SU(2) in 2+1 dimensions: Run A, beta=5.6, xi=2, (84 x 84) x 84 as * at * sigma = 0.025265(39) 1 / (as * at * sigma) = 39.581(61) xi = 2 Zxi = 0.9703(25) 1 / Zxi = 1.0306(27) a_s * sqrt(sigma) = 0.22143(33) a_t * sqrt(sigma) = 0.11410(17) 1 / (a_s * sqrt(sigma)) = 4.5162(69) 1 / (a_t * sqrt(sigma)) = 8.764(13) Energy gaps above the ground state. Energy-squared gaps over 2*pi*sigma orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg'^2 - Sg^2) / (2*pi*sigma) (18,0) 3.985659 0.005986 0.250900 0.000381 3.987177 0.007807 (20,0) 4.428510 0.006651 0.225810 0.000343 4.429944 0.008719 (22,0) 4.871361 0.007316 0.205282 0.000312 4.868065 0.010516 (24,0) 5.314212 0.007981 0.188175 0.000286 5.312935 0.013145 (2,2) 0.626286 0.000941 1.596719 0.002427 0.512792 0.004108 (4,4) 1.252572 0.001881 0.798359 0.001213 1.219273 0.004450 (6,6) 1.878858 0.002822 0.532240 0.000809 1.869838 0.004975 (8,8) 2.505144 0.003762 0.399180 0.000607 2.503489 0.005733 (10,10) 3.131430 0.004703 0.319344 0.000485 3.131092 0.006661 (12,12) 3.757716 0.005643 0.266120 0.000404 3.755452 0.007974 (14,14) 4.384002 0.006584 0.228103 0.000347 4.389716 0.008673 (16,16) 5.010287 0.007524 0.199590 0.000303 5.013025 0.010362 (18,18) 5.636573 0.008465 0.177413 0.000270 5.634230 0.011862 (2,0) 0.442851 0.000665 2.258101 0.003432 2.467809 0.007266 (4,0) 0.885702 0.001330 1.129051 0.001716 2.274074 0.006459 (6,0) 1.328553 0.001995 0.752700 0.001144 2.179982 0.005895 (8,0) 1.771404 0.002660 0.564525 0.000858 2.125923 0.006420 (10,0) 2.214255 0.003325 0.451620 0.000686 2.086872 0.006895 (12,0) 2.657106 0.003990 0.376350 0.000572 2.056727 0.008545 (14,0) 3.099957 0.004655 0.322586 0.000490 2.035098 0.010230 (16,0) 3.542808 0.005320 0.282263 0.000429 2.021702 0.014094 (18,0) 3.985659 0.005986 0.250900 0.000381 2.020770 0.017704 (20,0) 4.428510 0.006651 0.225810 0.000343 2.050576 0.020486 (22,0) 4.871361 0.007316 0.205282 0.000312 2.083215 0.035652 (24,0) 5.314212 0.007981 0.188175 0.000286 2.126214 0.053054 (2,2) 0.626286 0.000941 1.596719 0.002427 2.374295 0.007061 (4,4) 1.252572 0.001881 0.798359 0.001213 2.185633 0.006294 (6,6) 1.878858 0.002822 0.532240 0.000809 2.104056 0.006409 (8,8) 2.505144 0.003762 0.399180 0.000607 2.077199 0.007021 (10,10) 3.131430 0.004703 0.319344 0.000485 2.050277 0.010037 (12,12) 3.757716 0.005643 0.266120 0.000404 2.042774 0.012807 (14,14) 4.384002 0.006584 0.228103 0.000347 2.009052 0.016193 (16,16) 5.010287 0.007524 0.199590 0.000303 2.007493 0.020894 (18,18) 5.636573 0.008465 0.177413 0.000270 2.008205 0.046723 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg'' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg''^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 4.293870 0.025039 (4,0) 0.885702 0.001330 1.129051 0.001716 4.317356 0.022365 (6,0) 1.328553 0.001995 0.752700 0.001144 4.249514 0.023603 (8,0) 1.771404 0.002660 0.564525 0.000858 4.193866 0.024263 (10,0) 2.214255 0.003325 0.451620 0.000686 4.188327 0.025320 (12,0) 2.657106 0.003990 0.376350 0.000572 4.176385 0.030150 (14,0) 3.099957 0.004655 0.322586 0.000490 4.228514 0.028161 (16,0) 3.542808 0.005320 0.282263 0.000429 4.153984 0.033652 (18,0) 3.985659 0.005986 0.250900 0.000381 4.114298 0.034115 (20,0) 4.428510 0.006651 0.225810 0.000343 4.095820 0.039203 (22,0) 4.871361 0.007316 0.205282 0.000312 4.006332 0.071197 (24,0) 5.314212 0.007981 0.188175 0.000286 4.096607 0.067006 (2,2) 0.626286 0.000941 1.596719 0.002427 4.403355 0.018949 (4,4) 1.252572 0.001881 0.798359 0.001213 4.236807 0.015986 (6,6) 1.878858 0.002822 0.532240 0.000809 4.163259 0.014472 (8,8) 2.505144 0.003762 0.399180 0.000607 4.103333 0.020306 (10,10) 3.131430 0.004703 0.319344 0.000485 4.058584 0.022925 (12,12) 3.757716 0.005643 0.266120 0.000404 4.099768 0.027620 (14,14) 4.384002 0.006584 0.228103 0.000347 4.062570 0.043551 (16,16) 5.010287 0.007524 0.199590 0.000303 4.082394 0.049022 (18,18) 5.636573 0.008465 0.177413 0.000270 4.098221 0.053058 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg''' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Sg'''^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 4.676307 0.023433 (4,0) 0.885702 0.001330 1.129051 0.001716 4.819124 0.023793 (6,0) 1.328553 0.001995 0.752700 0.001144 4.594764 0.022562 (8,0) 1.771404 0.002660 0.564525 0.000858 4.609935 0.034207 (10,0) 2.214255 0.003325 0.451620 0.000686 4.554834 0.019630 (12,0) 2.657106 0.003990 0.376350 0.000572 4.364792 0.029448 (14,0) 3.099957 0.004655 0.322586 0.000490 4.181612 0.043504 (16,0) 3.542808 0.005320 0.282263 0.000429 4.234059 0.036592 (18,0) 3.985659 0.005986 0.250900 0.000381 4.239252 0.037311 (20,0) 4.428510 0.006651 0.225810 0.000343 4.174947 0.053461 (22,0) 4.871361 0.007316 0.205282 0.000312 4.159195 0.059992 (24,0) 5.314212 0.007981 0.188175 0.000286 4.110959 0.102543 (2,2) 0.626286 0.000941 1.596719 0.002427 4.724463 0.023480 (4,4) 1.252572 0.001881 0.798359 0.001213 4.604963 0.020546 (6,6) 1.878858 0.002822 0.532240 0.000809 4.420372 0.019852 (8,8) 2.505144 0.003762 0.399180 0.000607 4.344598 0.044543 (10,10) 3.131430 0.004703 0.319344 0.000485 4.212118 0.039866 (12,12) 3.757716 0.005643 0.266120 0.000404 4.140343 0.037453 (14,14) 4.384002 0.006584 0.228103 0.000347 4.118695 0.025401 (16,16) 5.010287 0.007524 0.199590 0.000303 4.108260 0.047395 (18,18) 5.636573 0.008465 0.177413 0.000270 4.098221 0.075160 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Su / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Su^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 3.813369 0.014446 (4,0) 0.885702 0.001330 1.129051 0.001716 3.562810 0.012804 (6,0) 1.328553 0.001995 0.752700 0.001144 3.389644 0.011714 (8,0) 1.771404 0.002660 0.564525 0.000858 3.322736 0.012622 (10,0) 2.214255 0.003325 0.451620 0.000686 3.231234 0.013824 (12,0) 2.657106 0.003990 0.376350 0.000572 3.176451 0.012343 (14,0) 3.099957 0.004655 0.322586 0.000490 3.119367 0.013814 (16,0) 3.542808 0.005320 0.282263 0.000429 3.120914 0.013658 (18,0) 3.985659 0.005986 0.250900 0.000381 3.078446 0.023560 (20,0) 4.428510 0.006651 0.225810 0.000343 3.083738 0.028045 (22,0) 4.871361 0.007316 0.205282 0.000312 3.096557 0.033091 (24,0) 5.314212 0.007981 0.188175 0.000286 3.077441 0.057247 (2,2) 0.626286 0.000941 1.596719 0.002427 3.667061 0.014627 (4,4) 1.252572 0.001881 0.798359 0.001213 3.373454 0.012405 (6,6) 1.878858 0.002822 0.532240 0.000809 3.227986 0.012192 (8,8) 2.505144 0.003762 0.399180 0.000607 3.169715 0.013203 (10,10) 3.131430 0.004703 0.319344 0.000485 3.105018 0.017435 (12,12) 3.757716 0.005643 0.266120 0.000404 3.038635 0.026685 (14,14) 4.384002 0.006584 0.228103 0.000347 3.008678 0.042401 (16,16) 5.010287 0.007524 0.199590 0.000303 3.055675 0.040096 (18,18) 5.636573 0.008465 0.177413 0.000270 3.015416 0.068441 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 2.605513 0.008320 (4,0) 0.885702 0.001330 1.129051 0.001716 2.493726 0.007495 (6,0) 1.328553 0.001995 0.752700 0.001144 2.386942 0.007554 (8,0) 1.771404 0.002660 0.564525 0.000858 2.311864 0.007897 (10,0) 2.214255 0.003325 0.451620 0.000686 2.235034 0.008731 (12,0) 2.657106 0.003990 0.376350 0.000572 2.170477 0.010269 (14,0) 3.099957 0.004655 0.322586 0.000490 2.127489 0.010090 (16,0) 3.542808 0.005320 0.282263 0.000429 2.091727 0.012610 (18,0) 3.985659 0.005986 0.250900 0.000381 2.083641 0.012299 (20,0) 4.428510 0.006651 0.225810 0.000343 2.076534 0.014093 (22,0) 4.871361 0.007316 0.205282 0.000312 2.079831 0.020579 (24,0) 5.314212 0.007981 0.188175 0.000286 2.095666 0.025330 (2,2) 0.626286 0.000941 1.596719 0.002427 2.561370 0.008756 (4,4) 1.252572 0.001881 0.798359 0.001213 2.413081 0.007045 (6,6) 1.878858 0.002822 0.532240 0.000809 2.284022 0.007186 (8,8) 2.505144 0.003762 0.399180 0.000607 2.190542 0.008482 (10,10) 3.131430 0.004703 0.319344 0.000485 2.124398 0.010972 (12,12) 3.757716 0.005643 0.266120 0.000404 2.048423 0.020790 (14,14) 4.384002 0.006584 0.228103 0.000347 2.024819 0.021689 (16,16) 5.010287 0.007524 0.199590 0.000303 2.007493 0.028563 (18,18) 5.636573 0.008465 0.177413 0.000270 2.006346 0.039881 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag'^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 4.813545 0.026710 (4,0) 0.885702 0.001330 1.129051 0.001716 4.604248 0.024156 (6,0) 1.328553 0.001995 0.752700 0.001144 4.428123 0.020166 (8,0) 1.771404 0.002660 0.564525 0.000858 4.431449 0.020733 (10,0) 2.214255 0.003325 0.451620 0.000686 4.327990 0.020196 (12,0) 2.657106 0.003990 0.376350 0.000572 4.262060 0.019823 (14,0) 3.099957 0.004655 0.322586 0.000490 4.228514 0.018344 (16,0) 3.542808 0.005320 0.282263 0.000429 4.207891 0.027011 (18,0) 3.985659 0.005986 0.250900 0.000381 4.193845 0.035746 (20,0) 4.428510 0.006651 0.225810 0.000343 4.107097 0.080059 (22,0) 4.871361 0.007316 0.205282 0.000312 4.232225 0.066905 (24,0) 5.314212 0.007981 0.188175 0.000286 4.139699 0.120492 (2,2) 0.626286 0.000941 1.596719 0.002427 4.787261 0.019060 (4,4) 1.252572 0.001881 0.798359 0.001213 4.431144 0.018229 (6,6) 1.878858 0.002822 0.532240 0.000809 4.254850 0.019468 (8,8) 2.505144 0.003762 0.399180 0.000607 4.204911 0.022769 (10,10) 3.131430 0.004703 0.319344 0.000485 4.133423 0.025562 (12,12) 3.757716 0.005643 0.266120 0.000404 4.106814 0.034562 (14,14) 4.384002 0.006584 0.228103 0.000347 4.135574 0.036016 (16,16) 5.010287 0.007524 0.199590 0.000303 4.080407 0.077897 (18,18) 5.636573 0.008465 0.177413 0.000270 4.030654 0.098985 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag'' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Ag''^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 5.065564 0.030523 (4,0) 0.885702 0.001330 1.129051 0.001716 4.917380 0.028106 (6,0) 1.328553 0.001995 0.752700 0.001144 4.631846 0.029897 (8,0) 1.771404 0.002660 0.564525 0.000858 4.746686 0.036937 (10,0) 2.214255 0.003325 0.451620 0.000686 4.671736 0.032382 (12,0) 2.657106 0.003990 0.376350 0.000572 4.763346 0.045620 (14,0) 3.099957 0.004655 0.322586 0.000490 4.673180 0.035754 (16,0) 3.542808 0.005320 0.282263 0.000429 4.550580 0.030463 (18,0) 3.985659 0.005986 0.250900 0.000381 4.431637 0.037766 (20,0) 4.428510 0.006651 0.225810 0.000343 4.530554 0.051274 (22,0) 4.871361 0.007316 0.205282 0.000312 4.373304 0.067340 (24,0) 5.314212 0.007981 0.188175 0.000286 4.515575 0.116847 (2,2) 0.626286 0.000941 1.596719 0.002427 5.110593 0.030650 (4,4) 1.252572 0.001881 0.798359 0.001213 4.680652 0.025750 (6,6) 1.878858 0.002822 0.532240 0.000809 4.568092 0.025512 (8,8) 2.505144 0.003762 0.399180 0.000607 4.571618 0.039225 (10,10) 3.131430 0.004703 0.319344 0.000485 4.458299 0.034028 (12,12) 3.757716 0.005643 0.266120 0.000404 4.591556 0.048733 (14,14) 4.384002 0.006584 0.228103 0.000347 4.328268 0.063085 (16,16) 5.010287 0.007524 0.199590 0.000303 4.128183 0.122622 (18,18) 5.636573 0.008465 0.177413 0.000270 4.283177 0.083133 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 1.401323 0.004820 (4,0) 0.885702 0.001330 1.129051 0.001716 1.238387 0.003953 (6,0) 1.328553 0.001995 0.752700 0.001144 1.145366 0.003559 (8,0) 1.771404 0.002660 0.564525 0.000858 1.094206 0.003362 (10,0) 2.214255 0.003325 0.451620 0.000686 1.061280 0.003692 (12,0) 2.657106 0.003990 0.376350 0.000572 1.043918 0.004006 (14,0) 3.099957 0.004655 0.322586 0.000490 1.031498 0.004595 (16,0) 3.542808 0.005320 0.282263 0.000429 1.015914 0.006433 (18,0) 3.985659 0.005986 0.250900 0.000381 1.017308 0.008625 (20,0) 4.428510 0.006651 0.225810 0.000343 1.020797 0.012369 (22,0) 4.871361 0.007316 0.205282 0.000312 1.030441 0.016137 (24,0) 5.314212 0.007981 0.188175 0.000286 1.052865 0.023681 (2,2) 0.626286 0.000941 1.596719 0.002427 1.324108 0.004357 (4,4) 1.252572 0.001881 0.798359 0.001213 1.160505 0.003487 (6,6) 1.878858 0.002822 0.532240 0.000809 1.082032 0.003351 (8,8) 2.505144 0.003762 0.399180 0.000607 1.046586 0.004351 (10,10) 3.131430 0.004703 0.319344 0.000485 1.020841 0.006702 (12,12) 3.757716 0.005643 0.266120 0.000404 1.014470 0.009942 (14,14) 4.384002 0.006584 0.228103 0.000347 0.991306 0.012629 (16,16) 5.010287 0.007524 0.199590 0.000303 1.002655 0.014162 (18,18) 5.636573 0.008465 0.177413 0.000270 1.004284 0.026490 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au'^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 3.519769 0.013715 (4,0) 0.885702 0.001330 1.129051 0.001716 3.292068 0.012892 (6,0) 1.328553 0.001995 0.752700 0.001144 3.191771 0.012027 (8,0) 1.771404 0.002660 0.564525 0.000858 3.167940 0.011481 (10,0) 2.214255 0.003325 0.451620 0.000686 3.113100 0.014513 (12,0) 2.657106 0.003990 0.376350 0.000572 3.071953 0.020505 (14,0) 3.099957 0.004655 0.322586 0.000490 3.063879 0.023015 (16,0) 3.542808 0.005320 0.282263 0.000429 3.065189 0.027119 (18,0) 3.985659 0.005986 0.250900 0.000381 3.188280 0.023770 (20,0) 4.428510 0.006651 0.225810 0.000343 3.172907 0.026750 (22,0) 4.871361 0.007316 0.205282 0.000312 3.124073 0.042645 (24,0) 5.314212 0.007981 0.188175 0.000286 3.106327 0.062435 (2,2) 0.626286 0.000941 1.596719 0.002427 3.446875 0.015586 (4,4) 1.252572 0.001881 0.798359 0.001213 3.228782 0.011708 (6,6) 1.878858 0.002822 0.532240 0.000809 3.149229 0.009839 (8,8) 2.505144 0.003762 0.399180 0.000607 3.100910 0.012036 (10,10) 3.131430 0.004703 0.319344 0.000485 3.064327 0.015119 (12,12) 3.757716 0.005643 0.266120 0.000404 3.057940 0.018976 (14,14) 4.384002 0.006584 0.228103 0.000347 3.039742 0.023470 (16,16) 5.010287 0.007524 0.199590 0.000303 3.037113 0.032006 (18,18) 5.636573 0.008465 0.177413 0.000270 3.111036 0.034955 orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au'' / sqrt(sigma) orientation R * sqrt(sigma) 1 / (R * sqrt(sigma)) Au''^2 - Sg^2) / (2*pi*sigma) (2,0) 0.442851 0.000665 2.258101 0.003432 3.866883 0.014578 (4,0) 0.885702 0.001330 1.129051 0.001716 3.639557 0.016092 (6,0) 1.328553 0.001995 0.752700 0.001144 3.547256 0.012663 (8,0) 1.771404 0.002660 0.564525 0.000858 3.545818 0.022446 (10,0) 2.214255 0.003325 0.451620 0.000686 3.439701 0.019186 (12,0) 2.657106 0.003990 0.376350 0.000572 3.445191 0.020279 (14,0) 3.099957 0.004655 0.322586 0.000490 3.320743 0.016612 (16,0) 3.542808 0.005320 0.282263 0.000429 3.235035 0.021140 (18,0) 3.985659 0.005986 0.250900 0.000381 3.159888 0.026440 (20,0) 4.428510 0.006651 0.225810 0.000343 3.139614 0.041496 (22,0) 4.871361 0.007316 0.205282 0.000312 3.206954 0.058861 (24,0) 5.314212 0.007981 0.188175 0.000286 3.267164 0.071476 (2,2) 0.626286 0.000941 1.596719 0.002427 3.745581 0.015594 (4,4) 1.252572 0.001881 0.798359 0.001213 3.576866 0.014456 (6,6) 1.878858 0.002822 0.532240 0.000809 3.446814 0.014755 (8,8) 2.505144 0.003762 0.399180 0.000607 3.410048 0.015657 (10,10) 3.131430 0.004703 0.319344 0.000485 3.260351 0.025984 (12,12) 3.757716 0.005643 0.266120 0.000404 3.200589 0.032357 (14,14) 4.384002 0.006584 0.228103 0.000347 3.112536 0.035273 (16,16) 5.010287 0.007524 0.199590 0.000303 3.113372 0.043468 (18,18) 5.636573 0.008465 0.177413 0.000270 3.095061 0.066881