171051025,
-1.152765154838562,
0.5562435984611511,
0.6105812788009644,
0.544447124004364,
-0.5356534719467163,
-0.1679135262966156,
0.27654755115509033,
0.1723913997411728,
0.052857328206300735,
0.16594858467578888,
-0.04662918671965599,
-0.5829142332077026,
-0.3303702771663666,
-0.016919340938329697,
0.4449082612991333,
-0.21459349989891052,
0.35450130701065063,
-0.4145989418029785,
0.1300867348909378,
0.6457655429840088,
0.0175579022616148,
0.569329559803009,
0.05015929415822029,
0.2961614429950714,
-0.19690380990505219,
0.11395694315433502,
0.3143300712108612,
1.0109838247299194,
-0.4630037844181061,
0.4351382255554199,
1.0675649642944336,
1.2057465314865112,
0.6046006679534912,
0.3627694547176361,
0.23630478978157043,
-0.0634789764881134,
0.24081161618232727,
1.0029184818267822,
-0.019260719418525696,
0.09697920829057693,
0.24717850983142853,
0.19696713984012604,
-1.0133262872695923,
0.14056961238384247,
-1.2938086986541748,
0.2697550058364868,
-0.7785568237304688,
0.996445894241333,
0.14367033541202545,
0.6022763848304749,
-0.5031532049179077,
-0.1595287322998047,
-0.5229795575141907,
0.039742305874824524,
-0.44800934195518494,
-0.16041266918182373,
-0.28122663497924805,
-0.20803476870059967,
-0.6984771490097046,
0.27908602356910706,
0.24428868293762207,
0.41678586602211,
-0.36251363158226013,
-0.393259733915329,
-0.6553925275802612,
-0.20751634240150452,
-1.1410877704620361,
-0.08534026890993118,
-0.37592625617980957,
0.17349614202976227,
0.5590457320213318,
0.002978818491101265,
0.4386555850505829,
-0.5534458160400391,
1.1248369216918945,
-0.07279914617538452,
-0.21809884905815125,
0.04059699922800064,
-0.2325618714094162,
0.323841392993927,
0.13010621070861816,
-0.5145037770271301,
-1.067010521888733,
0.2730104625225067,
-0.7179274559020996,
0.5943390727043152,
-0.276783287525177,
0.07727229595184326,
-0.2591358423233032,
-0.42909395694732666,
-0.5446315407752991,
0.08306365460157394,
-0.669751763343811,
-0.08243924379348755,
-0.49197715520858765,
-0.3700592815876007,
0.08168423175811768,
-0.21163694560527802,
-0.6435124278068542,
-0.5494686961174011,
-0.3727615177631378,
1.3933202028274536,
0.4069242477416992,
-0.16548919677734375,
0.48418059945106506,
-0.25635460019111633,
-0.48335856199264526,
0.3513040244579315,
-0.08964604884386063,
0.25292861461639404,
-0.6432455778121948,
0.4235968589782715,
0.5600073337554932,
0.4264955222606659,
0.14040842652320862,
-1.261359691619873,
-0.011384374462068081,
0.15489420294761658,
0.6023910045623779,
-0.6670332551002502,
-0.08261362463235855,
0.6906390190124512,
0.523756742477417,
-0.604142963886261,
0.45248550176620483,
-0.48327726125717163,
-0.6114104390144348,
-0.10557590425014496,
-0.5246593356132507,
0.036980386823415756,
-0.04129864647984505,
0.028853625059127808,
-0.244385227560997,
-0.08405603468418121,
-0.37206268310546875,
0.0733465850353241,
-0.1117403581738472,
0.08807738125324249,
-0.004569779150187969,
0.35168665647506714,
-0.772605836391449,
0.33608293533325195,
0.49330437183380127,
-0.654409646987915,
0.1380092352628708,
0.030790388584136963,
-0.8943382501602173,
0.06289032101631165,
0.9685121178627014,
0.006505533121526241,
-0.18784520030021667,
0.2783665955066681,
-0.43541857600212097,
-0.5135000944137573,
-0.2634330093860626,
-0.4493560791015625,
-0.35841986536979675,
0.25961753726005554,
-0.42061808705329895,
-0.008914399892091751,
-0.13620956242084503,
-0.19837084412574768,
0.8483881950378418,
0.6852784752845764,
0.4833512604236603,
-0.2631518840789795,
0.4751821458339691,
-0.010740434750914574,
-0.43711724877357483,
-0.014056787826120853,
0.23353341221809387,
0.06278097629547119,
0.1342700868844986,
0.46588218212127686,
1.0868932008743286,
-1.2671147584915161,
-0.841826856136322,
-0.28932178020477295,
0.9414627552032471,
0.7864772081375122,
0.5124670267105103,
0.37767693400382996,
-0.6174474954605103,
-0.008626524358987808,
-0.46880343556404114,
-0.2996112108230591,
-0.44803565740585327,
0.27090513706207275,
-0.46121203899383545,
-0.06446181982755661,
-0.07248228043317795,
-0.26336103677749634,
0.35493937134742737,
0.42520710825920105,
0.27953705191612244,
0.306263267993927,
0.10230337083339691,
-0.268183171749115,
0.07492087036371231,
0.4402450621128082,
-0.2645139694213867,
0.0007526489207521081,
-0.07759469002485275,
-0.046398285776376724,
-0.45698750019073486,
-0.3436897099018097,
-0.09332507103681564,
-0.15505467355251312,
-0.047646477818489075,
-0.21416792273521423,
0.2744588255882263,
0.6825923919677734,
-0.4214254319667816,
0.5693699717521667,
-0.15559235215187073,
-0.06688704341650009,
0.055353302508592606,
-0.7459217309951782,
0.18871626257896423,
0.690025269985199,
0.20165111124515533,
-0.5450218915939331,
0.06585431843996048,
-0.5614773631095886,
0.46936336159706116,
0.3714931905269623,
-0.6133440136909485,
-0.5062885880470276,
-0.5289738178253174,
-0.28931471705436707,
-0.412036269903183,
0.21144278347492218,
0.956181526184082,
-0.21448439359664917,
1.2138968706130981,
-0.01670193113386631,
0.12580515444278717,
0.3464711606502533,
-0.6513329744338989,
-0.3405107855796814,
0.7449917197227478,
0.7981337308883667,
0.6155503988265991,
0.7889557480812073,
-0.12156613171100616,
-0.7216207981109619,
-0.010943328030407429,
-0.25908926129341125,
0.21049921214580536,
-0.42034801840782166,
-0.7490221261978149,
0.018202604725956917,
-0.5902105569839478,
-0.6062718629837036,
0.7632101774215698,
0.07131773978471756,
0.08005984872579575,
0.2741074860095978,
-0.2819920480251312,
-0.43434247374534607,
-0.3101811110973358,
0.43338143825531006,
-0.13733278214931488,
0.5329380035400391,
1.4313524961471558,
0.01989714987576008,
0.1743163913488388,
0.034197788685560226,
0.027989400550723076,
-0.6038996577262878,
0.42498841881752014,
-0.5925658941268921,
-0.03590849041938782,
-0.4805549681186676,
-0.36368948221206665,
-0.105975441634655,
0.04276162385940552,
0.24619241058826447,
-0.46976780891418457,
0.3890381455421448,
0.7088331580162048,
-0.07453248649835587,
-0.00555900763720274,
0.0929141566157341,
-0.3789200186729431,
0.17012962698936462,
-0.11738856881856918,
-0.4114534854888916,
0.6029861569404602,
-1.2983919382095337,
0.06092602759599686,
-0.022277742624282837,
0.5526626706123352,
-0.19082581996917725,
-0.17931108176708221,
-0.03144523501396179,
-0.08352287113666534,
0.5082384347915649,
-1.0333921909332275,
0.9059444069862366,
0.21798358857631683,
-0.2733277678489685,
-0.23665347695350647,
-0.4704694151878357,
-0.5873025059700012,
0.27722543478012085,
-0.06862028688192368,
0.33021602034568787,
-0.2818440794944763,
-0.22335729002952576,
-0.03581331670284271,
0.46660739183425903,
0.6460959911346436,
-0.3062390685081482,
-0.14833562076091766,
0.5523690581321716,
0.09937053918838501,
-0.7661253809928894,
-0.23600861430168152,
1.314635992050171,
-0.6012040972709656,
-0.6951808333396912,
-0.17622347176074982,
-0.224843829870224,
0.3184627890586853,
-0.25756850838661194,
-0.11418921500444412,
-0.8477404713630676,
-0.8134697079658508,
-0.23121653497219086,
-0.29752081632614136,
-0.17154110968112946,
0.1656390279531479,
0.37629953026771545,
-0.2616938650608063,
-0.409629225730896,
-1.1374047994613647,
-0.48753851652145386,
-0.08617838472127914,
-0.4093257486820221,
-0.014921383000910282,
0.17645955085754395,
-1.7645139694213867,
0.7263410687446594,
-0.8268797993659973,
-0.5566429495811462,
0.444683313369751,
0.5743419528007507,
0.20294871926307678,
1.034214735031128,
-0.3291112780570984,
-0.10316387563943863,
-0.35563501715660095,
0.2225896120071411,
-0.5536705255508423,
0.6229871511459351,
-0.3745691776275635,
0.5261313915252686,
-1.514704704284668,
-0.05653081461787224,
-0.17680156230926514,
0.5910754203796387,
0.1654626876115799,
-0.9872108101844788,
1.0158085823059082,
-0.6345620155334473,
0.4159066081047058,
0.9615639448165894,
0.19265785813331604,
0.8644406795501709,
-0.020995143800973892,
-1.1020476818084717,
-0.028952738270163536,
-0.9928997755050659,
-1.2875877618789673,
0.8475510478019714,
0.46523404121398926,
-0.12798911333084106,
-0.39412403106689453,
-0.4031563997268677,
0.0504692867398262,
-0.4911525249481201,
-0.4195782244205475,
1.0623201131820679,
-0.7730752229690552,
-0.2708173394203186,
0.5450810790061951,
-0.2111307680606842,
0.3280503749847412,
-0.4631918668746948,
0.8326892852783203,
-0.4566863775253296,
-0.1384912133216858,
-0.5112440586090088,
-0.7421918511390686,
-0.7206839919090271,
-0.7852485179901123,
0.7254880666732788,
0.22264936566352844,
-0.07719466090202332,
0.782197117805481,
-0.08975433558225632,
-0.5801803469657898,
-0.07226314395666122,
0.1574498414993286,
-0.1452776938676834,
0.13282030820846558,
0.4191129803657532,
-0.2610968053340912,
-0.11746018379926682,
0.4272240996360779,
-0.2545054852962494,
-0.5788354277610779,
-0.28596362471580505,
1.3488409519195557,
-0.03578200936317444,
-0.6304183006286621,
-0.08480288833379745,
0.16344909369945526,
-0.2852824926376343,
-0.304690420627594,
-0.6775118112564087,
-0.03253999352455139,
-0.1332317292690277,
-0.41347888112068176,
0.00893442053347826,
0.33876240253448486,
-0.8602355718612671,
0.32845404744148254,
0.8373107314109802,
-0.045197419822216034,
0.25457918643951416,
-0.22056899964809418,
-0.2074684053659439,
-0.5504317879676819,
0.1914825588464737,
1.3401683568954468,
-0.18832650780677795,
-0.17209933698177338,
-0.3401947319507599,
-0.812410295009613,
-0.28073927760124207,
-0.00900211650878191,
0.11488044261932373,
0.2675214111804962,
-0.16040079295635223,
0.1456156075000763,
0.23459693789482117,
0.12410277873277664,
0.9139454364776611,
0.7647643685340881,
-0.6162078976631165,
-0.2844805121421814,
-0.9733392000198364,
-0.16458377242088318,
1.0784393548965454,
-0.09779822826385498,
0.07137253135442734,
-0.5108356475830078,
-0.10554879158735275,
-0.4458469748497009,
0.11757596582174301,
-0.4662509858608246,
-1.211793065071106,
-0.3412366211414337,
-0.9723426699638367,
-0.5359916090965271,
-1.6717724800109863,
-1.026280403137207,
0.06742358952760696,
0.4678385555744171,
-0.46385520696640015,
0.6190803050994873,
-0.3544866740703583,
0.5262328386306763,
-0.013369305059313774,
0.3826344311237335,
0.022532261908054352,
-0.8727047443389893,
-0.5512182712554932,
-0.3772972524166107,
-0.21113435924053192,
-0.34887978434562683,
0.029723890125751495,
0.6623743176460266,
-0.04931589215993881,
0.17315857112407684,
-0.5080269575119019,
0.7203428745269775,
-0.7755016088485718,
-0.0043797274120152,
0.10047770291566849,
-0.49334412813186646,
-0.08109535276889801,
-0.03330715000629425,
0.047350890934467316,
-0.22917042672634125,
0.19292913377285004,
-0.9272757768630981,
-0.4044041335582733,
0.4336123764514923,
-0.6547762751579285,
-0.127274751663208,
0.006994930095970631,
-0.08619529753923416,
-0.07040131092071533,
-0.38005146384239197,
0.3325002193450928,
0.766623318195343,
-0.966820240020752,
0.10459046065807343,
-0.7718158960342407,
0.6095765829086304,
0.2553863227367401,
-0.5811951160430908,
0.06884640455245972,
0.9235626459121704,
-0.2926845848560333,
0.352300763130188,
0.13527433574199677,
0.08277161419391632,
0.5148177146911621,
0.8619628548622131,
-0.09876380115747452,
-0.7187977433204651,
0.6096242070198059,
-1.6487853527069092,
0.295867383480072,
0.4754001796245575,
-0.5617434978485107,
0.42067545652389526,
0.33312395215034485,
-0.3885195553302765,
-0.2154008001089096,
-0.5209425091743469,
-0.6276984214782715,
0.7954345345497131,
-0.6388664841651917,
-0.3918307423591614,
-0.4582558274269104,
-0.3037606179714203,
-0.46518030762672424,
-0.3010160028934479,
0.07448700070381165,
-0.025157254189252853,
-0.06596492975950241,
-0.10113152116537094,
-0.39818090200424194,
-0.3921831548213959,
-0.5912437438964844,
-0.12905758619308472,
0.4429471790790558,
0.05820516496896744,
-0.07588960230350494,
0.526247501373291,
0.5217157602310181,
0.17830726504325867,
-0.7381764054298401,
0.6143612861633301,
0.15865495800971985,
0.018440837040543556,
-0.310051828622818,
-0.2000167816877365,
0.34920141100883484,
-0.3715957701206207,
-0.06001953035593033,
-0.23120999336242676,
-0.23904794454574585,
0.3461438715457916,
0.5661425590515137,
0.31484174728393555,
-0.7276144027709961,
0.07262818515300751,
-0.49467170238494873,
0.4454321563243866,
0.7813850045204163,
-0.15017609298229218,
0.8004271984100342,
0.08371811360120773,
0.2398744523525238,
0.05712897703051567,
-0.7460395693778992,
0.33183443546295166,
0.2555585205554962,
-0.2989881634712219,
0.742786705493927,
0.062013741582632065,
0.9885823726654053,
0.02559260092675686,
-0.3660103976726532,
-0.5437347888946533,
1.161741852760315,
0.4884348213672638,
0.3553052842617035,
0.8057786822319031,
0.40322497487068176,
0.30995994806289673,
0.2732514441013336,
0.34773147106170654,
0.04897666722536087,
0.33887067437171936,
-0.8697746992111206,
0.4366563558578491,
-0.42525187134742737,
0.5466254949569702,
-0.02093610167503357,
0.27925652265548706,
-1.437612533569336,
0.5437144637107849,
0.17613160610198975,
0.9092482328414917,
-0.3202681541442871,
0.15619291365146637,
-0.9788632988929749,
-0.6295624375343323,
-0.14500392973423004,
0.8318364024162292,
0.42229849100112915,
-0.06534958630800247,
0.029268208891153336,
-0.0034544975496828556,
0.3743918836116791,
0.417371928691864,
-0.24811778962612152,
0.7762154936790466,
-0.09594859182834625,
-0.3790143132209778,
0.28660330176353455,
0.628989040851593,
0.18407784402370453,
-0.36625608801841736,
0.4330751895904541,
-0.5783734917640686,
-0.35789167881011963,
0.8620083928108215,
-0.9311119318008423,
0.21530015766620636,
0.2547827363014221,
-0.24774381518363953,
0.053108036518096924,
-0.6034450531005859,
-0.008716490119695663,
-0.4716911315917969,
0.5233414769172668,
0.5109969973564148,
-0.12241775542497635,
0.49087342619895935,
0.2968151569366455,
0.22179371118545532,
0.34000739455223083,
0.35839778184890747,
0.23959344625473022,
-0.36430981755256653,
0.7435387969017029,
0.7307693958282471,
0.3073063790798187,
-0.17046299576759338,
0.18649475276470184,
-0.6710312366485596,
0.13307757675647736,
-0.11578071862459183,
-0.3906998336315155,
1.4502009153366089,
-0.8101473450660706,
-0.08345459401607513,
0.6105619072914124,
0.23823338747024536,
-0.11314218491315842,
-0.4245357811450958,
-0.04016328603029251,
0.7845849394798279,
-0.40031155943870544,
-0.2494686096906662,
0.7854668498039246,
0.7664993405342102,
0.44008153676986694,
0.05183633416891098,
0.5400819778442383,
0.037882525473833084,
-0.3001672625541687,
-0.21339552104473114,
0.05916781350970268,
0.30233585834503174,
0.12948617339134216,
0.10797511786222458,
-0.12850186228752136,
-0.1231137290596962,
-0.7389557361602783,
-0.12215264141559601,
-0.4926249086856842,
0.9909242987632751,
-0.04897157847881317,
0.8192578554153442,
0.006657860241830349,
-0.7437558770179749,
-0.1773136407136917,
0.3983609080314636,
0.8924950957298279,
0.4794257879257202,
0.417852520942688,
0.6451830863952637,
0.14336957037448883,
-0.449363112449646,
0.5168655514717102,
0.5800769329071045,
-0.25632914900779724,
0.6570418477058411,
-0.1008215919137001,
0.31116828322410583,
-0.05221905559301376,
-0.46491050720214844,
0.1520862877368927,
0.761791467666626,
0.3058663308620453,
-0.5152052044868469,
-0.30401861667633057,
-0.03810526430606842,
-1.360557198524475,
0.7344555854797363,
-0.8502373695373535,
0.2634674310684204,
0.8128575682640076,
0.2251589596271515,
0.37989282608032227,
-1.081864833831787,
4.074194431304932,
1.2973411083221436,
0.023944299668073654,
0.06531766057014465,
0.8724461197853088,
0.10453091561794281,
1.105281949043274,
-0.8241395950317383,
-0.004440913908183575,
-0.05582267791032791,
0.03931253403425217,
-0.005264918319880962,
0.9967201352119446,
-0.21970981359481812,
0.2941318452358246,
0.28128165006637573,
-0.977851390838623,
0.3109724223613739,
0.25186672806739807,
-0.7560944557189941,
-1.1322823762893677,
0.6177974343299866,
0.04156990349292755,
0.13204839825630188,
0.2039882391691208,
0.03690832480788231,
-0.28836414217948914,
-0.09435109794139862,
-0.5675551891326904,
-0.4260593056678772,
-0.5907216668128967,
-0.8474670648574829,
0.35919302701950073,
-0.10927800089120865,
-0.6996069550514221,
0.4778047204017639,
0.724632203578949,
-0.056883715093135834,
-0.037685368210077286,
0.5304675698280334,
0.10876693576574326,
0.16302616894245148,
-0.18316863477230072,
-0.3026847243309021,
-0.7712358832359314,
0.6604766845703125,
0.12210533767938614,
0.3766613006591797,
-0.5048685073852539,
-0.721481442451477,
0.49690303206443787,
-0.7702986598014832,
-0.010388883762061596,
-0.37266844511032104,
-1.6735169887542725,
-0.3096739649772644,
-0.10405145585536957,
-0.6713470220565796,
0.5295218825340271,
0.3667835295200348,
0.7447544932365417,
-0.23957236111164093,
-0.3490770757198334,
-0.11348636448383331,
-0.1342722475528717,
0.17082026600837708,
0.3012777864933014,
0.5056474804878235,
0.19059675931930542,
-0.43269723653793335,
-0.2405569851398468,
-0.8487706780433655,
-0.76430344581604,
-0.05447326600551605,
0.6987615823745728,
-0.39950838685035706,
0.008225558325648308,
0.7186937928199768,
0.2918117344379425,
0.914457380771637,
0.42020687460899353,
0.4455530047416687,
0.020072927698493004,
0.41762375831604004,
0.13372746109962463,
0.6253865361213684,
-0.5033631920814514,
0.0003812244103755802,
-0.0009982275078073144,
0.47429612278938293,
0.5565007328987122,
0.7371091246604919,
-0.11855685710906982,
0.13824757933616638,
-0.6864750385284424
] |
The Shape of Inflated Vesicles
|
The conformation and scaling properties of self-avoiding fluid vesicles with zero extrinsic bending rigidity subject to an internal pressure increment $\Delta p>0$ are studied using Monte Carlo methods and scaling arguments. With increasing pressure, there is a first-order transition from a collapsed branched polymer phase to an extended inflated phase. The scaling behavior of the radius of gyration, the asphericities, and several other quantities characterizing the average shape of a vesicle are studied in detail. In the inflated phase, continuously variable fractal shapes are found to be controlled by the scaling variable $x=\Delta p N^{3\nu/2}$ (or equivalently, $y = {<V>}/ N^{3\nu/2}$), where $N$ is the number of monomers in the vesicle and $V$ the enclosed volume. The scaling behavior in the inflated phase is described by a new exponent $\nu=0.787\pm 0.02$.
|
G. Gompper and D.M. Kroll
|
hep-lat cond-mat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210037
|
hep-lat/9210038
|
[
-0.2380973845720291,
0.15831661224365234,
-0.12643995881080627,
0.12561945617198944,
0.11937976628541946,
-0.9385389685630798,
-0.5986691117286682,
-0.45514658093452454,
-0.9729026556015015,
1.1690771579742432,
0.4782107472419739,
0.31379300355911255,
0.40198615193367004,
-0.5221600532531738,
0.6687979102134705,
0.8308467268943787,
-0.24627511203289032,
-1.009249210357666,
-1.858484148979187,
1.0133426189422607,
0.4433228075504303,
-0.3059472143650055,
-0.9570958018302917,
-1.0448552370071411,
0.302644819021225,
0.9770343899726868,
0.09749150276184082,
-0.19919076561927795,
1.2970564365386963,
0.8392713665962219,
0.4202272891998291,
-0.5163642764091492,
-0.7832514643669128,
0.06733324378728867,
-0.36484381556510925,
-0.3340524435043335,
-0.6394158005714417,
0.0404680110514164,
0.8150789141654968,
-0.3372555673122406,
0.5464234352111816,
-0.46740472316741943,
-0.13914170861244202,
-0.0014613039093092084,
-0.850420355796814,
0.3251248002052307,
0.19431829452514648,
0.30734291672706604,
0.5010789036750793,
-1.580219030380249,
0.23604315519332886,
0.1727214902639389,
0.5685920715332031,
-0.3767296075820923,
-0.49012690782546997,
0.24085824191570282,
0.48715469241142273,
-0.32693561911582947,
-0.6800978183746338,
-0.3518960177898407,
0.6639957427978516,
0.04212675243616104,
0.3631627559661865,
-0.6074874997138977,
0.2921592593193054,
0.7816820740699768,
-0.6826305985450745,
0.34617742896080017,
-0.2022867053747177,
-0.3981090784072876,
-0.06045034900307655,
-0.6543409824371338,
-0.45265838503837585,
0.12028837949037552,
-0.5355834364891052,
0.1472548246383667,
-0.2558707892894745,
-0.5428802967071533,
-0.5367993116378784,
-0.5392170548439026,
-0.41518980264663696,
0.10705547034740448,
-0.6741653084754944,
0.005509235430508852,
-0.4730697572231293,
-0.5187886953353882,
-0.02779393084347248,
-0.4801224172115326,
0.035618241876363754,
0.08772388100624084,
0.11510971188545227,
0.5877322554588318,
-0.1380760371685028,
-0.27676472067832947,
0.1510440856218338,
1.1499769687652588,
-0.1338794082403183,
0.8633114695549011,
0.4386853575706482,
-0.009651399217545986,
0.2463369518518448,
0.6093125343322754,
-1.2328647375106812,
0.3517319858074188,
-0.7665601968765259,
0.2887651324272156,
-0.4004520773887634,
-0.5541733503341675,
-0.7010884284973145,
-0.4047417640686035,
-0.02811160497367382,
0.09550701826810837,
0.7638433575630188,
0.6423144340515137,
0.12403888255357742,
0.46543818712234497,
-0.5186207294464111,
-0.24115058779716492,
-0.7356041073799133,
-0.36566635966300964,
0.789153516292572,
0.11078914254903793,
0.28611648082733154,
0.4586765766143799,
-0.09472742676734924,
-0.7147893905639648,
0.8058773279190063,
0.849443256855011,
-0.8527663946151733,
0.6951074600219727,
-0.24228313565254211,
-0.20841993391513824,
-0.5300653576850891,
0.4832085072994232,
-0.4875467121601105,
0.4624885320663452,
-0.7963793873786926,
-0.020350312814116478,
0.1520635187625885,
-0.6868855953216553,
0.7943968772888184,
-0.6286405920982361,
0.14532896876335144,
0.6756410002708435,
0.8284582495689392,
0.21541893482208252,
0.31048446893692017,
0.2657546103000641,
-0.27737241983413696,
0.2820737063884735,
-0.596616804599762,
-0.0104576600715518,
-0.15125435590744019,
0.43834972381591797,
0.48494893312454224,
0.2934395372867584,
-0.9171048402786255,
-0.04324035346508026,
-0.6602171659469604,
-0.3746154010295868,
0.13606968522071838,
-0.2739429771900177,
-0.6388615369796753,
0.6480045318603516,
-0.6101391315460205,
0.04807206988334656,
-0.48054972290992737,
-0.664401113986969,
0.6681559681892395,
-0.3927009403705597,
-0.25731900334358215,
0.20432323217391968,
-0.1461905539035797,
0.9866436719894409,
0.47073936462402344,
0.24582459032535553,
0.2255927473306656,
-0.7822055220603943,
0.6839191317558289,
0.02066933549940586,
-0.21132634580135345,
-0.4027886688709259,
0.42434999346733093,
0.07231403142213821,
-0.4074259400367737,
-0.12732312083244324,
-0.05160500481724739,
-0.38768061995506287,
0.05554458498954773,
0.5906906723976135,
-0.16182316839694977,
0.010399973019957542,
-0.19391964375972748,
0.6185750365257263,
-0.38450777530670166,
-0.18826629221439362,
-0.955474853515625,
-0.11601657420396805,
-0.8011097311973572,
-0.5478875637054443,
-0.03299230337142944,
0.30740970373153687,
-0.8729161620140076,
0.36393722891807556,
-1.6111080646514893,
-0.01589655503630638,
0.35019123554229736,
0.03790159896016121,
-0.05284701660275459,
-0.18972203135490417,
0.2637699246406555,
-0.057209163904190063,
0.3498918116092682,
-0.3698095977306366,
0.3518819212913513,
0.7717353701591492,
0.20118677616119385,
0.20966912806034088,
0.19095394015312195,
-0.01428478118032217,
0.6932650804519653,
0.3882545232772827,
0.03118630312383175,
0.34429022669792175,
-0.5888003706932068,
-1.093369960784912,
0.12573707103729248,
0.7586114406585693,
0.0462213009595871,
0.050278738141059875,
0.3684970438480377,
0.3588144779205322,
-0.17050763964653015,
0.7597012519836426,
0.6832971572875977,
0.6209220290184021,
0.4418278932571411,
0.6504495143890381,
0.29857298731803894,
0.5459669232368469,
0.20919224619865417,
0.3047088086605072,
0.5094245672225952,
0.02650243416428566,
-0.34157076478004456,
0.3487343490123749,
-0.620281994342804,
0.2828949987888336,
-0.9654263854026794,
0.29893559217453003,
-0.5326701402664185,
0.5135548710823059,
-0.5197528004646301,
0.44907402992248535,
-0.563300609588623,
0.34807950258255005,
0.32663536071777344,
-0.00025092068244703114,
-0.13647854328155518,
0.04643088951706886,
-0.05588291585445404,
0.037084951996803284,
-0.11118405312299728,
-1.0060462951660156,
-0.3073677122592926,
1.0571259260177612,
-0.11163610965013504,
-0.04092223942279816,
0.37346354126930237,
-0.22958146035671234,
-1.067859411239624,
0.0033976284321397543,
-0.6044630408287048,
0.3505615293979645,
-0.8066906929016113,
-0.4363204538822174,
0.5283136963844299,
-1.0162245035171509,
0.673876166343689,
0.30064356327056885,
-0.13988585770130157,
0.6844247579574585,
-0.5451977252960205,
0.233665332198143,
0.7523028254508972,
0.2750486731529236,
-1.2562836408615112,
-0.23913031816482544,
-0.7513990998268127,
-0.20156796276569366,
-0.18360260128974915,
-0.44784560799598694,
1.1180270910263062,
-0.09980287402868271,
1.0141037702560425,
0.08658695220947266,
-0.34870123863220215,
-0.5756679177284241,
-0.44448310136795044,
-0.7218782305717468,
0.3483181595802307,
0.4767296612262726,
0.061221733689308167,
-0.027559859678149223,
-0.8718771934509277,
0.9705137014389038,
0.15281371772289276,
-0.347322940826416,
0.7708486914634705,
0.029950184747576714,
-0.4857213497161865,
0.6344284415245056,
0.006386512890458107,
-0.16071371734142303,
0.023020051419734955,
1.1378735303878784,
0.7073098421096802,
0.39115017652511597,
-0.3910090923309326,
-0.42611369490623474,
-0.45031309127807617,
0.7976667881011963,
-0.015829062089323997,
-0.6895303726196289,
0.21026785671710968,
0.7122004628181458,
0.12439002096652985,
-0.5538026690483093,
0.4382624626159668,
-0.7477038502693176,
-0.2819291949272156,
-0.24697862565517426,
-0.7003829479217529,
0.2908779978752136,
0.21225278079509735,
0.5283806920051575,
-0.8510950803756714,
-0.017858082428574562,
0.07924793660640717,
-0.08828019350767136,
-0.005181357730180025,
-0.17216281592845917,
0.6831695437431335,
0.31491968035697937,
0.473871111869812,
-0.02353615313768387,
-0.27148059010505676,
-0.4940321147441864,
-0.23289942741394043,
0.08689039945602417,
-0.8246598839759827,
0.5571619868278503,
0.07993180304765701,
0.4052527844905853,
0.2723503112792969,
0.32852622866630554,
-0.44357526302337646,
-0.7865442037582397,
-0.3784407079219818,
0.005842346698045731,
0.46339333057403564,
0.548124372959137,
-0.15582455694675446,
-0.5806883573532104,
-0.8431858420372009,
0.0345696285367012,
0.30023637413978577,
0.17163391411304474,
1.0860605239868164,
-1.1191375255584717,
0.6930704712867737,
0.5646799802780151,
-0.19090743362903595,
0.07935026288032532,
0.06090102344751358,
0.3898792564868927,
0.4274274408817291,
0.24804404377937317,
1.0249049663543701,
-0.29492422938346863,
-1.0410710573196411,
0.10100534558296204,
0.8630192875862122,
0.5006742477416992,
0.644687831401825,
0.03204998001456261,
-0.3376409709453583,
-0.4135282337665558,
-0.7485674023628235,
-0.30101343989372253,
-0.31376904249191284,
-0.23730707168579102,
-0.030555618926882744,
-0.2111571729183197,
0.46417510509490967,
0.010568267665803432,
0.37414130568504333,
0.3461313545703888,
0.9520059823989868,
-0.220331609249115,
0.12475050240755081,
0.3325963020324707,
0.6403335332870483,
0.903490424156189,
-0.25514504313468933,
-0.03353773429989815,
-0.7631204128265381,
0.10250072181224823,
0.40837326645851135,
0.45461124181747437,
0.08530376106500626,
-0.7996578812599182,
0.04080545902252197,
-0.6986988186836243,
0.7388899326324463,
0.05147368460893631,
-0.807922899723053,
0.017491718754172325,
0.13653866946697235,
0.568585991859436,
-0.26340243220329285,
-0.1361178159713745,
1.1336798667907715,
0.48850974440574646,
0.3947235941886902,
-0.775348961353302,
0.4047938585281372,
-0.8250768780708313,
0.0757184848189354,
0.012242050841450691,
-0.5170688033103943,
-0.45417091250419617,
-0.746679961681366,
-0.058888472616672516,
-0.70625901222229,
0.7136145830154419,
1.047747015953064,
0.03750083968043327,
-0.1791141927242279,
-0.7081664800643921,
-0.35258057713508606,
0.7535109519958496,
-0.32864996790885925,
-0.705386221408844,
-0.04484258219599724,
-0.09575069695711136,
0.08068667352199554,
0.6678270101547241,
-0.09284394234418869,
-0.43347927927970886,
-0.20425251126289368,
-0.4485612213611603,
0.11071380227804184,
-0.766112744808197,
-0.5613218545913696,
-0.4805569648742676,
-0.21561363339424133,
-0.10844877362251282,
0.47717687487602234,
0.398747056722641,
-0.10481123626232147,
0.014152183197438717,
0.4987567365169525,
0.11187191307544708,
0.3835698366165161,
0.08419673889875412,
-0.034364424645900726,
0.7177730202674866,
0.8704368472099304,
0.3769151270389557,
-0.025192972272634506,
0.2546793222427368,
0.6149212121963501,
0.24273791909217834,
0.2312067598104477,
0.009090188890695572,
-0.42585936188697815,
-0.41866013407707214,
-0.15005625784397125,
-0.5167030096054077,
-0.7018973231315613,
0.24437570571899414,
-0.4248654246330261,
0.715435802936554,
0.021817393600940704,
-0.6187487840652466,
-0.683888852596283,
-1.036928415298462,
-0.48092222213745117,
0.21652764081954956,
-0.10833678394556046,
-0.20044375956058502,
1.0168129205703735,
-1.0501347780227661,
0.0052825771272182465,
0.040274478495121,
-0.33200252056121826,
-0.1997944861650467,
0.426714152097702,
1.0763095617294312,
-0.004080579150468111,
0.6199252009391785,
-0.7069395780563354,
-0.12120558321475983,
-0.9494968056678772,
0.30103933811187744,
-0.8244463205337524,
-0.7633666396141052,
0.08139020204544067,
-0.37986135482788086,
-0.13643473386764526,
-0.11619008332490921,
-0.1083078533411026,
0.3628382384777069,
0.20018187165260315,
-0.4373566508293152,
-0.019812097772955894,
-0.5159783959388733,
-0.09910356253385544,
0.6029835343360901,
0.037274062633514404,
-0.6619856357574463,
-0.05125775560736656,
0.3334726393222809,
-0.11040298640727997,
-0.06145446002483368,
0.7209998965263367,
-0.24951007962226868,
-0.08656629174947739,
-0.3839375674724579,
0.8144305944442749,
-0.9435490965843201,
-0.6242237687110901,
-0.06376294046640396,
-1.038543701171875,
0.8809352517127991,
0.8619909286499023,
0.2438787817955017,
0.08163347095251083,
-0.27894818782806396,
-0.33656781911849976,
0.021146969869732857,
-0.5491015315055847,
0.17603106796741486,
-0.8732934594154358,
-0.7585719227790833,
0.18648266792297363,
0.4911591112613678,
0.3699418008327484,
0.32576099038124084,
0.5403193831443787,
0.23505215346813202,
0.14525294303894043,
0.4337661862373352,
0.149528369307518,
-0.33058086037635803,
-0.5976758599281311,
-0.043157510459423065,
-0.1053420901298523,
0.35965555906295776,
-0.0758255124092102,
0.5287650227546692,
-1.0352482795715332,
1.0610326528549194,
-0.8789458870887756,
0.28973904252052307,
-0.34494805335998535,
0.03247655928134918,
0.7546690106391907,
-0.9797409176826477,
0.5152068138122559,
0.5040609836578369,
-0.2267557978630066,
-0.20890134572982788,
0.08866860717535019,
-0.1328333169221878,
-0.07978306710720062,
-0.6790807843208313,
-0.9311374425888062,
0.7679210901260376,
0.26702797412872314,
-0.468467116355896,
-0.7527530193328857,
-0.8327834606170654,
0.6054693460464478,
0.014975281432271004,
0.4050680696964264,
0.8393548130989075,
0.044750772416591644,
0.21968743205070496,
0.4981095492839813,
0.18465982377529144,
-0.17942246794700623,
0.35021182894706726,
-0.151153102517128,
-0.12843693792819977,
0.3792113959789276,
-0.022846370935440063,
-0.49906885623931885,
-0.8755618333816528,
0.07566658407449722,
0.4925824999809265,
0.14062318205833435,
-0.5689801573753357,
0.9697500467300415,
-0.5045779347419739,
-1.0703943967819214,
-0.634011447429657,
0.08046553283929825,
-0.22799454629421234,
0.19078980386257172,
0.5491892695426941,
0.06809971481561661,
0.6348364949226379,
-0.6167411804199219,
0.8088985681533813,
-0.7605761885643005,
-0.2829397916793823,
0.5651651620864868,
-0.88307785987854,
-0.7705094814300537,
0.17955629527568817,
0.10056295245885849,
-0.7988057732582092,
-0.32560694217681885,
-0.6803527474403381,
0.47202685475349426,
-0.6975678205490112,
-0.24553845822811127,
-0.0792650356888771,
-0.2163613736629486,
-0.14264710247516632,
0.621536135673523,
0.6541507244110107,
-0.6121795177459717,
0.102815181016922,
0.7509481906890869,
-0.5985718965530396,
0.2289755791425705,
0.22959457337856293,
0.8379960656166077,
0.0394887812435627,
-0.6728429794311523,
0.07506082952022552,
0.07592558115720749,
0.25581011176109314,
-0.19769011437892914,
0.1857701689004898,
0.02229407988488674,
0.5805370211601257,
0.3229452967643738,
0.46056899428367615,
-0.17696797847747803,
-0.1831817924976349,
0.47826582193374634,
-0.5490685701370239,
-0.436983197927475,
-0.2722867429256439,
-0.6573069095611572,
-0.5650238394737244,
0.3672587275505066,
0.8924242258071899,
-0.2555728554725647,
0.25281596183776855,
0.31075334548950195,
-0.6590837836265564,
-0.43386903405189514,
-0.9600145816802979,
-0.21776717901229858,
-1.5083850622177124,
0.5532932877540588,
-0.6606139540672302,
-0.42640140652656555,
-0.04498405382037163,
0.4487296938896179,
-0.08501064777374268,
-0.4710865318775177,
-0.31307414174079895,
-0.44963955879211426,
0.542600154876709,
0.19716492295265198,
-0.48211485147476196,
-0.7266253232955933,
-0.23510049283504486,
-0.4566921293735504,
-0.08572676032781601,
-0.06178297847509384,
0.04306810721755028,
-0.26459696888923645,
0.08160152286291122,
0.848697304725647,
-0.05018974468111992,
0.8677960634231567,
-0.8556717038154602,
-0.8419548869132996,
-0.0219308752566576,
0.293083518743515,
-0.4884483218193054,
0.3097459673881531,
-0.03220570087432861,
1.1949387788772583,
0.19919869303703308,
0.7116849422454834,
-0.6551166772842407,
0.21480929851531982,
-1.7171467542648315,
-0.47778773307800293,
0.29096361994743347,
0.14341150224208832,
-0.2889447808265686,
-0.8019416332244873,
0.2436700463294983,
0.32073453068733215,
-1.038711667060852,
0.39178794622421265,
-0.5880861282348633,
-0.12514203786849976,
-0.9570960998535156,
0.8334982991218567,
0.45910847187042236,
0.30848219990730286,
-0.11098014563322067,
0.6808009743690491,
-0.21445763111114502,
0.023279661312699318,
0.3312927782535553,
0.6286411285400391,
-0.5363835096359253,
-0.038454677909612656,
-0.1790149062871933,
-0.37099871039390564,
-0.14227190613746643,
0.18208254873752594,
-0.24430225789546967,
0.17603324353694916,
0.19957740604877472,
-0.39738067984580994,
-0.2846774756908417,
0.08578012138605118,
-0.18618717789649963,
0.5023125410079956,
0.3270528316497803,
-0.7937760353088379,
-0.15405391156673431,
-0.3887365758419037,
-0.8447741866111755,
-0.3256481885910034,
-0.6122854351997375,
0.25892582535743713,
0.25868868827819824,
-0.18479835987091064,
-0.040609292685985565,
0.3731136620044708,
0.03965389356017113,
0.4887615144252777,
0.0009114717249758542,
0.5241773128509521,
-0.015616785734891891,
-0.0027817520312964916,
-0.787651002407074,
0.3728511333465576,
-0.8335297703742981,
-0.02736305445432663,
-0.18280468881130219,
0.6134722828865051,
-0.8666276931762695,
-0.7437792420387268,
0.10470949858427048,
0.5149534344673157,
-0.18311364948749542,
0.8370440602302551,
-0.10570849478244781,
-0.43597179651260376,
-0.02966691181063652,
0.1727210283279419,
-0.11338961124420166,
0.025304891169071198,
-0.7933937907218933,
0.44432926177978516,
0.31999078392982483,
-0.7466359734535217,
0.2738746404647827,
0.5871334075927734,
0.13840128481388092,
-0.16469067335128784,
-0.004312629345804453,
0.8734667897224426,
-0.027687538415193558,
-0.641394317150116,
0.7249594330787659,
0.2113824188709259,
0.5500801801681519,
-0.2707948684692383,
-0.5135056376457214,
0.35156649351119995,
0.4879533350467682,
-0.013058966025710106,
0.6444078683853149,
0.49269911646842957,
0.40956422686576843,
0.4096844494342804,
0.30928128957748413,
-0.1378430724143982,
0.25484734773635864,
-0.09011087566614151,
0.9156550765037537,
0.6454013586044312,
0.08740170300006866,
-0.4369181990623474,
-0.532829225063324,
-0.1606067419052124,
0.09999126195907593,
-0.051364507526159286,
-0.4801861643791199,
-0.36249709129333496,
0.3836776316165924,
0.09187385439872742,
-0.4793124496936798,
-0.5792678594589233,
-0.20768491923809052,
-0.29522866010665894,
0.88409423828125,
-0.24287666380405426,
-0.055530086159706116,
0.23828226327896118,
0.6296324133872986,
-0.05543896555900574,
-0.018594207242131233,
0.7843841314315796,
0.14959339797496796,
0.9777020812034607,
0.691371738910675,
0.476157009601593,
0.6518495678901672,
0.5832147002220154,
0.3792375922203064,
-1.1522032022476196,
0.1540965884923935,
0.2291625589132309,
-1.221248745918274,
-0.1331888735294342,
-0.73721843957901,
0.21999165415763855,
-0.6314099431037903,
-0.3894137442111969,
1.0341984033584595,
0.3338419497013092,
0.5050290822982788,
0.3726250231266022,
-0.3677044212818146,
0.050384119153022766,
1.0844409465789795,
0.21511214971542358,
0.1616540402173996,
0.5835322141647339,
-0.25909554958343506,
0.29787158966064453,
0.9466993808746338,
1.3603891134262085,
0.22857356071472168,
0.8294426202774048,
0.30271247029304504,
-0.47487562894821167,
0.2909165322780609,
0.6010814309120178,
-0.08445502817630768,
0.24949263036251068,
-0.3281112015247345,
-0.4780275225639343,
0.5692927241325378,
0.19137123227119446,
-0.20428255200386047,
-0.45399242639541626,
0.31998199224472046,
0.3289664685726166,
-0.7052379846572876,
-0.49319207668304443,
1.41940438747406,
0.5239439010620117,
-0.5848507285118103,
-0.05631702020764351,
0.18872413039207458,
-0.4179309904575348,
0.4248652756214142,
-1.2551192045211792,
0.2169627845287323,
-0.4772487282752991,
-0.03936612233519554,
-0.0026590717025101185,
-0.5835127234458923,
-0.3313833773136139,
-1.2553937435150146,
0.3336530327796936,
-0.3150652348995209,
0.5301135778427124,
0.31079772114753723,
-0.2624441087245941,
0.5874137282371521,
-0.4843173921108246,
-0.07611767202615738,
-0.25877854228019714,
0.8469679355621338,
0.3675749599933624,
0.37784624099731445,
0.8377091288566589,
0.48529329895973206,
-0.9683707356452942,
0.004339012783020735,
0.9507771730422974,
-0.8067499399185181,
1.1067724227905273,
-0.4913545250892639,
0.09081550687551498,
0.21032199263572693,
-0.14438341557979584,
-0.11378604918718338,
-0.6313628554344177,
0.5513745546340942,
0.06727685034275055,
0.21609316766262054,
-0.28401997685432434,
-1.0408574342727661,
-0.35935699939727783,
-0.7789589166641235,
-0.17017816007137299,
0.4855819642543793,
0.4187804162502289,
0.031692612916231155,
-0.13552235066890717,
4.090657711029053,
0.5366379618644714,
0.6320738196372986,
0.46650829911231995,
1.1324408054351807,
1.059793472290039,
-0.30167698860168457,
0.18827849626541138,
0.219437375664711,
-0.8229614496231079,
-0.18171939253807068,
0.4606696665287018,
0.7180770039558411,
-0.02215290255844593,
0.14291219413280487,
1.1002117395401,
-0.1268376111984253,
-0.05131262168288231,
-0.22600677609443665,
-1.0575697422027588,
-0.8705447912216187,
0.11913157254457474,
-0.14287865161895752,
0.6162172555923462,
-0.11662518233060837,
0.18174900114536285,
0.10201442986726761,
-0.8054388165473938,
-0.6273331046104431,
-0.4120512306690216,
-0.5605592131614685,
-0.9104394912719727,
0.047074317932128906,
0.027541212737560272,
-0.6463403701782227,
0.4929460883140564,
0.4851640462875366,
-0.07635774463415146,
0.20770978927612305,
-0.08557035028934479,
-0.2964417636394501,
-0.2440764456987381,
0.27476295828819275,
0.010515530593693256,
-0.14940741658210754,
0.7294766306877136,
0.06796303391456604,
0.5414883494377136,
0.18896234035491943,
-0.434234082698822,
0.19688211381435394,
-0.00836979690939188,
1.124234914779663,
-0.5266932249069214,
-0.856020987033844,
-0.533879816532135,
-0.5821438431739807,
0.02946232445538044,
0.36101219058036804,
0.36306557059288025,
0.6492555737495422,
-0.24600768089294434,
0.14912688732147217,
0.1447989046573639,
-0.16777531802654266,
0.7137231826782227,
-0.17643626034259796,
0.030571188777685165,
-0.25018829107284546,
0.20768390595912933,
-0.13276953995227814,
-0.21077027916908264,
-0.2752062976360321,
0.3758912980556488,
0.13832348585128784,
-0.0030482944566756487,
-0.233750119805336,
0.7871618866920471,
0.22248412668704987,
-0.10883699357509613,
-0.08440786600112915,
-0.4117058217525482,
-0.5312150120735168,
0.010255868546664715,
0.19153840839862823,
0.43846699595451355,
-0.6826320290565491,
0.2440972775220871,
-0.37252601981163025,
0.4192452132701874,
0.25647321343421936,
1.3039401769638062,
0.11740413308143616,
-0.0504985973238945,
-0.6549592614173889
] |
Gauge invariant extremization
|
Recently, Duncan and Mawhinney introduced a method to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize $\int(\delta S/\delta A_\mu)^2$ instead of the action $S$ itself as in conventional `cooling'. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we present a gauge invariant formulaton of extremization on the lattice, applicable to any gauge group and any lattice action. The procedure is worked out in detail for U(1) and SU(N) lattice gauge theory with the plaquette action.
|
A.J. van der Sijs
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210038
|
hep-lat/9210039
|
[
0.06356325000524521,
-0.04941215738654137,
0.02362910285592079,
-0.09836285561323166,
0.19791913032531738,
-1.0945136547088623,
0.004494925029575825,
-0.5101572275161743,
-0.8298579454421997,
0.953102171421051,
0.5133672952651978,
-0.049543265253305435,
0.014471525326371193,
-0.7046167850494385,
-0.43501678109169006,
0.005056581925600767,
-0.026198094710707664,
-0.4563581645488739,
-1.0573252439498901,
0.2579801678657532,
1.0972272157669067,
-0.6661364436149597,
-1.0242719650268555,
0.11499889940023422,
-0.2263054996728897,
0.9792004227638245,
0.29482147097587585,
0.15386150777339935,
0.7536701560020447,
0.4055384695529938,
-0.12627331912517548,
-0.5200816988945007,
-0.5262635946273804,
-0.40953248739242554,
0.06342848390340805,
0.04243135079741478,
-0.45133596658706665,
-0.06790141016244888,
1.1149412393569946,
-0.24441313743591309,
0.7399143576622009,
-0.10662439465522766,
0.22549009323120117,
-0.2620563209056854,
-0.873637318611145,
-0.45712709426879883,
-0.27111950516700745,
0.6403235793113708,
0.09003117680549622,
-1.330811619758606,
-0.28265145421028137,
-0.030976204201579094,
0.004447089973837137,
-0.8838741779327393,
-0.719281017780304,
0.06573332101106644,
0.9271348714828491,
-0.053734190762043,
-0.3045699894428253,
-0.6219407916069031,
0.5992441177368164,
-0.04729577898979187,
-0.0570702999830246,
-0.6649866700172424,
0.14637160301208496,
0.3619064688682556,
-0.40834465622901917,
0.7847281098365784,
-0.15117280185222626,
-0.24210187792778015,
-0.4096947908401489,
-0.4136408865451813,
-0.6507521271705627,
0.09486690908670425,
-1.0729784965515137,
-0.06776554137468338,
-0.12668053805828094,
-0.5444039702415466,
-1.145045280456543,
-0.24294909834861755,
-0.17119739949703217,
0.04680104926228523,
-0.5142980217933655,
0.055627625435590744,
-0.220279723405838,
-0.5282372236251831,
0.15431155264377594,
-0.45318832993507385,
0.4042043387889862,
0.18984751403331757,
-0.11518936604261398,
0.7556641697883606,
-0.14229591190814972,
-0.020616546273231506,
0.7197432518005371,
0.9375011324882507,
0.2483556568622589,
0.3827618360519409,
-0.387044757604599,
-0.24342279136180878,
0.03562109172344208,
0.536560595035553,
-0.2658049762248993,
0.6648849248886108,
-0.7418543100357056,
0.8155524134635925,
-0.01584814116358757,
-0.23945225775241852,
0.424939900636673,
-0.36736077070236206,
0.3550175726413727,
-0.19962731003761292,
0.34831562638282776,
1.101298213005066,
-0.05343489348888397,
0.3700038194656372,
0.08386926352977753,
-0.14235366880893707,
-0.4665971100330353,
-0.07904057204723358,
0.7617897391319275,
-0.11559846252202988,
0.815475344657898,
0.641409158706665,
0.09087258577346802,
-0.6926039457321167,
0.2725318372249603,
0.8610637784004211,
-1.0630507469177246,
0.6850550174713135,
0.4158726632595062,
-0.2440393716096878,
-0.30931973457336426,
0.1986771821975708,
-1.0956270694732666,
0.17368192970752716,
-0.44834569096565247,
-0.10545333474874496,
-0.07411892712116241,
-0.004673576448112726,
1.253836750984192,
-1.001869559288025,
0.05631787329912186,
1.0678530931472778,
-0.21338491141796112,
0.16209676861763,
0.7438539862632751,
0.15322555601596832,
0.20586924254894257,
0.6195842027664185,
-0.3060598373413086,
-0.3184727430343628,
-0.16080111265182495,
0.19700686633586884,
-0.2781592607498169,
0.6304471492767334,
-0.4503551125526428,
-0.12354705482721329,
-0.262640118598938,
-0.581307053565979,
0.6704254150390625,
-0.10308371484279633,
-0.29554760456085205,
0.27384069561958313,
-0.6986268758773804,
0.36236369609832764,
-0.7650724649429321,
-0.26348793506622314,
0.7284022569656372,
-0.8911303281784058,
0.09528625756502151,
0.0785578265786171,
0.3299770653247833,
0.6914771199226379,
0.29901301860809326,
0.20792408287525177,
0.3306245505809784,
-0.5550001859664917,
-0.09674014151096344,
-0.1890537440776825,
0.1106811985373497,
-0.5036610960960388,
0.2553008198738098,
-0.09886978566646576,
-0.3719107508659363,
0.022453242912888527,
0.32545000314712524,
-0.02310371771454811,
-0.09389133006334305,
0.35950005054473877,
0.23190513253211975,
0.09011386334896088,
-0.6069663166999817,
0.7643572092056274,
-0.9736943244934082,
-0.13428562879562378,
-0.5762227177619934,
0.5400440692901611,
-0.3201710879802704,
-0.5991653203964233,
-0.47909146547317505,
0.32643139362335205,
-0.7391195297241211,
-0.07239944487810135,
-1.4508193731307983,
0.31643569469451904,
0.7105811238288879,
0.4792773723602295,
-0.47558021545410156,
-0.0834464579820633,
0.5842936038970947,
-0.876124918460846,
0.5727136731147766,
-0.06661691516637802,
0.3488314151763916,
0.6926133036613464,
0.9889898300170898,
0.8770513534545898,
0.7873702645301819,
0.32894712686538696,
0.2273360937833786,
0.08787607401609421,
-0.15876193344593048,
0.5088492631912231,
0.012062599882483482,
-0.6577126979827881,
0.21271830797195435,
0.7303678393363953,
0.5994139313697815,
0.11518529802560806,
-0.03243182227015495,
-0.22869163751602173,
0.09175537526607513,
0.39176177978515625,
0.30619683861732483,
-0.3569833040237427,
0.24653811752796173,
0.34640929102897644,
0.17477431893348694,
0.32333964109420776,
-0.150567889213562,
0.081280417740345,
-0.06332361698150635,
-0.058655861765146255,
-0.035019729286432266,
0.4463326930999756,
-0.533145546913147,
0.5313701629638672,
-0.46717143058776855,
0.721964955329895,
-0.5291469097137451,
0.7289677262306213,
-0.37418004870414734,
0.5236756205558777,
-1.3440418243408203,
-0.6412340998649597,
0.18356217443943024,
0.14101460576057434,
-0.44710099697113037,
0.07368840277194977,
-0.03336836397647858,
0.38014376163482666,
-0.21874353289604187,
-0.9274666905403137,
0.05286784842610359,
1.1556363105773926,
0.2743311822414398,
0.39192909002304077,
0.48915719985961914,
-0.4239373207092285,
-0.9215184450149536,
-0.13587717711925507,
-1.1983771324157715,
-0.10501112788915634,
-0.935512900352478,
-0.26901429891586304,
0.4599498212337494,
-0.8417342901229858,
0.5201085805892944,
-0.4730941355228424,
-0.5686509013175964,
0.15351860225200653,
0.23055270314216614,
0.33240556716918945,
0.5418590903282166,
-0.14801310002803802,
-0.31823137402534485,
0.6615874767303467,
-0.2555502951145172,
0.22141756117343903,
0.3061803877353668,
0.06614900380373001,
0.8614713549613953,
-0.1931745558977127,
0.34863680601119995,
-0.28479015827178955,
-0.3487994074821472,
0.14088596403598785,
-0.2972695827484131,
-0.454027384519577,
-0.2991586923599243,
0.5768530964851379,
-0.19783644378185272,
-0.27083954215049744,
-1.2693133354187012,
0.7070127725601196,
0.12986500561237335,
-0.7089372873306274,
0.31446653604507446,
0.27687451243400574,
-0.8279849886894226,
0.12326747924089432,
-0.36171191930770874,
-0.4127779006958008,
0.06275109201669693,
1.513900876045227,
0.5437409281730652,
-0.410521000623703,
-0.929911732673645,
-0.7225896716117859,
-0.21990324556827545,
0.06210388243198395,
-0.07412243634462357,
-0.18508128821849823,
-0.09974925220012665,
0.7007117867469788,
0.25240397453308105,
-0.3234962522983551,
0.46664783358573914,
-0.9393686652183533,
-0.8957873582839966,
0.17187289893627167,
-0.3780245780944824,
0.5520763993263245,
-0.2954496443271637,
0.8291736245155334,
-0.8775747418403625,
0.017195506021380424,
0.11966260522603989,
0.48175206780433655,
0.7736495137214661,
-0.5992992520332336,
-0.04567316919565201,
0.14932222664356232,
1.0688071250915527,
-0.2057664394378662,
-0.15700533986091614,
-0.09160951524972916,
-0.4399595558643341,
0.4116516411304474,
-0.20072095096111298,
0.5604007840156555,
-0.435150146484375,
0.3062613904476166,
0.5210874676704407,
-0.07895713299512863,
-0.24447427690029144,
-0.5742180943489075,
-0.4074254035949707,
-0.19656768441200256,
0.4115109145641327,
1.004567265510559,
0.291255921125412,
-0.2682487964630127,
-0.9227988123893738,
-0.04350920394062996,
-0.08532098680734634,
-0.013140236958861351,
0.6518465280532837,
0.0017051540780812502,
0.1074470579624176,
-0.20036004483699799,
-0.4443712532520294,
0.2238251119852066,
-0.029895756393671036,
0.4695897102355957,
0.3899013102054596,
0.9489493370056152,
1.1391959190368652,
0.15534713864326477,
-0.7997640371322632,
-0.0911451056599617,
0.7551555037498474,
0.7126998901367188,
0.7415800094604492,
-0.3673679530620575,
-0.255942702293396,
-0.4106897711753845,
-0.5399239659309387,
-0.4472118318080902,
-0.6317964196205139,
0.07713823765516281,
-0.10297734290361404,
-0.2024618238210678,
0.23974953591823578,
-0.26910674571990967,
0.28255438804626465,
0.001355527201667428,
-0.21157732605934143,
0.22907669842243195,
0.28196972608566284,
0.4506852924823761,
0.9885818958282471,
0.8566750884056091,
0.09354889392852783,
-0.3042674660682678,
-0.7155701518058777,
0.3744858503341675,
-0.15860262513160706,
0.22140303254127502,
-0.30938953161239624,
-0.0917731374502182,
0.08363915979862213,
-0.8570893406867981,
0.15530315041542053,
0.03236939013004303,
-0.5303511619567871,
-0.13520821928977966,
0.5335938334465027,
0.8241071105003357,
0.5591438412666321,
0.03148624300956726,
0.6782118082046509,
-0.17027145624160767,
0.6774988174438477,
-1.234875202178955,
0.5389927625656128,
-0.5446785092353821,
0.09448666125535965,
0.569135308265686,
-0.4649181067943573,
-0.9394167065620422,
-0.8325768709182739,
-0.4500373303890228,
-0.12172512710094452,
0.3797757625579834,
0.39821937680244446,
0.8348625898361206,
-0.3902447819709778,
-0.6404018998146057,
-0.12609794735908508,
1.218663215637207,
-0.3546953499317169,
-0.27433833479881287,
0.33609506487846375,
-0.12764166295528412,
-0.21451587975025177,
0.38402101397514343,
-0.13615255057811737,
-0.7221682667732239,
0.5300391912460327,
-0.6932929158210754,
-0.03263789042830467,
-0.5451000332832336,
-0.678954541683197,
-0.5055999159812927,
-0.18019992113113403,
-0.44679585099220276,
0.5658816695213318,
0.4951649308204651,
-0.5662843585014343,
-0.20137760043144226,
-0.23941351473331451,
-0.10621822625398636,
-0.487786203622818,
-0.018961306661367416,
0.642142653465271,
1.0679553747177124,
0.5395059585571289,
0.6004048585891724,
0.219988614320755,
0.3945031762123108,
0.020551778376102448,
-0.07677554339170456,
0.3788841664791107,
-0.03776443749666214,
-0.3568403720855713,
-0.7155908346176147,
-0.02976604364812374,
-0.07474180310964584,
-0.6224355101585388,
-0.6323309540748596,
-0.5367355942726135,
0.31615033745765686,
-0.23932349681854248,
-0.5716807246208191,
-0.9123569130897522,
-0.5217283964157104,
-0.7167732119560242,
0.27482080459594727,
-0.006129353307187557,
0.059565771371126175,
0.7307153940200806,
-0.6920106410980225,
0.0067467824555933475,
-0.24941757321357727,
-0.43950966000556946,
-0.41272884607315063,
0.86928790807724,
0.6441550254821777,
0.34557822346687317,
0.4773249626159668,
-0.4091428220272064,
0.24387559294700623,
-0.07481855154037476,
0.3702039122581482,
-0.6195698380470276,
-0.7922078967094421,
-0.3914823532104492,
-0.6623429656028748,
-0.07346717268228531,
-0.2933250069618225,
0.10542994737625122,
0.27076125144958496,
-0.4146782457828522,
0.029084743931889534,
0.25048840045928955,
-0.6730915307998657,
-0.5874257683753967,
0.5691847801208496,
0.25109946727752686,
-0.11883465945720673,
-0.22009976208209991,
0.2977778911590576,
0.05926726385951042,
0.2506415843963623,
0.09726773202419281,
-0.46560996770858765,
0.4537201225757599,
-0.3059634268283844,
1.0131765604019165,
-1.2888895273208618,
-0.44073566794395447,
-0.3148493468761444,
-1.2299944162368774,
0.2724981904029846,
0.5001226663589478,
0.2844119071960449,
-0.34007614850997925,
-0.3272486627101898,
-0.4273611605167389,
0.08032698184251785,
-0.2075779139995575,
-0.15170609951019287,
-0.13012152910232544,
-0.9282010197639465,
-0.18887165188789368,
0.31129637360572815,
-0.10796324908733368,
-0.09991379082202911,
0.2658740282058716,
-0.14801426231861115,
0.03331379219889641,
0.21826240420341492,
0.6568589210510254,
0.217398539185524,
0.09821256250143051,
0.288430392742157,
0.2564082741737366,
-0.3391173779964447,
-0.19366323947906494,
0.5247088670730591,
-1.2781810760498047,
1.2635159492492676,
-0.06168700009584427,
-0.41964206099510193,
-0.01665611006319523,
-0.1261969655752182,
0.4767514169216156,
-0.7806663513183594,
0.5191328525543213,
0.2523583769798279,
-0.4578131437301636,
0.07483693212270737,
0.2966327369213104,
-0.18834121525287628,
-0.4960494637489319,
-0.5641691088676453,
-0.43496450781822205,
0.691990077495575,
-0.06557491421699524,
0.12691834568977356,
0.1533653289079666,
-0.5537686944007874,
0.10550741851329803,
0.36574774980545044,
0.37798336148262024,
0.3492392897605896,
0.30550116300582886,
0.37057608366012573,
-0.08627745509147644,
0.2773037850856781,
-0.9574242234230042,
0.25858089327812195,
0.1355990469455719,
-0.12007909268140793,
0.27366819977760315,
0.09021610766649246,
-0.05003051459789276,
-0.6973100900650024,
0.27142804861068726,
0.5159223675727844,
-0.11999128013849258,
-0.6700916290283203,
0.5047146677970886,
0.30897802114486694,
-0.4760575592517853,
0.057317934930324554,
-0.3147565424442291,
-0.24307996034622192,
0.8273880481719971,
0.005331131163984537,
0.09810678660869598,
0.31915637850761414,
0.36936381459236145,
0.4303015470504761,
-0.19184762239456177,
-0.05599885433912277,
0.4533923268318176,
-0.6166082620620728,
-0.7780013084411621,
-0.14410099387168884,
-0.24060401320457458,
-0.5219787955284119,
-0.11483819037675858,
-0.6883425712585449,
0.2597774565219879,
-0.7054727673530579,
-0.4519602060317993,
-0.3664684593677521,
-0.0517190583050251,
-0.5386070609092712,
0.14170897006988525,
0.5471283793449402,
-0.03363353759050369,
0.04855894669890404,
0.4061706066131592,
-0.2770061194896698,
0.30419492721557617,
0.02278163656592369,
1.4940794706344604,
-0.6986229419708252,
-0.9693251848220825,
0.2697741687297821,
0.5762732625007629,
-1.047078013420105,
0.09639310091733932,
0.40272215008735657,
0.27242812514305115,
0.5779275298118591,
0.24903498589992523,
0.37196221947669983,
0.3982965350151062,
0.200520321726799,
0.3738037347793579,
-0.2543082535266876,
-0.6094825863838196,
-0.860950767993927,
-0.8719289898872375,
-0.40183451771736145,
0.24249760806560516,
0.9710509181022644,
0.04588396102190018,
0.3063134253025055,
0.37450551986694336,
-0.2589864432811737,
-0.4985550343990326,
-1.038405418395996,
-0.1627548784017563,
-0.6200523376464844,
-0.17011786997318268,
-0.696792721748352,
-0.8295406699180603,
0.3157045245170593,
0.7725216150283813,
-0.3131181597709656,
-0.054123274981975555,
-0.5202762484550476,
-0.30904924869537354,
-0.06002894043922424,
-0.23397484421730042,
-0.08646684885025024,
-0.6892974376678467,
0.07365456968545914,
-0.5989772081375122,
-0.1925133317708969,
-0.5391267538070679,
-0.2920219302177429,
-0.37637895345687866,
0.2084571272134781,
0.9717230200767517,
-0.15000922977924347,
0.8958895206451416,
-0.7987253069877625,
-0.9958274960517883,
0.04848742112517357,
-0.21184042096138,
-0.4678291976451874,
0.41058650612831116,
0.21709243953227997,
0.43778130412101746,
0.1886543184518814,
0.6243494749069214,
-0.3804919123649597,
0.12651506066322327,
-0.6962446570396423,
0.5383946299552917,
0.2893100678920746,
0.36747440695762634,
-0.5181127786636353,
-0.21899640560150146,
0.05376185104250908,
0.22677376866340637,
-0.4105149507522583,
0.3762719929218292,
-0.14848560094833374,
0.23280549049377441,
-0.510749340057373,
0.5099283456802368,
0.2354901134967804,
0.6982448101043701,
0.5063877105712891,
0.30929797887802124,
-0.5052993893623352,
0.08559550344944,
-0.023494916036725044,
0.27208012342453003,
0.045156534761190414,
0.34604576230049133,
0.10865864157676697,
-0.6580650806427002,
0.13958103954792023,
0.7940102219581604,
-0.17630310356616974,
0.41310548782348633,
-0.10901999473571777,
-0.436657577753067,
-0.20217527449131012,
-0.4836784303188324,
-0.29342594742774963,
0.7874040603637695,
0.3822181224822998,
-0.6706820726394653,
-0.3747427761554718,
-0.5149513483047485,
-0.8139504790306091,
0.6123659014701843,
-1.152538776397705,
-0.40745919942855835,
-0.05496383085846901,
-0.8218812346458435,
0.07123414427042007,
0.4386628270149231,
-0.15152397751808167,
0.34783506393432617,
0.08302561193704605,
0.5911572575569153,
0.5203183889389038,
-0.3656798005104065,
-0.09195373952388763,
0.0045474497601389885,
-0.9558326601982117,
0.14102883636951447,
-0.6132369637489319,
0.23891820013523102,
-1.2178934812545776,
-1.2660523653030396,
-0.08827932178974152,
0.6413683891296387,
0.023192692548036575,
-0.10495562106370926,
-0.2422419786453247,
-0.32926511764526367,
0.2712137699127197,
0.00045667323865927756,
-0.07744038850069046,
-0.1664610058069229,
-0.4694323241710663,
0.5948401689529419,
-0.09249509871006012,
-0.618500292301178,
0.21232545375823975,
0.6610926389694214,
0.09477977454662323,
0.50943523645401,
0.2679925262928009,
1.411224603652954,
-0.10008344799280167,
-0.5574407577514648,
0.8880174160003662,
0.622837483882904,
0.525635302066803,
-0.05503453314304352,
-0.43891265988349915,
0.3720802962779999,
0.41168296337127686,
0.12687353789806366,
0.9791497588157654,
0.4069192409515381,
0.6220262050628662,
0.32748985290527344,
0.1642078161239624,
-0.1917358636856079,
-0.08788543194532394,
0.6425454020500183,
0.48617804050445557,
0.011106785386800766,
-0.6325936317443848,
0.13109543919563293,
0.27866050601005554,
0.390354722738266,
0.4883107841014862,
-0.36068621277809143,
-0.1377231776714325,
0.38681560754776,
-0.36961129307746887,
0.23155750334262848,
-0.47145459055900574,
-0.5481148362159729,
-0.31270456314086914,
-0.0014378471532836556,
0.7213633060455322,
0.41011813282966614,
-0.027779949828982353,
0.23234595358371735,
0.8675310611724854,
-0.15004388988018036,
-0.4080088436603546,
0.9216488599777222,
0.14182023704051971,
0.4250752925872803,
0.5968155860900879,
0.36851632595062256,
0.6640251278877258,
0.6322593092918396,
0.03656834736466408,
-0.5922855734825134,
0.36817336082458496,
0.40141481161117554,
-1.300195574760437,
0.07633398473262787,
-0.4919777512550354,
0.25093361735343933,
-0.6921284198760986,
-0.7059798836708069,
0.7777991890907288,
-0.7933456301689148,
-0.17028942704200745,
0.42574217915534973,
-0.4579700827598572,
-0.30089905858039856,
0.32073065638542175,
0.3734830617904663,
0.01392251718789339,
0.520052433013916,
0.3717344105243683,
0.3902459442615509,
1.329604983329773,
0.6306767463684082,
0.19904500246047974,
-0.11377111077308655,
-0.09785337001085281,
-0.36608126759529114,
0.2303265780210495,
-0.03430577740073204,
0.12538495659828186,
0.3184261620044708,
-0.9076024889945984,
-0.7121748924255371,
-0.09867589920759201,
-0.24846404790878296,
-0.05125699192285538,
-0.11632949113845825,
0.5201104283332825,
0.2928912937641144,
-0.6331681609153748,
-0.22918035089969635,
1.7730975151062012,
0.30036506056785583,
-0.23749706149101257,
-0.48219776153564453,
0.12452033162117004,
-0.4965493977069855,
-0.6453394889831543,
-0.39738893508911133,
0.5064751505851746,
-0.1582115888595581,
-0.02571841888129711,
-0.13476087152957916,
-0.26396241784095764,
-0.20654693245887756,
-0.8537949323654175,
-0.006161325145512819,
-0.23313622176647186,
0.650734007358551,
0.19509972631931305,
-0.19505056738853455,
0.1725941151380539,
-0.5794348120689392,
0.09101306647062302,
0.5072354674339294,
0.7011208534240723,
-0.19516706466674805,
0.25911593437194824,
0.2522544860839844,
0.584192156791687,
-0.5601171851158142,
0.48278605937957764,
0.708825409412384,
-0.6588165163993835,
0.6918225288391113,
-0.5043417811393738,
0.6010236144065857,
0.6818152070045471,
0.05283379554748535,
-0.07881379872560501,
-0.3587610125541687,
0.292633056640625,
-0.25272709131240845,
-0.18296369910240173,
-0.16735926270484924,
-0.6201782822608948,
-0.18729327619075775,
-0.763676106929779,
0.09789825230836868,
-0.2721925973892212,
0.1679319441318512,
0.2534335255622864,
-0.5661724805831909,
4.25811243057251,
0.8523135781288147,
0.34839847683906555,
0.28313732147216797,
1.0273886919021606,
1.3293406963348389,
-0.3308517038822174,
-0.2063664346933365,
0.219732403755188,
-0.6369683742523193,
-0.630718469619751,
0.01272567082196474,
0.39790821075439453,
-0.19770875573158264,
-0.2854600250720978,
0.8454526662826538,
-0.1747412532567978,
-0.4707700312137604,
0.3592343330383301,
-0.90645831823349,
-0.6633239388465881,
0.618727445602417,
0.777340829372406,
-0.16616833209991455,
0.662750780582428,
0.4348137378692627,
0.07732177525758743,
-0.5821962356567383,
-0.01375286839902401,
0.05962241441011429,
-0.6746755838394165,
-0.451443076133728,
0.28851768374443054,
0.02175985462963581,
-0.5812187790870667,
0.7438285946846008,
-0.5574694871902466,
-0.28323060274124146,
-0.030813464894890785,
0.042211852967739105,
-0.07904806733131409,
-0.01630910485982895,
0.0048963092267513275,
0.1689552664756775,
-0.46597108244895935,
0.8872672319412231,
-0.4854013919830322,
0.6251347661018372,
0.5585461258888245,
-0.9073452353477478,
0.8350923657417297,
-0.44527214765548706,
0.27310171723365784,
-0.32637983560562134,
-0.3406473696231842,
-0.2529147267341614,
-0.09591871500015259,
0.07722914963960648,
0.13841401040554047,
0.12287680059671402,
0.47670412063598633,
-0.2974226772785187,
-0.16420945525169373,
0.38140350580215454,
-0.2315950095653534,
0.2902217209339142,
0.34330296516418457,
-0.025699112564325333,
-0.5662347674369812,
-0.04676668345928192,
-0.387361615896225,
-0.3714865744113922,
-0.20633529126644135,
0.6855713725090027,
0.47805365920066833,
-0.10981273651123047,
-0.12888860702514648,
0.20818600058555603,
-0.7963358759880066,
0.3074186146259308,
0.0065863230265676975,
-0.36958205699920654,
-0.5280557870864868,
-0.2627585232257843,
0.14977090060710907,
0.46035319566726685,
0.04490626975893974,
0.2122424989938736,
-0.09910432249307632,
0.3460592031478882,
0.420870840549469,
1.1251102685928345,
-0.10249944031238556,
0.21627698838710785,
-0.8034490942955017
] |
Perturbative Corrections for Staggered Fermion Bilinears
|
We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a $2^4$ hypercube, and for tree level improved operators which live on $4^4$ hypercubes. We also consider gauge invariant operators in which the ``tadpole'' contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.
|
Apoorva Patel and Stephen Sharpe
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210039
|
hep-lat/9210040
|
[
-0.5490971207618713,
-0.35211318731307983,
-0.3033302128314972,
-0.6121253967285156,
0.07605916261672974,
-0.4117918908596039,
-0.11947260051965714,
-0.7825080752372742,
-0.36024075746536255,
1.2526177167892456,
-0.02019263617694378,
0.5138657093048096,
0.768589973449707,
-0.5640407800674438,
0.3557170629501343,
0.7517862915992737,
-0.9345133900642395,
-0.5911440849304199,
-1.8837271928787231,
0.7583040595054626,
0.4752354323863983,
0.1199255883693695,
-1.4043083190917969,
-0.865210235118866,
-0.048488594591617584,
1.3287204504013062,
0.48171892762184143,
0.40553635358810425,
1.4153006076812744,
0.9396069049835205,
0.2188229113817215,
-0.3799586594104767,
0.06725064665079117,
-0.4627818763256073,
-0.6088702082633972,
-0.8841879963874817,
-0.585605263710022,
-0.2539038360118866,
0.5834887623786926,
-0.299778014421463,
0.6607872247695923,
-0.3828071653842926,
-0.1855468451976776,
-0.23603329062461853,
-0.78790283203125,
0.4250803291797638,
0.14530915021896362,
-0.5782045125961304,
0.2822679579257965,
-1.4289207458496094,
0.3355993628501892,
0.32170072197914124,
0.4249359965324402,
-0.31577229499816895,
-0.7092195749282837,
0.2247975766658783,
0.06944959610700607,
-0.270381361246109,
-0.7730646133422852,
-0.13930337131023407,
0.25974446535110474,
-0.30816778540611267,
-0.14117561280727386,
-1.145645022392273,
0.41697704792022705,
0.1508491039276123,
0.4421301484107971,
0.211627796292305,
0.0708138644695282,
-0.45441123843193054,
-0.13917052745819092,
-0.1255735605955124,
-1.3448107242584229,
-0.20310497283935547,
-0.751652181148529,
0.47730883955955505,
-0.22032706439495087,
-0.5466924905776978,
-0.9640493392944336,
-0.6293091177940369,
-0.14825034141540527,
0.007470705080777407,
-0.8113064765930176,
0.5602725148200989,
-1.5205926895141602,
0.036222945898771286,
-0.4113399386405945,
-0.5894789695739746,
-0.0681271031498909,
0.1136612817645073,
0.6274086833000183,
1.1525993347167969,
-0.536445140838623,
0.8113344311714172,
0.3728669583797455,
0.9465342164039612,
0.1777483969926834,
1.2162342071533203,
0.38936275243759155,
0.37420105934143066,
0.04758722707629204,
1.3518047332763672,
-1.349707007408142,
0.09981710463762283,
-1.1074323654174805,
-0.33505910634994507,
-0.9919054508209229,
-0.5296469330787659,
-0.5236858129501343,
-0.8101726174354553,
0.4418099820613861,
-0.14963462948799133,
0.4274342656135559,
0.3332674205303192,
0.22385968267917633,
0.5131093859672546,
-0.37811705470085144,
0.5846665501594543,
0.08164307475090027,
-0.5522826313972473,
-0.24886631965637207,
-0.1207786574959755,
0.23544742166996002,
0.5752003788948059,
-0.07871651649475098,
0.32823285460472107,
0.6173810362815857,
0.7584638595581055,
-0.7483106255531311,
0.5033817887306213,
0.5442030429840088,
-0.20734140276908875,
-0.22890794277191162,
0.34970009326934814,
-0.8554047346115112,
-0.21888040006160736,
-0.6489349603652954,
0.20231184363365173,
0.7952344417572021,
-0.12615743279457092,
0.8601731657981873,
-0.8232297301292419,
0.06563755124807358,
1.181522250175476,
0.7835578322410583,
0.14977863430976868,
0.11623527109622955,
0.2910076379776001,
-0.966495931148529,
0.3920748829841614,
-0.04360078647732735,
0.029777204617857933,
-0.10524654388427734,
0.6780939698219299,
0.12640389800071716,
0.935633659362793,
-0.8660382032394409,
-0.36802437901496887,
0.025990862399339676,
-0.010101061314344406,
0.17884574830532074,
-0.6360089182853699,
-0.7368261814117432,
0.3063313364982605,
-0.4562506377696991,
-0.15406373143196106,
-0.7377657890319824,
-0.19661922752857208,
0.030112795531749725,
-0.38238033652305603,
-0.520104706287384,
-0.011945297010242939,
-0.4676121175289154,
0.6964172720909119,
0.8313734531402588,
0.9285255670547485,
0.6845394968986511,
-0.24400560557842255,
0.0983082503080368,
0.3324851095676422,
-0.26680585741996765,
-0.6868259906768799,
0.3184237778186798,
0.23100587725639343,
-0.12801331281661987,
-0.47791504859924316,
0.5999846458435059,
-0.10395411401987076,
0.3831770718097687,
-0.20243078470230103,
-0.25440579652786255,
0.4550149738788605,
-0.011361852288246155,
0.7580788731575012,
-0.12823492288589478,
0.16454418003559113,
-1.0994703769683838,
0.11550868302583694,
-1.0722744464874268,
-0.3885229229927063,
0.19969706237316132,
0.2866355776786804,
-0.7163496017456055,
0.03404654189944267,
-1.2886887788772583,
-0.1046530082821846,
0.6115195751190186,
0.5062049627304077,
-0.8937704563140869,
-0.04714032635092735,
0.47321656346321106,
-0.11927789449691772,
-0.08364991098642349,
-0.30214476585388184,
1.1790467500686646,
0.47799286246299744,
0.596875011920929,
0.7949008345603943,
-0.06639178842306137,
0.10882896929979324,
0.38492637872695923,
0.5701264142990112,
-0.24124543368816376,
0.4248429834842682,
-0.7823011875152588,
-0.6085229516029358,
0.1974882185459137,
0.9874756932258606,
0.5046882629394531,
-0.0915524810552597,
-0.09147148579359055,
0.054676879197359085,
0.04529808089137077,
0.8193381428718567,
0.2646690011024475,
0.30997222661972046,
0.41072478890419006,
0.35291579365730286,
0.6014562249183655,
0.51907879114151,
-0.028959525749087334,
0.29781103134155273,
0.7595708966255188,
-0.5976374745368958,
0.03642629459500313,
0.32753658294677734,
-0.45190882682800293,
0.50780189037323,
-1.078569769859314,
0.27946847677230835,
-0.4036986529827118,
0.47058120369911194,
0.199065700173378,
0.41237688064575195,
-0.8772470951080322,
0.005375675391405821,
0.34673961997032166,
0.47818320989608765,
0.2656450867652893,
0.01802251487970352,
0.7478904128074646,
0.26951074600219727,
-0.3532746136188507,
-0.3690800070762634,
-0.07053419947624207,
1.2169089317321777,
-0.11317393183708191,
0.0767541453242302,
0.19160926342010498,
-0.39430588483810425,
-0.7920483350753784,
-0.4396390914916992,
-0.7590314745903015,
0.20866644382476807,
-1.2106374502182007,
-0.09011416882276535,
1.0264400243759155,
-1.4546533823013306,
1.1907192468643188,
0.21781674027442932,
-0.3121362328529358,
0.6909819841384888,
-1.1622004508972168,
0.11524253338575363,
1.0806218385696411,
0.23994481563568115,
-0.7489304542541504,
-0.14349523186683655,
-0.4127930700778961,
-0.3445892930030823,
0.24570317566394806,
0.3641620874404907,
0.6292157173156738,
-0.38061264157295227,
0.9081241488456726,
-0.011743907816708088,
-0.6251392960548401,
-0.4984249174594879,
-0.09787353128194809,
-1.0477666854858398,
0.3208892047405243,
0.3816606402397156,
-0.05727817863225937,
0.040310338139534,
-0.7298156023025513,
0.6711116433143616,
0.5180660486221313,
-0.10299340635538101,
-0.10076577961444855,
0.17790162563323975,
-0.37576133012771606,
0.6964966654777527,
0.3184472918510437,
0.23775771260261536,
-0.4096451699733734,
1.1630096435546875,
0.7364739179611206,
0.15231254696846008,
-0.4948514997959137,
-0.09813820570707321,
0.14142407476902008,
0.24227099120616913,
0.04363279789686203,
-0.9046071767807007,
-0.30090728402137756,
0.9161282777786255,
0.3781110942363739,
-1.111138939857483,
0.10681729018688202,
-0.6494578123092651,
-0.737525224685669,
0.17849291861057281,
-0.42907142639160156,
0.2778001129627228,
0.3574889898300171,
0.7629842758178711,
-0.35072061419487,
0.3348545432090759,
0.9057512879371643,
-0.29002252221107483,
1.0302459001541138,
-0.2840936481952667,
0.6877622008323669,
0.4070693254470825,
0.21868711709976196,
0.11214612424373627,
-0.058406706899404526,
-0.779133141040802,
-0.1452898532152176,
0.6422617435455322,
-0.3478509485721588,
0.5697923302650452,
-0.09462807327508926,
-0.1386847198009491,
-0.03767156973481178,
1.1243891716003418,
-1.0390161275863647,
-0.32629474997520447,
-0.5213425159454346,
-0.01916373521089554,
1.0251085758209229,
0.8613735437393188,
-0.45191094279289246,
-1.1912312507629395,
-0.4133957624435425,
-0.7781814336776733,
-0.44909152388572693,
0.3193952143192291,
0.7452788352966309,
-1.6630498170852661,
0.308611661195755,
0.5187395811080933,
-0.03434516862034798,
0.4948355257511139,
-0.5385519862174988,
-0.06976571679115295,
0.7929319739341736,
0.2683529555797577,
0.8197731971740723,
-0.19612152874469757,
-0.6521689891815186,
-0.0681958869099617,
0.8117589354515076,
0.38327860832214355,
0.2141202837228775,
-0.28770068287849426,
-0.3893248736858368,
-0.08193133026361465,
-0.23825706541538239,
-0.7197281122207642,
-0.31613829731941223,
-0.23348651826381683,
0.3322153687477112,
0.16039295494556427,
0.13956265151500702,
0.4013783037662506,
0.503747284412384,
0.7124800086021423,
0.455055296421051,
-0.4518616497516632,
0.3826722204685211,
0.48231086134910583,
0.5853649973869324,
1.1029154062271118,
-0.9574039578437805,
0.12251846492290497,
-0.44369035959243774,
0.38802099227905273,
0.7635822296142578,
0.3778650462627411,
-0.3188733458518982,
-0.2988746762275696,
-0.9053723812103271,
-0.8056594729423523,
0.45658159255981445,
0.3179122507572174,
-0.6957972049713135,
0.813607394695282,
0.09867898374795914,
0.3026251494884491,
-0.18698646128177643,
-0.17498107254505157,
1.0205862522125244,
0.9518249034881592,
0.7549081444740295,
-1.096208930015564,
0.47595691680908203,
-0.43592965602874756,
-0.2856052815914154,
0.542984127998352,
-0.7595337629318237,
-0.6793367862701416,
-0.7872503995895386,
-0.1133311465382576,
-0.6536860466003418,
0.41815072298049927,
1.3109785318374634,
0.049642164260149,
0.2779463231563568,
-0.7826822400093079,
0.36377379298210144,
1.1593830585479736,
-0.6442703008651733,
-0.43044614791870117,
-0.0384887270629406,
-0.3292427957057953,
0.05454247444868088,
0.8355666399002075,
-0.27542340755462646,
-0.47405222058296204,
0.20511746406555176,
-0.9442963600158691,
-0.18206292390823364,
-0.6650490164756775,
-0.9499890208244324,
-0.49560868740081787,
-0.3527502715587616,
-0.23300480842590332,
0.5312979817390442,
0.002205080585554242,
-0.592879593372345,
-0.44925862550735474,
0.1179666593670845,
-0.05105426907539368,
0.4885728359222412,
0.18953865766525269,
0.05615992471575737,
0.8745460510253906,
0.49947744607925415,
0.33114758133888245,
-0.2587735652923584,
0.16450786590576172,
-0.27570050954818726,
-0.1093471497297287,
0.5018972158432007,
0.2432427704334259,
-0.8280828595161438,
-0.08986581861972809,
-0.838792622089386,
-0.6325994729995728,
-0.5950286984443665,
-0.3676333427429199,
0.02796846441924572,
0.1771858185529709,
0.31172287464141846,
-0.7566897869110107,
-0.22707492113113403,
-0.5144376754760742,
-1.2349966764450073,
0.1456526666879654,
0.7435536980628967,
0.1437215358018875,
0.6268867254257202,
-0.9710410833358765,
0.3161584734916687,
-0.8043075799942017,
0.07964292168617249,
-0.3319918215274811,
0.29005828499794006,
1.019140601158142,
-0.04855330288410187,
1.3676183223724365,
-0.875515878200531,
-0.0325215719640255,
-0.9772249460220337,
0.35794317722320557,
-0.534658670425415,
-0.23620206117630005,
-0.4769655466079712,
-0.3046889007091522,
0.030325520783662796,
-0.48466047644615173,
-0.03743961453437805,
0.3683413863182068,
0.9451200366020203,
-0.34043246507644653,
-0.3746175467967987,
-0.40246155858039856,
-0.6120103001594543,
0.364470511674881,
0.1932976394891739,
-0.5057834982872009,
-0.4053826630115509,
0.1875866949558258,
0.11823917180299759,
0.5122275948524475,
0.007150048855692148,
-0.09642653912305832,
-0.46973544359207153,
-0.5336708426475525,
0.5268638134002686,
-0.5839909911155701,
-0.45387017726898193,
-0.3054511249065399,
-0.00879546906799078,
1.1714292764663696,
0.8507778644561768,
0.5306841135025024,
-0.008920314721763134,
-0.6520920395851135,
-0.2655255198478699,
0.20002438127994537,
-0.4846929609775543,
0.056016188114881516,
-0.8508175015449524,
-0.5791618227958679,
-0.10491964221000671,
0.7524973750114441,
-0.0772586241364479,
0.5991869568824768,
0.2500759959220886,
-0.13254918158054352,
0.39755338430404663,
0.6156019568443298,
0.4706173241138458,
-0.15532582998275757,
-0.37321245670318604,
0.5237959623336792,
0.22164396941661835,
0.3604212701320648,
-0.5452302694320679,
0.7235293984413147,
-0.5506525635719299,
1.0066273212432861,
-0.44731616973876953,
-0.23081505298614502,
-0.1141771525144577,
-0.02775290422141552,
0.9907017946243286,
-1.0013333559036255,
-0.3873101770877838,
-0.4035857021808624,
0.16023647785186768,
0.8229458928108215,
-0.0959399864077568,
-0.5154054760932922,
-0.3507710099220276,
-0.40059372782707214,
-0.7653822898864746,
0.08358309417963028,
-0.34387943148612976,
-0.5811084508895874,
-1.1579898595809937,
-0.9252248406410217,
0.6332404017448425,
0.17889437079429626,
-0.2712838649749756,
0.5543547868728638,
0.33362042903900146,
0.24579450488090515,
-0.18664556741714478,
-0.8910579681396484,
-0.27845439314842224,
-0.02191477082669735,
-0.6837571859359741,
-0.17080238461494446,
0.09427309781312943,
0.5629093647003174,
-0.3584694266319275,
-0.7463935017585754,
0.17681744694709778,
0.0023274484556168318,
0.13094530999660492,
-0.5574226379394531,
0.5353285670280457,
-0.3645905554294586,
-0.2883239686489105,
-0.6167235374450684,
0.3268401026725769,
0.140536829829216,
0.1893463432788849,
0.6294048428535461,
0.4705103039741516,
0.006704140454530716,
0.1907655894756317,
0.9103422164916992,
-0.0920872837305069,
-0.1818581223487854,
0.5960754156112671,
0.20783010125160217,
-0.40524187684059143,
0.6957076787948608,
0.2810288667678833,
-0.7586907148361206,
-0.2773514986038208,
-0.6189693212509155,
0.055758148431777954,
-0.3675670623779297,
0.1215430200099945,
-0.015189042314887047,
0.05256908759474754,
0.13206951320171356,
0.312581330537796,
0.5332061052322388,
0.018872037529945374,
0.1770406812429428,
0.21311159431934357,
-0.3500605523586273,
-0.6298760175704956,
0.042284127324819565,
0.6560546159744263,
0.0052562919445335865,
-0.5176513195037842,
0.6195294857025146,
0.13924086093902588,
-0.5430577397346497,
-0.28494352102279663,
0.9199646711349487,
-0.580988883972168,
0.6557276248931885,
0.2760452330112457,
-0.06457406282424927,
0.7730908393859863,
-0.31865864992141724,
-0.23307456076145172,
-0.03911963850259781,
-0.8096629977226257,
-1.0505558252334595,
-0.3446199893951416,
-0.29190126061439514,
0.07452932745218277,
0.8166705965995789,
-0.20041286945343018,
0.2096259742975235,
0.808786928653717,
-0.6168238520622253,
-0.4840528964996338,
-1.1251145601272583,
-0.39309927821159363,
-0.9202778935432434,
-0.2365245670080185,
-0.24529561400413513,
0.019464876502752304,
0.20492683351039886,
0.16621463000774384,
-0.5120898485183716,
0.10691234469413757,
-0.5684816837310791,
-0.33732908964157104,
-0.22747404873371124,
0.2476658970117569,
-0.2968897223472595,
-1.071075677871704,
-0.37474513053894043,
-0.12082943320274353,
-0.12448522448539734,
0.03887137770652771,
0.17747944593429565,
0.09013751149177551,
-0.05711840093135834,
0.6528283953666687,
-0.0693710446357727,
1.0827370882034302,
-1.1255450248718262,
-0.5353567004203796,
-0.26270750164985657,
-0.35558265447616577,
-0.7322023510932922,
0.5483996272087097,
-0.04613196477293968,
0.6099569201469421,
0.7154648303985596,
0.1326902061700821,
-0.3880234658718109,
0.8489235639572144,
-1.0739586353302002,
0.4544040858745575,
0.32183387875556946,
0.03746262192726135,
-0.4448714852333069,
-0.8591678738594055,
-0.4419998228549957,
-0.33370357751846313,
-1.1294760704040527,
0.5112131834030151,
0.27217990159988403,
-0.200034499168396,
-0.7437410950660706,
0.8574491739273071,
0.2220706194639206,
-0.18891803920269012,
0.09856851398944855,
1.1259280443191528,
-0.15559136867523193,
-0.10800136625766754,
-0.08277543634176254,
0.39708030223846436,
-0.1694827377796173,
-0.3232642412185669,
0.4351504445075989,
-0.21944253146648407,
0.31841790676116943,
0.2412254959344864,
0.4301949441432953,
0.3254517912864685,
-0.10542465001344681,
-0.6342577934265137,
-0.4838685989379883,
-0.2579491436481476,
0.08845267444849014,
0.830333411693573,
0.6337993741035461,
-0.14294995367527008,
0.39981770515441895,
-0.7532030940055847,
-0.9121315479278564,
-0.1081826388835907,
-0.7219600081443787,
-0.4041993021965027,
0.6339284777641296,
-0.7027794718742371,
0.2915453016757965,
-0.10181473940610886,
-0.30900728702545166,
-0.2224915623664856,
0.23733073472976685,
0.3969316780567169,
-0.21688401699066162,
0.2704239785671234,
-0.18520672619342804,
0.28720226883888245,
-0.8701270818710327,
-0.3472284972667694,
-0.0821518823504448,
0.6526590585708618,
-0.5583770871162415,
-1.1679054498672485,
-0.4743037819862366,
0.05100163817405701,
-0.5487477779388428,
-0.19855527579784393,
-0.20551954209804535,
-0.3984060287475586,
-0.6559721827507019,
0.32953178882598877,
0.09061379730701447,
0.46345892548561096,
-0.8463858962059021,
0.097148098051548,
0.11522210389375687,
-0.9544326663017273,
0.13474151492118835,
0.48009830713272095,
-0.440559983253479,
-0.5324649214744568,
0.6291645169258118,
1.2813771963119507,
0.18441283702850342,
-0.5808819532394409,
0.763715922832489,
-0.13709944486618042,
0.5309013724327087,
0.012432761490345001,
-0.7073646187782288,
0.245384082198143,
0.35044384002685547,
0.6655429601669312,
0.7002164125442505,
0.5203917622566223,
0.17160452902317047,
1.075782060623169,
0.6974288821220398,
0.8720528483390808,
-0.2876113951206207,
-0.7026534676551819,
0.769892156124115,
-0.03421200439333916,
-0.6902289986610413,
0.22161053121089935,
0.582002580165863,
-0.1659746915102005,
0.010245143435895443,
-0.6398122310638428,
-0.8398371338844299,
-0.29788729548454285,
0.2559480369091034,
-0.1946081668138504,
-0.5191724896430969,
-0.15194937586784363,
-0.5567746162414551,
-0.040151625871658325,
0.6681215763092041,
0.5826697945594788,
0.05895254760980606,
0.09780696034431458,
0.8270583748817444,
0.3297165632247925,
-0.5258267521858215,
0.4135277569293976,
0.6528421640396118,
0.8957291841506958,
0.7282182574272156,
-0.1724725067615509,
1.0252447128295898,
0.13006076216697693,
0.6436243057250977,
-1.2479135990142822,
0.03001338802278042,
0.03900432959198952,
-0.9457281231880188,
-0.16319380700588226,
-0.4106772541999817,
-0.09498409181833267,
-1.0602142810821533,
-0.7822091579437256,
0.564502477645874,
-0.5289803147315979,
0.2120712399482727,
0.456118643283844,
-0.3447498381137848,
-0.29939350485801697,
0.8477628827095032,
0.02836432307958603,
-0.005635598674416542,
0.10168057680130005,
0.42468947172164917,
0.5141147971153259,
0.9305175542831421,
1.837905764579773,
0.24423813819885254,
0.31108391284942627,
-0.10328546166419983,
-0.20797839760780334,
0.390137642621994,
0.951725959777832,
-0.3591577708721161,
-0.21933911740779877,
-0.5790939331054688,
-0.8486210107803345,
0.1178910881280899,
0.1799522042274475,
-0.11787401139736176,
-0.3448179364204407,
0.26266714930534363,
0.32138973474502563,
-0.6365252733230591,
0.04532493278384209,
0.7358688712120056,
0.6321211457252502,
-0.202190563082695,
0.15568958222866058,
0.1700582504272461,
-0.8832528591156006,
0.36994215846061707,
-0.6276537775993347,
0.25639623403549194,
-0.6440690159797668,
-0.14459924399852753,
-0.216704860329628,
-0.6319442391395569,
-0.48973020911216736,
-0.1593886911869049,
0.10219860821962357,
-0.02074378915131092,
0.16136936843395233,
1.0933672189712524,
-0.31293216347694397,
0.6422731876373291,
-0.5794277787208557,
-0.1799296736717224,
-0.29249778389930725,
0.24673300981521606,
0.4472928047180176,
0.8099582195281982,
0.8537760376930237,
-0.09370799362659454,
-0.5371125340461731,
0.18657302856445312,
1.1865289211273193,
-0.7290094494819641,
0.6390715837478638,
-1.04879629611969,
0.6577602028846741,
0.43227532505989075,
-0.035884104669094086,
0.42032161355018616,
0.47046568989753723,
0.28776052594184875,
0.21423391997814178,
-0.0005025663413107395,
-0.23641642928123474,
-0.05956421047449112,
0.23342199623584747,
-1.387886881828308,
-0.05903210863471031,
0.5392733216285706,
0.5536369681358337,
0.21638411283493042,
-0.7640244960784912,
3.723367214202881,
0.37304794788360596,
0.8525046706199646,
0.7211751937866211,
0.8990550637245178,
1.2293009757995605,
-0.6684921383857727,
-0.3009008467197418,
0.13086003065109253,
-0.8155277371406555,
-0.4913312792778015,
-0.11561811715364456,
0.018404820933938026,
0.6455869674682617,
0.1840589940547943,
0.7960076332092285,
-0.21000781655311584,
0.1815854161977768,
0.07454627752304077,
-0.8779799342155457,
-0.9838840365409851,
0.07502772659063339,
0.5700840353965759,
0.4493027627468109,
0.5674031972885132,
-0.14994138479232788,
-0.061259303241968155,
-0.7176133394241333,
-1.1934514045715332,
-0.7598164081573486,
-0.5689164996147156,
0.18655788898468018,
0.6574220061302185,
-0.569658637046814,
-0.7006963491439819,
0.13747185468673706,
-0.20080985128879547,
-0.656905472278595,
0.5494208335876465,
0.9439892172813416,
-0.45034030079841614,
-0.8590711355209351,
0.6997058987617493,
-0.6311635375022888,
-0.2489262968301773,
1.1230721473693848,
-0.6185182332992554,
0.8509188294410706,
0.3182052969932556,
-0.3932250738143921,
0.3374326527118683,
0.023823045194149017,
0.7405118942260742,
-0.5226051807403564,
-0.37465494871139526,
0.11421683430671692,
-0.5988777279853821,
-0.08389201760292053,
0.2758397161960602,
0.0037797929253429174,
-0.2901846170425415,
0.12503670156002045,
-0.38197562098503113,
-0.3191360533237457,
-0.37717917561531067,
0.4628274738788605,
0.26121628284454346,
0.23386026918888092,
-0.028379635885357857,
0.14753217995166779,
0.3347894549369812,
-0.08700090646743774,
0.29939013719558716,
-0.16875801980495453,
0.5130705833435059,
0.6997540593147278,
-0.38569149374961853,
0.5551596283912659,
0.43688833713531494,
-0.2535795569419861,
-0.7878460884094238,
-0.44908449053764343,
-0.51541668176651,
-0.03661426156759262,
0.24733664095401764,
0.3342352509498596,
-0.5537193417549133,
-0.21621842682361603,
-0.5689118504524231,
0.48914697766304016,
0.7113186717033386,
1.4734188318252563,
0.22207525372505188,
0.5136297941207886,
-0.5218492746353149
] |
On reflection positive formulation of chiral gauge theories on a lattice
|
A formulation of chiral gauge theories on a lattice which is both reflection positive and gauge invariant is discussed.
|
Sergei V. Zenkin
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210040
|
hep-lat/9210041
|
[
0.3023243546485901,
-0.2106398493051529,
0.6580071449279785,
0.7979505062103271,
0.07086041569709778,
-0.19483725726604462,
-0.5122219324111938,
-0.5059176683425903,
-0.6156670451164246,
1.3239083290100098,
0.2999214231967926,
-0.19384361803531647,
0.5184745192527771,
-0.7637566924095154,
0.07087098807096481,
0.9146369099617004,
0.14013785123825073,
-0.4832952618598938,
-1.48160982131958,
0.35047340393066406,
0.17763231694698334,
-0.30133387446403503,
-1.448506236076355,
-1.2325153350830078,
-0.09650598466396332,
0.9869024753570557,
0.12272218614816666,
0.19976942241191864,
1.1115094423294067,
0.16019174456596375,
-0.019166773185133934,
-0.28178220987319946,
-0.5634647607803345,
-0.7329784035682678,
-0.48148563504219055,
-0.16281162202358246,
0.24025742709636688,
-0.11088328063488007,
0.4093312919139862,
-0.09770754724740982,
0.5330349206924438,
-0.18896499276161194,
-0.428986132144928,
-0.7340137958526611,
-0.12847845256328583,
0.014191236346960068,
-0.15668214857578278,
0.2412533462047577,
0.11823658645153046,
-0.9399418234825134,
-0.222987100481987,
0.4163467288017273,
0.6612312197685242,
-1.0912567377090454,
-0.4166773557662964,
0.11374000459909439,
-0.21975570917129517,
-0.016152063384652138,
-0.8140102624893188,
0.09214028716087341,
0.5867806077003479,
0.2508399188518524,
0.3785778284072876,
-0.3543880581855774,
0.42511633038520813,
0.6636903882026672,
-0.631733238697052,
0.9216638207435608,
0.162595734000206,
-0.4388362169265747,
-0.2345464825630188,
-0.19561229646205902,
-0.8498086929321289,
-0.02454298548400402,
-1.1863559484481812,
-0.444375216960907,
-0.09746789932250977,
-0.09051138162612915,
-0.12064192444086075,
-0.6138182878494263,
-0.07146105170249939,
-0.08062373101711273,
-0.7451841235160828,
0.5624520182609558,
-0.003227613400667906,
-0.46636542677879333,
-0.4816345274448395,
-0.21829450130462646,
-0.3462490737438202,
0.8335235714912415,
-0.12524843215942383,
0.7975121736526489,
-0.22112765908241272,
-0.45536819100379944,
0.20063386857509613,
0.3967117369174957,
0.029993925243616104,
0.6718845367431641,
0.06109577417373657,
0.447925865650177,
0.20593592524528503,
1.1410467624664307,
-1.0958731174468994,
0.46795937418937683,
-0.24358808994293213,
-0.04515382647514343,
-0.31483644247055054,
-0.16498428583145142,
-0.10631837695837021,
-0.28491413593292236,
0.3581496477127075,
-0.821817934513092,
0.3104773163795471,
1.0397114753723145,
0.08921657502651215,
0.3246263861656189,
-0.3443410396575928,
0.06753294169902802,
-0.3146387040615082,
-0.4150232970714569,
0.48410558700561523,
0.49903032183647156,
0.09772570431232452,
0.18063421547412872,
-0.2263861894607544,
-0.326205313205719,
0.399718701839447,
0.35060811042785645,
-0.6777462959289551,
0.2113446742296219,
0.0019605252891778946,
-0.05804914981126785,
-0.8245531320571899,
0.5816699266433716,
-0.3736115097999573,
0.31933918595314026,
0.007683154195547104,
0.3708878457546234,
0.27626705169677734,
0.15083710849285126,
0.759277880191803,
-0.7253901362419128,
0.6486853361129761,
0.9254508018493652,
0.5659615993499756,
0.26181986927986145,
0.24255317449569702,
0.23336821794509888,
-0.14733313024044037,
-0.13760027289390564,
-1.4220081567764282,
0.055423516780138016,
-0.1738712042570114,
-0.18708312511444092,
0.06192062050104141,
0.38158050179481506,
-0.4555973708629608,
0.9205625057220459,
-0.7504712343215942,
-0.7727758884429932,
-0.056032441556453705,
-0.4452095031738281,
-0.4801514148712158,
0.03643316403031349,
-0.36133813858032227,
-0.14684714376926422,
-0.44856327772140503,
-0.2857663929462433,
0.5896766185760498,
-0.3873276114463806,
0.10428467392921448,
0.7104863524436951,
0.3347141742706299,
0.5293689370155334,
0.2869243025779724,
0.5309127569198608,
0.20074529945850372,
-0.10372354835271835,
0.09042003750801086,
1.0201858282089233,
0.2770287096500397,
-0.7500112056732178,
0.19783839583396912,
0.2638497054576874,
-0.1851276308298111,
0.34951141476631165,
-0.1887691468000412,
-0.38363543152809143,
0.004333470482379198,
0.3775504231452942,
-0.3028314709663391,
0.5572420358657837,
-0.791126549243927,
1.1088159084320068,
-0.7063463926315308,
-0.223271906375885,
-0.690410315990448,
0.532159149646759,
-0.8076485991477966,
-0.2976249158382416,
-0.009892378933727741,
0.38118353486061096,
-0.642207682132721,
-0.2773204743862152,
-1.5432952642440796,
0.08629052340984344,
0.9808578491210938,
-0.26248660683631897,
-0.7982816100120544,
-1.0623201131820679,
-0.06720369309186935,
-0.18978315591812134,
0.1513577401638031,
-0.7417261600494385,
0.49864745140075684,
0.1388307809829712,
0.32586780190467834,
-0.17367637157440186,
0.8571269512176514,
0.11828013509511948,
0.6334790587425232,
0.37379544973373413,
-0.33950600028038025,
0.9738285541534424,
-0.7078725099563599,
-0.2320968210697174,
-0.1361197978258133,
0.32032084465026855,
0.18526194989681244,
-0.6482045650482178,
0.5409690141677856,
0.9494851231575012,
-0.054296210408210754,
0.566083550453186,
0.758338212966919,
0.5547810792922974,
0.30668285489082336,
0.200301393866539,
0.5341895818710327,
0.11635546386241913,
-0.6661406755447388,
0.49960392713546753,
0.41573765873908997,
0.20781390368938446,
-0.21705223619937897,
-0.20663432776927948,
-1.0792593955993652,
0.4132261872291565,
-0.9394000172615051,
0.13831208646297455,
-0.362098753452301,
1.1558092832565308,
-0.016789082437753677,
0.0642918273806572,
-0.9910421371459961,
-0.2089015394449234,
0.03636641055345535,
0.13128045201301575,
-0.0015651332214474678,
-0.1154899001121521,
0.3730522096157074,
0.11421673744916916,
0.3981197774410248,
-0.47376611828804016,
-0.5143774151802063,
1.4751923084259033,
0.4670778512954712,
-0.28983259201049805,
0.41086888313293457,
-0.470089316368103,
-1.1769905090332031,
-0.010664325207471848,
-1.1921186447143555,
0.1770898699760437,
-0.13223804533481598,
0.6677567362785339,
0.9236099123954773,
-0.6966463327407837,
0.5173365473747253,
0.017234165221452713,
-0.31118425726890564,
0.572268545627594,
-0.5779130458831787,
0.2819245755672455,
0.5068538784980774,
0.03267550840973854,
-0.5356367230415344,
0.5531018376350403,
-0.476203590631485,
-0.09620964527130127,
-0.38365620374679565,
0.1709960401058197,
0.6424014568328857,
-0.6680163741111755,
0.17824964225292206,
-0.11083546280860901,
-0.6690554618835449,
-0.623431921005249,
0.26937156915664673,
-0.6580949425697327,
-0.11780701577663422,
0.2588442862033844,
-0.4538339674472809,
-0.6009096503257751,
-0.7530518770217896,
0.42233845591545105,
0.11013586819171906,
-0.13784292340278625,
0.3931887745857239,
0.26468002796173096,
0.037296492606401443,
0.30381765961647034,
-0.10619458556175232,
-0.3061292767524719,
-0.11134736984968185,
0.9797360301017761,
0.887454092502594,
0.41047003865242004,
-0.14714743196964264,
-0.22677278518676758,
-0.4219638407230377,
0.719694972038269,
-0.031861912459135056,
-1.4376145601272583,
-0.1305481493473053,
0.8019835352897644,
-0.014657038263976574,
-0.523600697517395,
0.5281654596328735,
-1.0373139381408691,
-0.8183265924453735,
-0.09272721409797668,
-0.5448331832885742,
0.2799080014228821,
-0.3738544285297394,
-0.12563420832157135,
-1.3275171518325806,
0.26830536127090454,
0.02909880504012108,
0.12175807356834412,
-0.006762158125638962,
-0.606127917766571,
1.1571898460388184,
0.3082989752292633,
0.8464597463607788,
-0.47088271379470825,
0.03445776551961899,
-0.3874994218349457,
0.1885969340801239,
0.2527637779712677,
-1.1158229112625122,
-0.2195414900779724,
-0.10516182333230972,
0.6890000104904175,
-0.27400168776512146,
0.49981799721717834,
-1.018906831741333,
-0.6600902080535889,
-0.5009011626243591,
-0.5988262891769409,
0.5007696747779846,
0.7557653188705444,
0.050715018063783646,
0.1921778917312622,
-0.8963577151298523,
-0.8150118589401245,
-0.03193686902523041,
-0.022874286398291588,
0.7009261250495911,
-0.5271920561790466,
0.2801358103752136,
0.6475772261619568,
-0.6082510948181152,
0.38873493671417236,
0.1321437954902649,
0.5952439308166504,
0.39626556634902954,
-0.05848991125822067,
1.0681301355361938,
-0.3074599504470825,
-0.8911548256874084,
0.1356011927127838,
1.1242789030075073,
0.7361608743667603,
1.138975739479065,
0.6782184839248657,
-0.07434197515249252,
-0.005268591921776533,
-0.49835658073425293,
-0.626196026802063,
0.07292501628398895,
-0.15209972858428955,
-0.43469351530075073,
-0.3992388844490051,
0.28556743264198303,
-0.25708064436912537,
0.8250031471252441,
0.1175694465637207,
0.11954810470342636,
0.29670265316963196,
0.6091492176055908,
0.1462911069393158,
0.5897462368011475,
0.7654849290847778,
0.24576033651828766,
0.2637755572795868,
-0.3985273241996765,
0.18970200419425964,
0.10026572644710541,
-0.3197099566459656,
-0.35523349046707153,
-0.37885722517967224,
-0.14216406643390656,
-0.3144822418689728,
0.47694528102874756,
0.5694447755813599,
-0.9805101156234741,
0.9535652995109558,
-0.8084976077079773,
0.5157444477081299,
-0.17558780312538147,
-0.5386958718299866,
1.131486177444458,
0.4160843789577484,
0.32662665843963623,
-0.6288604140281677,
0.6890302896499634,
-0.3732151687145233,
0.12627863883972168,
-0.11968415975570679,
-1.3505693674087524,
-0.6485826373100281,
-0.4800708293914795,
0.2209375649690628,
-0.9236881732940674,
0.48165127635002136,
0.8665822744369507,
0.08529746532440186,
0.2815113961696625,
-0.6720876693725586,
-0.787391722202301,
0.12527546286582947,
-0.549940824508667,
-0.6209089159965515,
0.6877351999282837,
0.20329837501049042,
-0.21509870886802673,
0.8948229551315308,
0.22582794725894928,
-0.25203120708465576,
-0.2644970715045929,
-0.285230427980423,
0.3075718283653259,
-0.23624028265476227,
-0.3741467595100403,
-0.1754007339477539,
-0.39087632298469543,
-0.4753539264202118,
0.8005984425544739,
-0.14273644983768463,
-0.17999224364757538,
0.37952691316604614,
-0.329352468252182,
-0.45471063256263733,
-0.18463169038295746,
-0.10702501982450485,
0.27459803223609924,
0.5220442414283752,
0.6264071464538574,
0.341449499130249,
0.18366172909736633,
0.20129360258579254,
0.5950708985328674,
0.030994726344943047,
0.049435727298259735,
-0.018351437523961067,
0.20514598488807678,
-0.447316437959671,
-0.2555564045906067,
-0.41182979941368103,
-0.8973049521446228,
0.6451744437217712,
-0.5139241814613342,
0.9353978037834167,
0.04551972821354866,
-0.16782693564891815,
-0.1791945993900299,
-0.3517407476902008,
-0.5065505504608154,
0.4307345449924469,
-0.02441641502082348,
-0.6103370785713196,
0.796456515789032,
-0.7913724780082703,
0.289704829454422,
0.11963710188865662,
0.11554326862096786,
-0.32097870111465454,
0.11974403262138367,
0.5598021745681763,
-0.4848783314228058,
0.2878625988960266,
-1.1781914234161377,
0.5675540566444397,
-0.11928710341453552,
-0.012980914674699306,
-0.633581280708313,
-0.5105579495429993,
-0.018156832084059715,
-0.21120426058769226,
-0.03435168042778969,
0.17663098871707916,
-0.32625824213027954,
-0.3560769259929657,
-0.09974592179059982,
0.19535905122756958,
-0.1599753350019455,
0.005000756122171879,
-0.11358145624399185,
0.842854917049408,
0.049507226794958115,
-0.6361615061759949,
-0.0036323817912489176,
1.4517366886138916,
0.4487070143222809,
0.06803540140390396,
0.0025843987241387367,
-0.3307414948940277,
0.16392794251441956,
0.44494473934173584,
0.040941040962934494,
-0.3064139187335968,
-0.4868834912776947,
0.2178594321012497,
-0.3521925210952759,
0.8985415697097778,
0.5774977207183838,
-0.2421216070652008,
-0.6549246907234192,
-0.6716921329498291,
-0.6601057052612305,
0.38381221890449524,
0.2894228994846344,
-0.44723236560821533,
-0.5701550245285034,
-0.16209609806537628,
-0.6798422336578369,
0.8228926658630371,
0.05795632675290108,
0.28578031063079834,
0.1763313263654709,
0.5413067936897278,
0.4432418942451477,
0.670249342918396,
-0.11587747931480408,
-0.41469019651412964,
0.3794914782047272,
0.31812572479248047,
-0.35255348682403564,
0.6811602115631104,
-0.7044231295585632,
0.3742368519306183,
-1.3926706314086914,
0.9548664689064026,
-0.42074403166770935,
-0.19270570576190948,
0.3406374156475067,
-0.30688488483428955,
0.5511680841445923,
-0.6475348472595215,
0.7620158195495605,
0.7754737734794617,
-0.002717234194278717,
1.1489580869674683,
0.8369399905204773,
-0.31884047389030457,
-0.08006797730922699,
-0.743980884552002,
-1.0503331422805786,
0.45865651965141296,
0.23124349117279053,
-0.13765859603881836,
-0.7737709283828735,
-0.5964766144752502,
0.14127668738365173,
-0.14172427356243134,
0.5968745350837708,
0.6032370924949646,
0.14710795879364014,
0.2141186147928238,
0.39823171496391296,
-0.40101948380470276,
-0.18968304991722107,
-0.17514032125473022,
0.019813524559140205,
-0.34417465329170227,
-0.1734318882226944,
0.4257030487060547,
-0.8257538676261902,
-0.6923071146011353,
-0.10266762971878052,
0.5115562677383423,
0.37381643056869507,
-0.7114865779876709,
0.8455132246017456,
-0.027531137689948082,
-0.8850875496864319,
-0.2914954125881195,
-0.3899979591369629,
0.3256896734237671,
0.466555118560791,
0.23878145217895508,
-0.12570132315158844,
0.2764979600906372,
-0.3489445149898529,
0.6469184160232544,
0.19896799325942993,
-0.5242185592651367,
0.3547041714191437,
-0.5908527970314026,
-0.4440755844116211,
0.1889304518699646,
0.12206681072711945,
-0.5820983052253723,
-0.8710283041000366,
-0.6155661940574646,
0.42954039573669434,
-0.9324788451194763,
-0.6627368330955505,
0.08622468262910843,
-0.46741634607315063,
-0.45511797070503235,
0.5813911557197571,
0.8791665434837341,
-0.356193482875824,
-0.10635257512331009,
-0.29915472865104675,
-0.625921368598938,
-0.2635996341705322,
-0.630991518497467,
1.352811574935913,
0.18366403877735138,
-0.6098828315734863,
-0.5159013867378235,
-0.29282501339912415,
-0.13755805790424347,
0.17019958794116974,
0.13151617348194122,
-0.13643310964107513,
0.3151639699935913,
-0.5448840260505676,
0.3306482136249542,
0.8955844044685364,
1.2967674732208252,
0.4493418335914612,
-0.8344563245773315,
0.3577601909637451,
-0.9646940231323242,
0.10463978350162506,
-0.29551106691360474,
0.08803874254226685,
0.5107325911521912,
-0.05233468487858772,
0.49874237179756165,
-0.31758567690849304,
-0.7173086404800415,
-0.3499726355075836,
-1.2620038986206055,
0.40649932622909546,
-1.2491698265075684,
-0.1813739836215973,
-0.14832136034965515,
-0.571760892868042,
-0.000466661062091589,
0.4512318968772888,
0.4008181393146515,
0.1647278368473053,
-0.8027894496917725,
0.5502442717552185,
0.5709168910980225,
0.20373545587062836,
-0.46371546387672424,
-0.7179588079452515,
-0.3058040142059326,
-0.4095797538757324,
-0.7634641528129578,
-0.28624290227890015,
-0.027777399867773056,
0.3212380111217499,
-0.12401823699474335,
-0.3589804172515869,
-0.08778349310159683,
1.0189883708953857,
-1.1630799770355225,
-0.5439286828041077,
0.4496011734008789,
-0.7891687750816345,
-0.6630697250366211,
0.5041990280151367,
0.1577308028936386,
0.46148476004600525,
0.7489956617355347,
0.17657820880413055,
-0.9194179773330688,
0.23545336723327637,
-1.0424201488494873,
0.01905917003750801,
0.663621723651886,
0.6585966348648071,
-0.17895793914794922,
-0.08641795814037323,
-0.22094343602657318,
-0.028495188802480698,
-0.8604499101638794,
0.4011772871017456,
-0.326823353767395,
-0.02664041891694069,
-0.4500404894351959,
0.3808649778366089,
0.5341362357139587,
0.6575506925582886,
-0.5218786597251892,
0.49085041880607605,
-0.19270920753479004,
-0.24403278529644012,
0.4315505027770996,
-0.12796106934547424,
-0.599984884262085,
0.1452658623456955,
0.41927826404571533,
-0.39923039078712463,
0.12003704160451889,
1.0443240404129028,
-0.08791747689247131,
0.4390641450881958,
-0.06241960451006889,
-0.2801191508769989,
-0.08072483539581299,
-0.6236926317214966,
-0.6380622386932373,
0.5037561058998108,
-0.16281089186668396,
-0.9421300292015076,
-0.30853384733200073,
-0.7274570465087891,
-0.48730364441871643,
0.21147772669792175,
-0.13838161528110504,
-0.4076736569404602,
-0.12705223262310028,
0.373274028301239,
-0.1743241548538208,
-0.0903143435716629,
0.10576440393924713,
0.37624719738960266,
0.1733829528093338,
0.4227127432823181,
-0.882131040096283,
-0.20469142496585846,
-0.011061377823352814,
-0.2857185900211334,
-0.9696224927902222,
0.10051035135984421,
-0.1354902982711792,
0.9596513509750366,
-0.6996375918388367,
-0.5004116296768188,
0.044997893273830414,
0.9782598614692688,
0.4786469638347626,
0.001789749483577907,
-0.7200325727462769,
0.3565543293952942,
-0.07398940622806549,
-0.4423049986362457,
-0.1342635601758957,
-0.2922888398170471,
-0.5436577796936035,
0.5347188115119934,
0.07875198125839233,
-0.7981755137443542,
0.20499011874198914,
0.25910133123397827,
-0.053560178726911545,
-0.04504188522696495,
-0.4842088222503662,
0.9724754095077515,
0.3311128318309784,
-0.04490968585014343,
0.7557331323623657,
0.08082111179828644,
0.018418019637465477,
0.006796891801059246,
-0.46253758668899536,
0.14364853501319885,
0.1618640422821045,
0.3049534857273102,
0.3821604549884796,
0.07409939169883728,
0.274081826210022,
0.49713289737701416,
0.7605012059211731,
0.4473987817764282,
-0.2422572374343872,
0.3578180968761444,
0.21158024668693542,
0.5056723356246948,
0.1370438188314438,
0.004944475833326578,
0.71969074010849,
0.4288657009601593,
-0.2588176727294922,
-0.46918079257011414,
-0.4067617654800415,
0.2479761391878128,
0.07106436789035797,
0.13121122121810913,
-0.6756523847579956,
-0.1846882402896881,
0.08454112708568573,
-0.03437335789203644,
0.34367835521698,
-0.15489676594734192,
0.10239602625370026,
0.5217951536178589,
0.36240848898887634,
0.7258485555648804,
-0.048766784369945526,
0.5664832592010498,
0.2936938405036926,
0.8394949436187744,
0.22033897042274475,
0.9168533682823181,
0.9602731466293335,
0.6362517476081848,
0.4859570860862732,
-0.48894941806793213,
-0.07566557079553604,
0.5134835839271545,
-1.0284911394119263,
-0.04681839048862457,
-0.5271531343460083,
0.014828707091510296,
-0.3641602396965027,
-0.8414543271064758,
0.10292381048202515,
-0.29049426317214966,
0.08153004199266434,
0.44843682646751404,
-0.15022020041942596,
0.17370495200157166,
0.9148064255714417,
-0.4261164963245392,
0.14433467388153076,
0.6881681680679321,
-0.508651614189148,
0.2853846251964569,
0.8254180550575256,
1.327640414237976,
0.07354755699634552,
0.3614484965801239,
0.47788411378860474,
-0.4296134412288666,
-0.03542669489979744,
0.3016180098056793,
-0.23260320723056793,
0.8638507723808289,
-1.0169848203659058,
0.10171592235565186,
0.15572857856750488,
0.016703298315405846,
-0.4975999593734741,
0.17863932251930237,
0.2898038625717163,
-0.31689056754112244,
-0.7451244592666626,
-0.8888174891471863,
1.5774316787719727,
0.6019149422645569,
-0.30167627334594727,
-0.07291153818368912,
0.059039294719696045,
-0.30427828431129456,
-0.4940052926540375,
-0.37078335881233215,
0.5986723899841309,
0.272106796503067,
-0.3353334665298462,
-0.1866384744644165,
-0.6775139570236206,
-0.4052036702632904,
-0.514136791229248,
0.07368730008602142,
-0.8527774214744568,
0.3172334134578705,
0.6481911540031433,
0.6126936078071594,
0.11145491153001785,
-0.7658259272575378,
-0.26189082860946655,
0.3706735074520111,
0.9451897740364075,
0.3401573896408081,
0.37875786423683167,
1.3563921451568604,
0.14515729248523712,
-0.41592612862586975,
0.13586962223052979,
0.5741506814956665,
-0.7079986929893494,
0.6058877110481262,
-0.2827068865299225,
0.2203092873096466,
0.2195255309343338,
-0.3466654419898987,
0.1748736947774887,
0.14425179362297058,
0.4201395809650421,
-0.5312730669975281,
-0.25943076610565186,
0.08293937146663666,
-0.7405322194099426,
0.21954874694347382,
-0.38964173197746277,
0.10612840205430984,
0.7288321256637573,
0.3095415532588959,
-0.09153120219707489,
-0.46531906723976135,
4.086305141448975,
0.5802918076515198,
0.6724207997322083,
-0.06940698623657227,
0.540766716003418,
0.2169233113527298,
0.15865975618362427,
-0.7559548616409302,
0.354530930519104,
-0.09953770786523819,
-0.3487139344215393,
0.08108757436275482,
0.4690805673599243,
-0.8083987832069397,
-0.12375608086585999,
0.7947037816047668,
-0.1712392419576645,
-0.22468943893909454,
0.8268042206764221,
-0.9511422514915466,
-0.7524815201759338,
0.14207173883914948,
0.3096969723701477,
-0.21618591248989105,
0.21474194526672363,
-0.14312896132469177,
0.3819786012172699,
-0.7846487760543823,
-0.52536541223526,
-0.39095839858055115,
-0.7654619216918945,
-0.8446022868156433,
0.1943589597940445,
-0.014753611758351326,
-0.4735988676548004,
0.8200152516365051,
1.1055176258087158,
-0.4497576951980591,
-0.14892075955867767,
0.19322192668914795,
-0.11182373017072678,
-0.2628212869167328,
0.2325967699289322,
-0.29570069909095764,
-0.12054857611656189,
1.0857750177383423,
-0.07059455662965775,
0.6528911590576172,
-0.16410155594348907,
-0.5079050064086914,
-0.021577375009655952,
-0.5291624069213867,
0.39300405979156494,
-0.38093456625938416,
-1.1089246273040771,
-0.22139205038547516,
-0.7072610855102539,
-0.039610207080841064,
0.3265937268733978,
-0.16712801158428192,
0.4955281615257263,
-0.048751167953014374,
0.09354192763566971,
0.2529695928096771,
-0.501551628112793,
-0.016727132722735405,
0.5072498917579651,
0.059346944093704224,
0.08735871315002441,
0.18933738768100739,
-0.1841277927160263,
-0.5572660565376282,
-0.20976890623569489,
0.4596561789512634,
0.34924590587615967,
-0.17597579956054688,
-0.3385591208934784,
0.5489459037780762,
0.44710347056388855,
-0.030944760888814926,
0.4642789959907532,
-0.22041399776935577,
-0.3786787986755371,
-0.10664629936218262,
-0.504315197467804,
0.5978313088417053,
-0.2331462949514389,
-0.47433072328567505,
-0.08999833464622498,
0.2321980595588684,
0.35301193594932556,
0.9305731654167175,
0.4139380156993866,
-0.2770638167858124,
-0.6015634536743164
] |
The Interface Tension in Quenched QCD at the Critical Temperature
|
We present results for the confinement-deconfinement interface tension $\alpha_{cd}$ of quenched QCD. They were obtained by applying Binder's histogram method to lattices of size $L^2\times L_z\times L_t$ for $L_t=2$ and $L=8,10,12\mbox{ and }14$ with $L_z=30$ for $L=8$ and $L_z=3L$ otherwise. The use of a multicanonical algorithm and cylindrical geometries have turned out to be crucial for the numerical studies.
|
B. Grossmann, M. L. Laursen, T. Trappenberg, U. J. Wiese
|
hep-lat
|
October
| 1,992 |
https://arxiv.org/abs/hep-lat/9210041
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.