# (a) Logarithm of the average sign divided by xi and particel number ('y'), as a function of xi ('x'). # Shaded areas showing the extrapolation. # N = 14 # x,y 0.01,0.03490385462774 0.01,0.0347677376230672 0.02,0.0347677379472986 0.05,0.0347677389199666 0.1,0.0347677405409981 0.2,0.0347677437827522 0.4,0.0347677502650251 0.6,0.0347677567456517 0.8,0.0347677632246329 1,0.0347677697019691 1,0.0349038867478295 1,0.0349038867478295 0.8,0.0349038802556641 0.6,0.0349038737651493 0.4,0.0349038672762842 0.2,0.0349038607890682 0.1,0.0349038575460784 0.05,0.034903855924738 0.02,0.0349038549519834 0.01,0.03490385462774 # Shaded areas showing the extrapolation. # N = 30 # x,y 0.01,0.03547780609473 0.01,0.0353533976023676 0.02,0.0353533981827509 0.05,0.035353399923815 0.1,0.0353534028252997 0.2,0.0353534086271866 0.4,0.0353534202266321 0.6,0.0353534318203107 0.8,0.0353534434082272 1,0.0353534549903866 1,0.0354778636271496 1,0.0354778636271496 0.8,0.0354778519930008 0.6,0.0354778403646481 0.4,0.0354778287420865 0.2,0.0354778171253112 0.1,0.0354778113190919 0.05,0.0354778084165241 0.02,0.0354778066751569 0.01,0.03547780609473 # Shaded areas showing the extrapolation. # N = 66 # x,y 0.01,0.0361154910516464 0.01,0.0359817042831991 0.02,0.0359817057597281 0.05,0.0359817101887931 0.1,0.0359817175688306 0.2,0.0359817323223939 0.4,0.0359817618035032 0.6,0.0359817912499801 0.8,0.0359818206618933 1,0.0359818500393111 1,0.0361156376769343 1,0.0361156376769343 0.8,0.0361156079865795 0.6,0.0361155783312727 0.4,0.0361155487109441 0.2,0.0361155191255243 0.1,0.0361155043458834 0.05,0.0361154969593265 0.02,0.036115492528436 0.01,0.0361154910516464 # Shaded areas showing the extrapolation. # N = 132 # x,y 0.01,0.0363775962580124 0.01,0.0362160376188768 0.02,0.0362160419246555 0.05,0.0362160548383202 0.1,0.0362160763488655 0.2,0.0362161193241627 0.2,0.0363776782076027 0.2,0.0363776782076027 0.1,0.0363776350486179 0.05,0.0363776134921508 0.02,0.0363776005656281 0.01,0.0363775962580124 # Shaded areas showing the extrapolation. # N = 264 # x,y 0.01,0.0365901557335163 0.01,0.0364063909485932 0.02,0.0364064020871224 0.05,0.0364064354811161 0.1,0.03640649106591 0.1,0.0365902562076539 0.1,0.0365902562076539 0.05,0.036590200352541 0.02,0.0365901668828582 0.01,0.0365901557335163 # Shaded areas showing the extrapolation. # N = 528 # x,y 0.01,0.0366615453597072 0.01,0.0364125555172469 0.02,0.0364125963808259 0.05,0.0364127187572382 0.1,0.0364129220066632 0.1,0.0366619153995283 0.1,0.0366619153995283 0.05,0.0366617094603859 0.02,0.0366615863308715 0.01,0.0366615453597072 # Shaded areas showing the extrapolation. # N = 1000 # x,y 0.01,0.0368526628980649 0.01,0.0364377761746809 0.02,0.0364379904483524 0.05,0.0364386297426531 0.05,0.0368535307499073 0.05,0.0368535307499073 0.02,0.0368528789571234 0.01,0.0368526628980649 # Markers with limits for the lower (y_low) and upper (y_upper) error bars # N = 14 # x,y,y_lower,y_upper 0.01,0.034915137936186,0.0347335174124074,0.0350967584599645 0.02,0.0349664545644158,0.0348258489087654,0.0351070602200662 0.05,0.0348770507732819,0.0347861491176237,0.0349679524289402 0.1,0.0349004182381646,0.0348287922197168,0.0349720442566123 0.2,0.0348357958011664,0.0347677372988322,0.0349038543035007 0.4,0.0349020549403412,0.0348492866616076,0.0349548232190749 0.6,0.0349614078999265,0.0349177543806055,0.0350050614192476 0.8,0.0350383254760998,0.0350020222140815,0.0350746287381181 1.0,0.0351768319062535,0.0351404421480617,0.0352132216644453 # N = 30 # x,y,y_lower,y_upper 0.01,0.0354535466276928,0.0352648025881365,0.0356422906672491 0.02,0.0354017291650188,0.0352669999845355,0.0355364583455021 0.05,0.0352904283693292,0.0351865752128428,0.0353942815258156 0.1,0.0353915301484579,0.0353236307915986,0.0354594295053171 0.2,0.0354156012681434,0.0353533970219694,0.0354778055143174 0.4,0.0354183102552405,0.0353672961653255,0.0354693243451555 0.6,0.0354612571014685,0.03541676142908,0.035505752773857 0.8,0.0354710227433064,0.0354262232558518,0.035515822230761 1.0,0.0355676176802289,0.0355209109404236,0.0356143244200342 # N = 66 # x,y,y_lower,y_upper 0.01,0.0359539763105702,0.0357093478856993,0.0361986047354411 0.02,0.0360479356378344,0.0358590447473708,0.036236826528298 0.05,0.0361208662730975,0.0359962198886918,0.0362455126575031 0.1,0.0360169633525693,0.0359344100396149,0.0360995166655237 0.2,0.0360485961907636,0.0359817028065835,0.0361154895749437 0.4,0.0361308069462353,0.0360570776919327,0.0362045362005379 0.6,0.0361384090495277,0.0360709102086883,0.0362059078903671 0.8,0.0361314225441902,0.0360483395679798,0.0362145055204006 1.0,0.0361406453674975,0.0360605937273321,0.0362206970076629 # N = 132 # x,y,y_lower,y_upper 0.01,0.0362993445508927,0.0360716417107229,0.0365270473910625 0.02,0.036299328853189,0.0361384956524319,0.0364601620539462 0.05,0.0363889552243014,0.0362823774938692,0.0364955329547337 0.1,0.0362968126317477,0.036216033312486,0.0363775919510094 0.2,0.0364446512360516,0.0363718482947457,0.0365174541773575 # N = 264 # x,y,y_lower,y_upper 0.01,0.0364740410080801,0.0362590526521598,0.0366890293640004 0.02,0.0365231015564107,0.0363701111518936,0.0366760919609277 0.05,0.0365427134567485,0.0364297576367286,0.0366556692767684 0.1,0.0364982621971211,0.0364063798064617,0.0365901445877805 # N = 528 # x,y,y_lower,y_upper 0.01,0.0362924730885947,0.0360872152724396,0.0364977309047498 0.02,0.0365160134076743,0.0363644584163003,0.0366675683990483 0.05,0.0365566040099988,0.0364369246974224,0.0366762833225753 0.1,0.0365370095211586,0.0364125146178593,0.0366615044244578 # N = 1000 # x,y,y_lower,y_upper 0.01,0.0366811899369198,0.036416489582421,0.0369458902914186 0.02,0.0366450043727857,0.0364375613086551,0.0368524474369163 0.05,0.0367950584695495,0.0365775656527115,0.0370125512863875 # (b) Difference in free energy between PIMC results and the GDSMFB parametrisation in Hartree ('y'), as a function of inverse particle number ('x'). # Markers with limits for the lower (y_low) and upper (y_upper) error bars # Accelerated, xi = -1, P = 100 # x,y,y_low,y_upper 0.0714285714285714,0.000153182650640744,0.000152209099244431,0.000154156202037058 0.0333333333333333,5.99064059564405e-05,5.8952271121575e-05 ,6.08605407913061e-05 0.0151515151515152,2.11316161032385e-05,1.94841747696671e-05,2.27790574368099e-05 # Accelerated, xi = -0.2, P = 100 # x,y,y_low,y_upper 0.0714285714285714,0.000146902183353385,0.000145463572273186,0.000148340794433585 0.0333333333333333,5.71068956142576e-05,5.58891945832065e-05,5.83245966453086e-05 0.0151515151515152,1.94364529381638e-05,1.80017697688863e-05,2.08711361074413e-05 # Accelerated, xi > -1, P = 20 # x,y,y_low,y_upper 0.0151515151515152,1.98161918472106e-05,1.77800899750406e-05 ,2.18522937193806e-05 0.00757575757575758,3.08751813631047e-06,1.54481312926647e-06 ,4.63022314335448e-06 0.00378787878787879,-1.12614322547722e-07,-1.81941382773525e-06,1.59418518263981e-06 0.00189393939393939,-8.08223083813286e-06,-1.05676896219715e-05,-5.59677205429427e-06 0.001,-3.25967155721807e-06,-7.18650038091824e-06,6.67157266482098e-07 # Accelerated, xi > -1, P = 8 # x,y,y_low,y_upper 0.00378787878787879,-1.14940346030989e-05,-1.34418136017183e-05,-9.54625560447957e-06 0.00189393939393939,-1.5801310676751e-05,-1.88890776000083e-05,-1.27135437534937e-05 0.001,-1.58531078417665e-05,-2.12120066039857e-05,-1.04942090795473e-05 # Fitted line # x,y 0.0007,-6.73530055152888e-06 0.00105541995692749,-6.25576924152133e-06 0.00141083991385499,-5.75360294919475e-06 0.00176625987078248,-5.23395453060765e-06 0.00212167982770998,-4.69995936373813e-06 0.00247709978463747,-4.15374353997244e-06 0.00283251974156497,-3.59685110942753e-06 0.00318793969849246,-3.03045813516284e-06 0.00354335965541996,-2.45549241775084e-06 0.00389877961234745,-1.87270594497607e-06 0.00425419956927495,-1.28272141734775e-06 0.00460961952620244,-6.86063549810989e-07 0.00496503948312993,-8.3180936576166e-08 0.00532045944005743,5.255381958294e-07 0.00567587939698492,1.1397543403513e-06 0.00603129935391242,1.75916790388919e-06 0.00638671931083991,2.3835124225019e-06 0.00674213926776741,3.01254924615219e-06 0.0070975592246949,3.64606331339223e-06 0.0074529791816224,4.28385974864803e-06 0.00780839913854989,4.92576109024229e-06 0.00816381909547739,5.57160500857384e-06 0.00851923905240488,6.22124241014821e-06 0.00887465900933237,6.87453584871656e-06 0.00923007896625987,7.5313581834463e-06 0.00958549892318736,8.19159143759796e-06 0.00994091888011486,8.85512582143866e-06 0.0102963388370424,9.52185889065149e-06 0.0106517587939698,1.01916948174463e-05 0.0110071787508973,1.08645437559909e-05 0.0113625987078248,1.15403212872719e-05 0.0117180186647523,1.22189479313389e-05 0.0120734386216798,1.29003487168294e-05 0.0124288585786073,1.35844527996698e-05 0.0127842785355348,1.42711931240339e-05 0.0131396984924623,1.49605061197863e-05 0.0134951184493898,1.56523314316856e-05 0.0138505384063173,1.6346611676217e-05 0.0142059583632448,1.70432922225738e-05 0.0145613783201723,1.77423209949193e-05 0.0149167982770998,1.84436482932732e-05 0.0152722182340273,1.91472266309889e-05 0.0156276381909548,1.98530105868927e-05 0.0159830581478823,2.05609566703707e-05 0.0163384781048098,2.12710231981481e-05 0.0166938980617373,2.19831701814346e-05 0.0170493180186647,2.26973592223484e-05 0.0174047379755922,2.34135534187205e-05 0.0177601579325197,2.41317172764224e-05 0.0181155778894472,2.48518166285211e-05 0.0184709978463747,2.55738185604981e-05 0.0188264178033022,2.62976913411039e-05 0.0191818377602297,2.70234043582701e-05 0.0195372577171572,2.77509280595598e-05 0.0198926776740847,2.84802338968854e-05 0.0202480976310122,2.92112942749875e-05 0.0206035175879397,2.99440825034525e-05 0.0209589375448672,3.06785727519215e-05 0.0213143575017947,3.14147400082496e-05 0.0216697774587222,3.21525600393419e-05 0.0220251974156497,3.28920093545029e-05 0.0223806173725772,3.36330651710612e-05 0.0227360373295047,3.437570538211e-05 0.0230914572864322,3.51199085261988e-05 0.0234468772433596,3.58656537588209e-05 0.0238022972002871,3.66129208256016e-05 0.0241577171572146,3.73616900370133e-05 0.0245131371141421,3.81119422445259e-05 0.0248685570710696,3.88636588180974e-05 0.0252239770279971,3.96168216249548e-05 0.0255793969849246,4.03714130094365e-05 0.0259348169418521,4.11274157740352e-05 0.0262902368987796,4.18848131613428e-05 0.0266456568557071,4.26435888370019e-05 0.0270010768126346,4.34037268735241e-05 0.0273564967695621,4.41652117348992e-05 0.0277119167264896,4.49280282620521e-05 0.0280673366834171,4.56921616589431e-05 0.0284227566403446,4.64575974793852e-05 0.0287781765972721,4.72243216145043e-05 0.0291335965541996,4.79923202807847e-05 0.0294890165111271,4.87615800087021e-05 0.0298444364680546,4.95320876318234e-05 0.030199856424982,5.03038302765227e-05 0.0305552763819095,5.10767953520383e-05 0.030910696338837,5.18509705410494e-05 0.0312661162957645,5.26263437906974e-05 0.031621536252692,5.34029033039049e-05 0.0319769562096195,5.41806375311746e-05 0.032332376166547,5.49595351626853e-05 0.0326877961234745,5.57395851207287e-05 0.033043216080402,5.65207765524656e-05 0.0333986360373295,5.73030988230139e-05 0.033754055994257,5.80865415087742e-05 0.0341094759511845,5.88710943910734e-05 0.034464895908112,5.96567474500029e-05 0.0348203158650395,6.04434908585763e-05 0.035175735821967,6.12313149770741e-05 0.0355311557788945,6.20202103476103e-05 0.035886575735822,6.28101676889078e-05 0.0362419956927495,6.36011778913093e-05 0.0365974156496769,6.43932320119264e-05 0.0369528356066044,6.51863212700055e-05 0.0373082555635319,6.59804370424649e-05 0.0376636755204594,6.67755708595591e-05 0.0380190954773869,6.75717144007631e-05 0.0383745154343144,6.83688594907486e-05 0.0387299353912419,6.91669980955531e-05 0.0390853553481694,6.99661223188194e-05 0.0394407753050969,7.07662243982499e-05 0.0397961952620244,7.15672967021089e-05 0.0401516152189519,7.23693317259133e-05 0.0405070351758794,7.31723220891711e-05 0.0408624551328069,7.39762605322727e-05 0.0412178750897344,7.47811399134865e-05 0.0415732950466619,7.55869532060305e-05 0.0419287150035894,7.63936934952622e-05 0.0422841349605169,7.72013539759517e-05 0.0426395549174444,7.80099279496377e-05 0.0429949748743719,7.88194088220881e-05 0.0433503948312993,7.96297901008158e-05 0.0437058147882268,8.04410653927057e-05 0.0440612347451543,8.12532284016759e-05 0.0444166547020818,8.2066272926451e-05 0.0447720746590093,8.28801928583756e-05 0.0451274946159368,8.36949821793054e-05 0.0454829145728643,8.45106349595878e-05 0.0458383345297918,8.53271453560359e-05 0.0461937544867193,8.61445076100406e-05 0.0465491744436468,8.69627160456979e-05 0.0469045944005743,8.77817650679902e-05 0.0472600143575018,8.86016491610381e-05 0.0476154343144293,8.94223628863794e-05 0.0479708542713568,9.02439008813316e-05 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