changed figures to screenshot pngs for publication, added first two proof responses

17 files changed, 216 insertions, 131 deletions

diff --git a/data/correlation-times/heisenberg-pert.dat b/data/correlation-times/heisenberg-pert.dat
index 453bf29..11a6708 100644
--- a/data/correlation-times/heisenberg-pert.dat
+++ b/data/correlation-times/heisenberg-pert.dat
@@ -94,7 +94,11 @@ L T H S dS t dt
 64 1.44325 0.1 26715.47363923077 21.80487027547604 29.00819256963733 0.259179815903674
 64 1.44325 0.316228 40918.33412611247 53.44529134484493 19.35207659063876 0.2623871123313593
 64 1.44325 1. 59423.18256666666 91.2124821915958 14.134628333514 0.2254659063928293
-64 1.44325 3.16228 78169.3047970735 109.5910776495144 11.7916228640994 0.1795640697908674
+64 1.44325 3.16228 78178.42510444445 104.8711082079363 11.82233463125535 0.172225984816705
+64 1.44325 10. 91799.0396016667 111.8491401562014 11.32359167603755 0.1614687527581651
+64 1.44325 31.6228 98962.2382805556 114.957238719823 11.95176536179842 0.1750207168240775
+64 1.44325 100.00000000000000 101360.5539005555 116.425037100599 12.34166260511696 0.1835181206186158
+64 1.44325 316.22800000000001 102192.1287144444 116.7615224486451 12.22849507049797 0.1809192885201424
 
 128 1.44325 0.000000316228 7737.228152685185 16.90610371681803 1123.445680245412 64.82071362726517
 128 1.44325 0.000001 7754.873250648148 16.92685698104313 1187.671897559639 70.45852340665157
@@ -108,7 +112,9 @@ L T H S dS t dt
 128 1.44325 0.01 84967.1990766219 119.8358076762023 76.87003100807919 1.448480554724095
 128 1.44325 0.0316228 135695.7818519379 174.6112812112161 45.75321854444867 0.6998345919725421
 128 1.44325 0.1 213940.2132357407 256.7359332775548 29.38143847530791 0.3888854931979229
-128 1.44325 0.316228 327275.0013575393 596.631309888479 19.2179982993354 0.3632700133337567
+128 1.44325 0.316228 327384.4816485203 364.2243557915442 19.28372595044302 0.2231437270097496
+128 1.44325 1. 474888.1638680555 515.5750645909047 14.15018448147361 0.1596039335300559
+128 1.44325 3.16228 624512.3048810776 2148.029291068525 12.24414558112792 0.4644791443652886
 
 256 1.44325 0.000000316228 25736.69038793651 91.8985860154056 2791.11662581606 332.3358588203989
 256 1.44325 0.000001 25865.246304435 93.5631403192945 3088.096806649422 392.7536435871764
diff --git a/data/correlation-times/ising-3d.dat b/data/correlation-times/ising-3d.dat
index 82e6e4b..c61be7f 100644
--- a/data/correlation-times/ising-3d.dat
+++ b/data/correlation-times/ising-3d.dat
@@ -107,8 +107,9 @@ L T H S dS t dt
 128 4.511527855977594 0.01 301694.4733388888 406.8419887651353 9.48094645387296 0.1236164178513723
 128 4.511527855977594 0.0316228 473657.9822633333 525.0969096566845 5.389503259615959 0.05359477938196742
 128 4.511527855977594 0.0316228 473810.393276046 248.1637429922758 5.42504130501244 0.02550335499361629
-128 4.511527855977594 0.1 731433.3788871951 2860.376016181089 3.182539211446089 0.1081211753987908
+128 4.511527855977594 0.1 731299.9300727776 640.9139736832347 3.239029081137422 0.02485601643215623
 128 4.511527855977594 0.1 734327.7342035004 2627.63536024904 3.111575662928636 0.0956810839001747
+128 4.511527855977594 0.316228 1092608.251198789 737.0740922945666 2.041937385008792 0.01312848887246472
 
 256 4.511527855977594 0.000000316228 82326.9296077778 319.4289551490305 573.2942361728692 47.26217758244279
 256 4.511527855977594 0.000000316228 83676.2395361383 169.1673003995497 612.3878284881115 27.35407014627743
@@ -120,10 +121,12 @@ L T H S dS t dt
 256 4.511527855977594 0.00001 147087.6588092692 479.9962585092091 327.3747097315912 22.55770765664332
 256 4.511527855977594 0.0000316228 230428.5631922222 486.8113385046164 173.2844082931849 6.803849975774163
 256 4.511527855977594 0.0000316228 231241.4835405555 690.9766473805729 176.0991408063061 9.85561024324474
+256 4.511527855977594 0.0001 369028.6550261111 941.702087960847 96.2946060508223 3.987160049091943
 256 4.511527855977594 0.0001 369087.7374438083 718.7006424051432 101.5480026056146 3.299456635565838
-256 4.511527855977594 0.0001 369196.0151928154 976.612635513245 95.5959996997236 4.089854341175419
 256 4.511527855977594 0.000316228 590683.7955970371 1060.473562168052 54.39261407562467 1.383184676028584
+256 4.511527855977594 0.000316228 592311.5359683332 1302.133803980267 54.60144596511925 1.702499196866055
 256 4.511527855977594 0.001 950330.768211111 1463.132604002818 29.91433293330963 0.5646573385300568
+256 4.511527855977594 0.001 951587.569987586 2194.226838599926 29.64503664083455 0.835218222124276
 256 4.511527855977594 0.00316228 1518083.428362593 1989.973570134875 16.40983160170885 0.2299112258581515
 256 4.511527855977594 0.01 2413324.488125926 2656.083630611885 9.3475907760363 0.0988601535681594
 256 4.511527855977594 0.0316228 3792312.713659259 3425.023162600829 5.423172991232216 0.04403333477215846
diff --git a/data/correlation-times/planar-pert.dat b/data/correlation-times/planar-pert.dat
index 2ccec13..bc77d28 100644
--- a/data/correlation-times/planar-pert.dat
+++ b/data/correlation-times/planar-pert.dat
@@ -95,7 +95,10 @@ L T H S dS t dt
 64 2.20167 0.316228 35933.31660075755 30.88345734518931 15.15142210917954 0.1073565791694017
 64 2.20167 1. 50606.28575944444 89.1466719237892 10.68145598672134 0.1480922229384029
 64 2.20167 3.16228 63704.62395722223 101.0098549493077 8.51251505306987 0.1057898590051419
-64 2.20167 10. 71410.76213111084 107.7599856696656 7.352799320594897 0.0861594304905618
+64 2.20167 10. 71397.74830888889 105.6618410605934 7.357428920585185 0.0846015463363678
+64 2.20167 31.6228 75199.50434111112 107.964370675161 7.180540181497009 0.0818707545387979
+64 2.20167 100.00000000000000 76707.92809277778 108.7249166938582 7.246912454553089 0.0826275148852631
+64 2.20167 316.22800000000001 77157.93556555556 109.1081360905099 7.335826424468737 0.0843531437223699
 
 128 2.20167 0.000000316228 7527.854320777777 19.50849171413825 -75976.3161699774 2964.0502259161
 128 2.20167 0.000001 7538.854289333332 19.50017544269328 -75948.54995229473 2962.966987507817
@@ -109,9 +112,9 @@ L T H S dS t dt
 128 2.20167 0.01 77443.98246963894 125.6055697399933 62.13503566497229 1.118106664511062
 128 2.20167 0.0316228 122669.8183904444 203.5036254771335 38.14850919537809 0.6296751423808226
 128 2.20167 0.1 190667.6108136287 291.7886591363135 23.07654320955112 0.3126733623245518
-128 2.20167 0.316228 287458.3309478462 419.6784317777746 15.03185342789501 0.1803264687718583
-128 2.20167 1. 405817.1447283935 1937.631163500249 10.6933239895578 0.3984654753072863
-128 2.20167 316.22800000000001 617703.4864595631 3194.702407616145 6.727261293892746 0.269814227605772
+128 2.20167 0.316228 287570.2883569078 407.2319350402718 15.01323467314337 0.1747006602170654
+128 2.20167 1. 404877.0795609374 668.6356932130861 10.85446305527562 0.1418573650902887
+128 2.20167 3.16228 508679.5390603988 839.430996413746 8.70801442293849 0.1133030630544888
 
 256 2.20167 0.000000316228 32673.96623873016 117.6679461163064 -374609.6316784495 17467.76118186272
 256 2.20167 0.000001 33056.5226631746 118.4688764648069 -374494.7461492168 17462.40415732789
@@ -120,4 +123,6 @@ L T H S dS t dt
 256 2.20167 0.0000316228 64039.33107256288 208.7387164186404 -538832.345218083 27671.5363891305
 256 2.20167 0.0001 97104.8274691111 304.4665277469609 -657778.3321377984 36291.24667734729
 256 2.20167 0.000316228 152906.2809616713 469.4261725061255 316.4923960371564 16.59776809188589
-256 2.20167 0.001 244362.5787809288 901.64250150279 202.8466949694594 11.59792325741977
\ No newline at end of file
+256 2.20167 0.001 244129.432726446 708.0221334683237 194.0467594365449 8.53046871194669
+256 2.20167 0.00316228 389050.652325 1325.904655763318 108.9683248187532 4.798182201520612
+256 2.20167 0.01 620755.3948297273 3596.829319089289 62.89993681202724 4.078675238537467
diff --git a/data/harmonic-susceptibilities/order-4.dat b/data/harmonic-susceptibilities/order-4.dat
index 6771ad9..af47238 100644
--- a/data/harmonic-susceptibilities/order-4.dat
+++ b/data/harmonic-susceptibilities/order-4.dat
@@ -7,7 +7,7 @@ H T L X dX
 0.00000001 0.7 64 4.957742422694277 0.02438117097171551
 0.00000001 0.7 128 17.7962626495225 0.3262798939933926
 0.00000001 0.7 256 63.64728674037386 1.126290310101313
-0.00000001 0.7 512 230.3869649315519 3.771341028200669
+0.00000001 0.7 512 230.5842010800137 3.483701050008471
 0.00000001 0.7 1024 828.916205514522 13.95459042173237
 0.00000001 0.7 2048 2999.630395848571 49.49145603697337
 
@@ -18,9 +18,9 @@ H T L X dX
 0.0000000316228 0.7 64 4.969745346592 0.02448929190416269
 0.0000000316228 0.7 128 17.6564206002435 0.3084190661079949
 0.0000000316228 0.7 256 63.28337563147736 1.11251300156455
-0.0000000316228 0.7 512 233.8596476303272 3.545027780951424
+0.0000000316228 0.7 512 233.8443487403233 3.33239535006757
 0.0000000316228 0.7 1024 828.376679511941 11.67579409332817
-0.0000000316228 0.7 2048 2993.047668402682 97.1912717720616
+0.0000000316228 0.7 2048 2986.378410961812 92.8036349705639
 
 0.0000001 0.7 4 0.05223401950140071 0.0003731975829630369
 0.0000001 0.7 8 0.1429694873983018 0.000843343260972821
@@ -29,7 +29,7 @@ H T L X dX
 0.0000001 0.7 64 4.963898312835877 0.02447266791770779
 0.0000001 0.7 128 17.73229335142397 0.3092177231064138
 0.0000001 0.7 256 63.83324711812228 1.173203979279074
-0.0000001 0.7 512 231.4377346405984 3.731618938600505
+0.0000001 0.7 512 231.1744231151741 3.486732391831165
 0.0000001 0.7 1024 822.979910435388 13.09823070176746
 0.0000001 0.7 2048 3009.361915960908 52.00020955261389
 
@@ -40,8 +40,8 @@ H T L X dX
 0.000000316228 0.7 64 4.97673759421884 0.02475769327612048
 0.000000316228 0.7 128 17.8772267048875 0.3191707490968942
 0.000000316228 0.7 256 63.6614588259025 1.172903505813813
-0.000000316228 0.7 512 229.6359576371365 3.425581269185279
-0.000000316228 0.7 1024 847.094364706261 12.2701829933698
+0.000000316228 0.7 512 229.9501136170459 3.239101452421541
+0.000000316228 0.7 1024 847.137810571419 11.94776398600306
 
 0.000001 0.7 4 0.05244740361039899 0.0003716246026832923
 0.000001 0.7 8 0.143228230196237 0.000834659680737813
@@ -50,7 +50,7 @@ H T L X dX
 0.000001 0.7 64 4.9579550810079 0.02463404765919623
 0.000001 0.7 128 17.36785216098854 0.3039606956331071
 0.000001 0.7 256 64.57856465603982 1.194759451248703
-0.000001 0.7 512 232.4735045161132 3.676088957109831
+0.000001 0.7 512 231.4565291988921 3.409413595574002
 0.000001 0.7 1024 823.774117544776 13.60921075104826
 0.000001 0.7 2048 3073.399658086377 54.64456369647887
 
@@ -61,8 +61,8 @@ H T L X dX
 0.00000316228 0.7 64 4.948406569918526 0.02434011513556493
 0.00000316228 0.7 128 18.18130786337471 0.3273645562821928
 0.00000316228 0.7 256 64.71996941366731 1.23724237210937
-0.00000316228 0.7 512 228.4982647126058 3.394168701456801
-0.00000316228 0.7 1024 827.802689028738 12.16640597232898
+0.00000316228 0.7 512 228.8453951975472 3.201134483367691
+0.00000316228 0.7 1024 827.531616174217 11.49664018649275
 
 0.00001 0.7 4 0.0525371976374294 0.0003793764816669719
 0.00001 0.7 8 0.1434924769898771 0.000852840225274723
@@ -71,7 +71,7 @@ H T L X dX
 0.00001 0.7 64 4.974102897682704 0.02482223479250783
 0.00001 0.7 128 17.75203171854498 0.3139298490840297
 0.00001 0.7 256 63.62397373026137 1.146778620246743
-0.00001 0.7 512 226.4243360369333 3.695411654798611
+0.00001 0.7 512 227.5921425888581 3.444834835842586
 0.00001 0.7 1024 839.546515345407 15.37289738929801
 0.00001 0.7 2048 3004.724444351824 68.84712222473252
 
@@ -82,8 +82,8 @@ H T L X dX
 0.0000316228 0.7 64 4.968578661732214 0.02467462587748773
 0.0000316228 0.7 128 17.78684202225252 0.3172002972616996
 0.0000316228 0.7 256 64.20873580554533 1.191110396179633
-0.0000316228 0.7 512 226.9584364578935 3.531685848399257
-0.0000316228 0.7 1024 823.282743488256 35.65376222183384
+0.0000316228 0.7 512 226.4800762130056 3.34401756507889
+0.0000316228 0.7 1024 846.319874431772 22.01910281212445
 
 0.0001 0.7 4 0.05221027446338868 0.0003689921496302841
 0.0001 0.7 8 0.143758862358508 0.000845215603430712
@@ -92,7 +92,7 @@ H T L X dX
 0.0001 0.7 64 4.957098514180091 0.02454095119385487
 0.0001 0.7 128 17.57474937226886 0.3154909675317406
 0.0001 0.7 256 64.08255066704442 1.245281403388658
-0.0001 0.7 512 230.209586620601 4.523992538486834
+0.0001 0.7 512 230.502038257234 4.231669317785378
 0.0001 0.7 1024 827.115724875309 22.62210967208504
 0.0001 0.7 2048 3006.315151814571 179.9457102490299
 
@@ -103,8 +103,8 @@ H T L X dX
 0.000316228 0.7 64 4.987251932040765 0.0248153310632547
 0.000316228 0.7 128 17.9811654752718 0.3262961714887608
 0.000316228 0.7 256 64.0651007507144 1.400721869482135
-0.000316228 0.7 512 233.0323138165945 6.510803106663363
-0.000316228 0.7 1024 915.682098829005 221.4660114868885
+0.000316228 0.7 512 231.9026881457415 5.961136860073213
+0.000316228 0.7 1024 904.471397495779 106.1304606509817
 
 0.001 0.7 4 0.05238277020889319 0.0003690576516976455
 0.001 0.7 8 0.1430492792823657 0.000848175390354642
@@ -113,7 +113,7 @@ H T L X dX
 0.001 0.7 64 4.961454498122423 0.02513864062178955
 0.001 0.7 128 17.53736408624588 0.3702425593477615
 0.001 0.7 256 65.8476714810448 1.967191522681203
-0.001 0.7 512 225.163313530294 10.68692239314697
+0.001 0.7 512 228.4507336602214 9.80286503037356
 0.001 0.7 1024 823.074643835924 43.17304453953839
 
 0.00316228 0.7 4 0.05200180823795872 0.0003609437360906834
@@ -123,7 +123,8 @@ H T L X dX
 0.00316228 0.7 64 4.986028650251423 0.0284847921667286
 0.00316228 0.7 128 17.55176641305817 0.4560406116270804
 0.00316228 0.7 256 64.68841775611509 2.79363380114009
-0.00316228 0.7 512 231.7651946099276 15.80434993179176
+0.00316228 0.7 512 234.2401808138363 14.49192410322624
+0.00316228 0.7 1024 824.816888758381 270.4328070389396
 
 0.01 0.7 4 0.05208928783866743 0.0003655423446733593
 0.01 0.7 8 0.1442910847639313 0.00085503626007378
@@ -132,7 +133,7 @@ H T L X dX
 0.01 0.7 64 5.093212913575371 0.03870922709370573
 0.01 0.7 128 18.07311017080922 0.807801869102432
 0.01 0.7 256 71.68993675843272 6.900969374490879
-0.01 0.7 512 255.841078458013 43.76366473183405
+0.01 0.7 512 261.6298399312655 41.56227668643603
 0.01 0.7 1024 458.7535503607277 108.4709665747754
 
 0.0316228 0.7 4 0.05244101281736135 0.0003713312097060542
@@ -142,7 +143,8 @@ H T L X dX
 0.0316228 0.7 64 5.409142350196946 0.0812740998757673
 0.0316228 0.7 128 17.74073933187537 2.323051555845365
 0.0316228 0.7 256 26.5960198034944 2.7907610662326
-0.0316228 0.7 512 36.24676081593082 3.551947649496119
+0.0316228 0.7 512 35.18274935710776 3.101068259324922
+0.0316228 0.7 1024 43.76778914160761 16.3935577349514
 
 0.1 0.7 4 0.05332617816755457 0.0003879512199012261
 0.1 0.7 8 0.1520278055579029 0.001054469877021083
@@ -151,7 +153,7 @@ H T L X dX
 0.1 0.7 64 2.516837465640752 0.07599503133573952
 0.1 0.7 128 3.054604290131725 0.4103816445966279
 0.1 0.7 256 3.056688849215529 0.2151475565993234
-0.1 0.7 512 3.129812673973252 0.2218506945173745
+0.1 0.7 512 3.120458410038347 0.2008340745203421
 0.1 0.7 1024 3.203270172234625 0.2438102647389073
 
 0.316228 0.7 4 0.05672151711334093 0.0004961416770965382
@@ -161,7 +163,8 @@ H T L X dX
 0.316228 0.7 64 0.3300023632709781 0.00397266135383278
 0.316228 0.7 128 0.340574245996582 0.01350280713738239
 0.316228 0.7 256 0.3366840235581289 0.01296408021543593
-0.316228 0.7 512 0.3419107607416144 0.01280965643223309
+0.316228 0.7 512 0.3450340075401722 0.00995157975771307
+0.316228 0.7 1024 0.3419119197808738 0.02219394415121152
 
 1. 0.7 4 0.03909925176928247 0.0005921324368033164
 1. 0.7 8 0.0517399317491396 0.0007377861469729919
@@ -170,7 +173,7 @@ H T L X dX
 1. 0.7 64 0.05724461064281579 0.000475826425665011
 1. 0.7 128 0.05739336686019669 0.001659073879347687
 1. 0.7 256 0.05715812963899225 0.001662193423723626
-1. 0.7 512 0.05824504702884171 0.001760375324564952
+1. 0.7 512 0.05766117517071377 0.0014885187166849
 1. 0.7 1024 0.05767396152285594 0.001662801439053119
 
 3.16228 0.7 4 0.01959319682612204 0.0004610017074237797
@@ -180,7 +183,8 @@ H T L X dX
 3.16228 0.7 64 0.02315679569944353 0.0001958014254311941
 3.16228 0.7 128 0.02335755712400506 0.000703972857804686
 3.16228 0.7 256 0.02328700219680156 0.0006991358420846234
-3.16228 0.7 512 0.02332921060899805 0.0007680194815514161
+3.16228 0.7 512 0.02295894851808303 0.0005965727663244737
+3.16228 0.7 1024 0.02228547303405191 0.001274334265087758
 
 10. 0.7 4 0.01639289914940128 0.0005238634886134714
 10. 0.7 8 0.01828619453519309 0.0004006701188743056
@@ -189,7 +193,7 @@ H T L X dX
 10. 0.7 64 0.01842188462108295 0.0001803980255426141
 10. 0.7 128 0.01838836934569242 0.0006137644293692731
 10. 0.7 256 0.01803520992065647 0.0006372153484996153
-10. 0.7 512 0.01807339539352272 0.0006136358449834677
+10. 0.7 512 0.01831160222146926 0.0005432219182669343
 10. 0.7 1024 0.01842747342639736 0.000648586148912217
 
 31.6228 0.7 4 0.01572532570267222 0.0006312207694860157
@@ -199,7 +203,8 @@ H T L X dX
 31.6228 0.7 64 0.01746287924106582 0.0002103997083130282
 31.6228 0.7 128 0.01745661240160449 0.000761585990409997
 31.6228 0.7 256 0.01747891082361873 0.0007374557557766864
-31.6228 0.7 512 0.01779498328687623 0.0006741380625634703
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 100.00000000000000 0.7 4 0.01612624848754812 0.000852154333007129
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@@ -208,7 +213,7 @@ H T L X dX
 100.00000000000000 0.7 64 0.01685907815499377 0.0002663058871984808
 100.00000000000000 0.7 128 0.01702086681949108 0.000901650179397355
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-100.00000000000000 0.7 512 0.01676921441685408 0.000889578876910434
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 100.00000000000000 0.7 1024 0.01714154778580581 0.0007023953805638529
 
 316.22800000000001 0.7 4 0.01446032375387826 0.000972207863508842
@@ -218,7 +223,9 @@ H T L X dX
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 316.22800000000001 0.7 128 0.01660501343264644 0.001159349581697939
 316.22800000000001 0.7 256 0.01754071689252409 0.001212186113612658
-316.22800000000001 0.7 512 0.01671620894090406 0.0006055121479906857
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 1000.00000000000000 0.7 4 0.01444353215117695 0.001198039279480816
 1000.00000000000000 0.7 8 0.01640843659898345 0.000875533068053843
@@ -227,7 +234,7 @@ H T L X dX
 1000.00000000000000 0.7 64 0.01697410068248116 0.0004423600511363388
 1000.00000000000000 0.7 128 0.01684433232834895 0.001593633171479882
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 1000.00000000000000 0.7 1024 0.01779298148384052 0.000751872902173977
 
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@@ -237,5 +244,6 @@ H T L X dX
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-3162.28000000000020 0.7 512 0.01694215382615637 0.0006727133700737935
-3162.28000000000020 0.7 1024 0.01651809051898973 0.000914933730857445
\ No newline at end of file
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\ No newline at end of file
diff --git a/data/harmonic-susceptibilities/order-6.dat b/data/harmonic-susceptibilities/order-6.dat
index 2f1943c..616e157 100644
--- a/data/harmonic-susceptibilities/order-6.dat
+++ b/data/harmonic-susceptibilities/order-6.dat
@@ -7,7 +7,7 @@ H T L X dX
 0.00000001 0.7 64 4.971265902005533 0.02428171442130225
 0.00000001 0.7 128 17.71999835462599 0.06000818549971747
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-0.00000001 0.7 512 231.5264681673268 2.131185066455962
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 0.0000000316228 0.7 4 0.05226848474164468 0.0003546781285001131
@@ -17,9 +17,9 @@ H T L X dX
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-0.0000000316228 0.7 2048 3047.65818538111 45.58680627289052
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 0.0000001 0.7 4 0.05201378524144928 0.0002562378207161276
 0.0000001 0.7 8 0.1437063682635856 0.0007284042734721861
@@ -28,7 +28,7 @@ H T L X dX
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@@ -38,7 +38,7 @@ H T L X dX
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@@ -49,7 +49,7 @@ H T L X dX
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@@ -59,8 +59,8 @@ H T L X dX
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@@ -70,7 +70,7 @@ H T L X dX
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@@ -79,8 +79,8 @@ H T L X dX
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@@ -90,7 +90,7 @@ H T L X dX
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@@ -99,8 +99,8 @@ H T L X dX
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@@ -110,7 +110,7 @@ H T L X dX
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\ No newline at end of file
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+3162.28000000000020 0.7 512 134.776083361898 11.55158161701916
+3162.28000000000020 0.7 1024 302.709944629127 7.842618972795385
diff --git a/fig_cluster-scaling.png b/fig_cluster-scaling.png
new file mode 100644
index 0000000..12c5f27
--- /dev/null
+++ b/fig_cluster-scaling.png
diff --git a/fig_correlation-times.png b/fig_correlation-times.png
new file mode 100644
index 0000000..3a3b72a
--- /dev/null
+++ b/fig_correlation-times.png
diff --git a/fig_generator-times.png b/fig_generator-times.png
new file mode 100644
index 0000000..55d7cc7
--- /dev/null
+++ b/fig_generator-times.png
diff --git a/fig_harmonic-susceptibilities-out.png b/fig_harmonic-susceptibilities-out.png
new file mode 100644
index 0000000..99c2424
--- /dev/null
+++ b/fig_harmonic-susceptibilities-out.png
diff --git a/fig_harmonic-susceptibilities.png b/fig_harmonic-susceptibilities.png
new file mode 100644
index 0000000..ef747a0
--- /dev/null
+++ b/fig_harmonic-susceptibilities.png
diff --git a/figs/fig_cluster-scaling.gplot b/figs/fig_cluster-scaling.gplot
index d22be31..921e2ce 100644
--- a/figs/fig_cluster-scaling.gplot
+++ b/figs/fig_cluster-scaling.gplot
@@ -69,7 +69,7 @@ unset colorbox
 set nokey
 set logscale xy
 
-scaledylabel = '"$\\avg{s_{\\text{\\sc 1c}}}L^{-D\\gamma/\\nu}$" offset 2,0'
+scaledylabel = '"$\\langle s_{\\textsc{\\scriptsize 1c}}L^{-D\\gamma/\\nu}\\rangle$" offset 2,0'
 
 # plotting the first row
 set format x ""
@@ -80,7 +80,7 @@ set ylabel @scaledylabel
 set xrange @isingRange
 set yrange [0.8:6]
 
-set title '\twodee Ising' offset -6.5,-2.5
+set title '(a) \textsc{2d} Ising' offset -6,-2.5
 
 plot dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("S") * exp(-log(column("L")) * (gammaIsing2D / nuIsing2D))):(column("dS") * exp(-log(column("L")) * (gammaIsing2D / nuIsing2D))):1 with yerrorbars pt 0 lw 2 palette,\
   dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("S") * exp(-log(column("L")) * (gammaIsing2D / nuIsing2D))):1 with lines palette,\
@@ -92,7 +92,7 @@ unset ylabel
 set xrange @pottsRange
 set yrange [0.9:6]
 
-set title '\twodee 3-State Potts' offset -4,-2.5
+set title '(c) \textsc{2d} 3-State Potts' offset -3.5,-2.5
 
 set key above center vertical maxrows 1
 
@@ -114,7 +114,7 @@ unset key
 set xrange @vectorRange
 set yrange [0.2:80]
 
-set title '\threedee O(2)' offset -6.5,-2.5
+set title '(e) \textsc{3d} O(2)' offset -6,-2.5
 
 plot data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("S") * exp(-log(column("L")) * (gamma2Vector3D / nu2Vector3D))):(column("dS") * exp(-log(column("L")) * (gamma2Vector3D / nu2Vector3D))):1 with yerrorbars pt 0 lw 2 palette,\
   data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("S") * exp(-log(column("L")) * (gamma2Vector3D / nu2Vector3D))):1 with lines palette,\
@@ -129,7 +129,7 @@ set ylabel @scaledylabel
 set xrange @isingRange
 set yrange [0.5:200]
 
-set title '\threedee Ising' offset -6.5,-2.5
+set title '(b) \textsc{3d} Ising' offset -6,-2.5
 
 plot dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("S") * exp(-log(column("L")) * (gammaIsing3D / nuIsing3D))):(column("dS") * exp(-log(column("L")) * (gammaIsing3D / nuIsing3D))):1 with yerrorbars pt 0 lw 2 palette,\
   dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("S") * exp(-log(column("L")) * (gammaIsing3D / nuIsing3D))):1 with lines palette,\
@@ -141,7 +141,7 @@ unset ylabel
 set xrange @pottsRange
 set yrange [0.8:6]
 
-set title '\twodee 4-State Potts' offset -4,-2.5
+set title '(d) \textsc{2d} 4-State Potts' offset -3.5,-2.5
 
 plot data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("S") * exp(-log(column("L")) * (gamma4Potts2D / nu4Potts2D))):(column("dS") * exp(-log(column("L")) * (gamma4Potts2D / nu4Potts2D))):1 with yerrorbars pt 0 lw 2 palette,\
   data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("S") * exp(-log(column("L")) * (gamma4Potts2D / nu4Potts2D))):1 with lines palette,\
@@ -151,7 +151,7 @@ plot data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4P
 set xrange @vectorRange
 set yrange [0.3:100]
 
-set title '\threedee O(3)' offset -6.5,-2.5
+set title '(f) \textsc{3d} O(3)' offset -6,-2.5
 
 plot data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("S") * exp(-log(column("L")) * (gamma3Vector3D / nu3Vector3D))):(column("dS") * exp(-log(column("L")) * (gamma3Vector3D / nu3Vector3D))):1 with yerrorbars pt 0 lw 2 palette,\
   data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("S") * exp(-log(column("L")) * (gamma3Vector3D / nu3Vector3D))):1 with lines palette,\
diff --git a/figs/fig_correlation-times.gplot b/figs/fig_correlation-times.gplot
index 6415279..28da0ad 100644
--- a/figs/fig_correlation-times.gplot
+++ b/figs/fig_correlation-times.gplot
@@ -86,7 +86,7 @@ set ylabel @scaledylabel
 set xrange @isingRange
 set yrange [0.2:1.2]
 
-set title '\twodee Ising' offset -6.5,-8
+set title '(a) \twodee Ising' offset -6,-8
 
 plot dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):1 with yerrorbars pt 0 lw 2 palette,\
   dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):1 with lines palette,\
@@ -98,7 +98,7 @@ unset ylabel
 set xrange @pottsRange
 set yrange [0.07:2]
 
-set title '\twodee 3-State Potts' offset -4,-8
+set title '(c) \twodee 3-State Potts' offset -3.5,-8
 
 set key above center vertical maxrows 1
 
@@ -120,7 +120,7 @@ unset key
 set xrange @vectorRange
 set yrange [0.7:2]
 
-set title '\threedee O(2)' offset -6.5,-8
+set title '(e) \threedee O(2)' offset -6,-8
 
 plot data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
   data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):1 with lines palette,\
@@ -135,7 +135,7 @@ set ylabel @scaledylabel
 set xrange @isingRange
 set yrange [0.2:1]
 
-set title '\threedee Ising' offset -6.5,-8
+set title '(b) \threedee Ising' offset -6,-8
 
 plot dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
   dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):1 with lines palette,\
@@ -147,7 +147,7 @@ unset ylabel
 set xrange @pottsRange
 set yrange [0.009:3]
 
-set title '\twodee 4-State Potts' offset -4,-8
+set title '(d) \twodee 4-State Potts' offset -3.5,-8
 
 plot data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):1 with yerrorbars pt 0 lw 2 palette,\
   data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):1 with lines palette,\
@@ -157,7 +157,7 @@ plot data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4P
 set xrange @vectorRange
 set yrange [0.9:5]
 
-set title '\threedee O(3)' offset -6.5,-8
+set title '(f) \threedee O(3)' offset -6,-8
 
 plot data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
   data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):1 with lines palette,\
diff --git a/figs/fig_harmonic-susceptibilities.gplot b/figs/fig_harmonic-susceptibilities.gplot
index 1b65a88..3d180ff 100644
--- a/figs/fig_harmonic-susceptibilities.gplot
+++ b/figs/fig_harmonic-susceptibilities.gplot
@@ -23,18 +23,18 @@ unset xlabel
 set ylabel '$\chi$' offset 3
 set format x ''
 
-set title "fourfold symmetric" offset -9, -3
+set title "(a) fourfold symmetric" offset -8, -3
 
 plot data4 using "L":"X":"dX":"H" with yerrorbars pt 0 lw 2 palette,\
      data4 using "L":"X":"H"      with lines palette
 
 set xlabel '$L$' 
 set colorbox horizontal user origin 0.15, 0.89 size 0.84, 0.03
-set cblabel '(Top) $h_4$ or (bottom) $h_6$' offset 0,6.5
+set cblabel '(a) $h_4$ or (b) $h_6$' offset 0,6.5
 set cbtics format '$10^{%T}$' offset 0,2.8
 set format x
 
-set title "sixfold symmetric" offset -9, -3
+set title "(b) sixfold symmetric" offset -8, -3
 
 plot data6 using "L":"X":"dX":"H" with yerrorbars pt 0 lw 2 palette,\
      data6 using "L":"X":"H"      with lines palette
diff --git a/makefile b/makefile
index c3d9764..96ddfe3 100644
--- a/makefile
+++ b/makefile
@@ -6,10 +6,10 @@ DATA=correlation correlation_temp metastable_raw metastable_func
 all: ${DOC}.pdf
 
 %.tex: figs/%.gplot $(shell find data -type f)
-	gnuplot $< > $@
+	gnuplot $<
 
 ${DOC}.pdf: ${DOC}.tex ${DOC}.bib ${FIGS:%=%.tex}
-	latexmk -pdfdvi $(DOC).tex
+	latexmk -pdf $(DOC).tex
 
 clean:
 	latexmk -C -f ${DOC}
diff --git a/monte-carlo.tex b/monte-carlo.tex
index d535c3b..8322d6c 100644
--- a/monte-carlo.tex
+++ b/monte-carlo.tex
@@ -4,7 +4,7 @@
 
 \documentclass[aps,pre,reprint]{revtex4-1}
 
-\usepackage{amsmath,amssymb,latexsym,mathtools,algorithm}
+\usepackage{amsmath,amssymb,latexsym,mathtools,algorithm,graphicx}
 
 
 % uncomment to label only equations that are referenced in the text
@@ -519,7 +519,7 @@ times and these numeric experiments can be found in section
 \ref{sec:performance}.
 
 \begin{figure}
-  \include{fig_generator-times}
+  \includegraphics[width=\linewidth]{fig_generator-times.png}
   \caption{
     The scaled autocorrelation time of the energy $\H$ for the Wolff algorithm
     on a $32\times32\times32$ \textsc{xy} model at its critical temperature as a
@@ -610,7 +610,7 @@ roughly like $h^{-z\nu/\beta\delta}$ and collapse appropriately as a function
 of $hL^{\beta\delta/\nu}$.
 
 \begin{figure*}
-  \include{fig_correlation-times}
+  \includegraphics[width=\textwidth]{fig_correlation-times.png}
   \caption{
     Scaling collapse of autocorrelation times $\tau$ for the energy $\H$
     scaled by the average cluster size as a function of external field for
@@ -680,7 +680,7 @@ proportional to their size, or
 \]
 
 \begin{figure*}
-  \input{fig_cluster-scaling}
+  \includegraphics[width=\linewidth]{fig_cluster-scaling.png}
   \caption{Collapses of rescaled average Wolff cluster size $\avg s_{\text{\sc
     1c}}L^{-\gamma/\nu}$ as a function of field scaling variable
     $hL^{\beta\delta/\nu}$ for a variety of models. Critical exponents
@@ -740,7 +740,7 @@ two-dimensional melting of argon on a graphite substrate
 \cite{zhang_melting_1991}.
 
 \begin{figure}
-  \include{fig_harmonic-susceptibilities}
+  \includegraphics[width=\linewidth]{fig_harmonic-susceptibilities.png}
   \caption{Susceptibilities as a function of system size for a \twodee O(2)
     model at $T=0.7$ and with (top) fourfold symmetric and (bottom) sixfold
     symmetric perturbing fields. Different field strengths are shown in
diff --git a/proof_response_1.txt b/proof_response_1.txt
new file mode 100644
index 0000000..a4707c9
--- /dev/null
+++ b/proof_response_1.txt
@@ -0,0 +1,37 @@
+
+Response to comment 1: No changes besides those indicated in the response to comments 6 and 8 created incorrect meaning.
+
+Response to comment 2: The zip code is correct.
+
+Response to comment 3: The meaning is preserved and the changes are satisfactory.
+
+Response to comment 4: This change is satisfactory.
+
+Response to comment 5: The meaning is preserved and the changes are satisfactory.
+
+Response to comment 6:
+
+We are concerned about the choice to remove the dots throughout since the meaning is not preserved. The dots are not used to imply multiplication or inner vector products at any point in the manuscript, and in fact we took pains to ensure that the use was consistent (see Table I, entry for Coupling of O(n) model). The dots are meant to portray a group action, for which they are the canonical notation. See https://en.wikipedia.org/wiki/Group_action. 
+
+The removal of dots was made inconsistently. For instance, in equations (10), (11), and the inline equation on line 212 the dots are kept and not removed, presumably because they are next to a bolded roman character. These dots also represent group actions, here applied piecewise to an array of objects, and must be treated identically to dots used elsewhere in the manuscript.
+
+If the dots may not be used to signify group action, we would like to replace them with another infix symbol rather than remove them. Replacing every \cdot with the LaTeX symbols \star (a line-centered star) or \ast (a line-centered asterisk) would be preferred to removal. Example typesetting of these options are shown in the attached image group_action.png.
+
+If this replacement is made, we would like to use the dots to indicate inner vector products in the places that transposes are now used. This would involve the Coupling and Common Field entries for O(n) in Table I, changing "a^T b" to "a \cdot b".
+
+Response to comment 7: The algorithm is OK as set.
+
+Response to comment 8: In equation (5), the limits for the first product should be set as "{i, j} \in C", without the partial sign.
+
+Response to comment 9: The figures appear satisfactory.
+
+Response to comment 10: The definitions and acronyms used for 2D and 3D are satisfactory.
+
+Response to comment 11: For consistency's sake, it can be set as capital "XY" without small caps.
+
+Response to comment 12: The citation we have is Loos, Ottmar. "Symmetric spaces." (1969). A CERN library record can be found here: https://cds.cern.ch/record/106345
+
+Response to comment 13: The information is correct.
+
+Response to comment 14: The information is correct.
+
diff --git a/proof_response_2.txt b/proof_response_2.txt
new file mode 100644
index 0000000..5e09ce6
--- /dev/null
+++ b/proof_response_2.txt
@@ -0,0 +1,26 @@
+Table I must be further corrected. In row 1, replace "s^T ⋅ t" with "s ⋅ t" and "H^T ⋅ s" with "H ⋅ s"
+
+Algorithm 1 looks fine.
+
+A great number of changes must be made to restore "★" to everything that had "⋅" notation and was removed in the first proof. A list follows.
+
+ - On line 72, replace "denoted rs" to "denoted r ★ s"
+ - On line 75, replace "\mu(rA)" to "\mu(r ★ A)" 
+ - In Table I row 1, replace "0s" and "1s" to "0 ★ s" and "1 ★ s", respectively
+ - In Table I row 2, replace "Ms" to "M ★ s"
+ - In Table I row 3, replace "(i_1, …, i_q)s" with "(i_1, …, i_q) ★ s"
+ - In Table I row 4, replace "r_m s" and "s_m s" to "r_m ★ s" and "s_m ★ s", respectively
+ - In Table I row 5, replace "r_m s" and "s_m s" to "r_m ★ s" and "s_m ★ s", respectively
+ - On line 93, replace "rs" and "rt" with "r ★ s" and "r ★ t", respectively
+ - In Algorithm I step 2, replace "Z(s, rs)" with "Z(s, r ★ s)"
+ - In equation (4), replace "rs_m" to "r ★ s_m"
+ - In Algorithm I step 3(b)iii, replace "rs_m" with "r ★ s_m"
+ - On line 143, replace "rs" with "r ★ s"
+ - On line 151, replace "Z(rs', s') = Z(rs, s)" with "Z(r ★ s', s') = Z(r ★ s, s)"
+ - In equation (7), replace "s_0^{-1}s_i" with "s_0^{-1} ★ s_i"
+ - In equation (8), replace "s^{-1}t" and "t^{-1}s" with "s^{-1} ★ t" and "t^{-1} ★ s", respectively
+ - In equation (9) line 1, replace "\tilde Z(rs_0, rs) = B[(rs_0)^{-1}(rs)]" with "\tilde Z(rs_0, r ★ s) = B[(rs_0)^{-1} ★ (r ★ s)]"
+ - In equation (9) line 2, replace "s_0^{-1}s" with "s_0^{-1} ★ s"
+ - On line 323, replace "r_n m" and "s_n m" with "r_n ★ m" and "s_n ★ m", respectively
+ - On line 336, replace "r_i j" and "s_i j" with "r_i ★ j" and "s_i ★ j", respectively
+ - In equation (13), replace "r s_m" with "r ★ s_m"