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| -rw-r--r-- | ising_scaling.tex | 281 |
1 files changed, 101 insertions, 180 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex index aea42d0..47b58ec 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -21,6 +21,8 @@ \usepackage{xcolor} \usepackage{tikz-cd} \usepackage[subfolder]{gnuplottex} % need to compile separately for APS +\usepackage{setspace} +\usepackage{tabularx} \begin{document} @@ -507,186 +509,105 @@ fixing $B$ and $F_c$. Since $A$ and $\tilde B$ are known exactly, these forms ca \end{table} \begin{table} - \begin{tabular}{c|cccccccccc} - & \multicolumn{9}{c}{$n$} \\ - & 0 & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\ - \hline\hline - $n_-$ & 2 & 2 & 3 & 3 & 4 & 5 & 6 & 6 & 6 \\ - $n_0$ & 0 & 1 & 2 & 3 & 4 & 4 & 5 & 7 & 8 \\ - $n_+$ & 2 & 2 & 2 & 4 & 4 & 6 & 6 & 6 & 8 - \\ \hline - $\theta_c$ & - 1.19426 & - 1.19022 & - 1.24954 & - 1.24954 & - 1.27419 & - 1.28016 & - 1.31927 & - 1.32612 & - 1.33347 & - \\ - $A_c$ & - 0.0982351 & - 0.100228 & - 0.0720104 & - 0.0809725 & - 0.0561657 & - 0.0530319 & - 0.0377424 & - 0.0353443 & - 0.0328499 & - \\ - $A_{\mathrm{YL}}$ & - 2.38365 & - 2.3876 & - 2.37518 & - 2.46094 & - 2.45696 & - 2.47971 & - 2.4754 & - 2.47666 & - 2.4769 & - \\ - $F_0$ & - 1.07666 & - 1.07383 & - 1.14375 & - 1.16003 & - 1.23109 & - 1.25496 & - 1.31044 & - 1.32179 & - 1.33327 & - \\ - $F_1$ & - 2.00381 & - 1.99663 & - 2.14753 & - 2.15397 & - 2.30314 & - 2.34538 & - 2.46209 & - 2.48527 & - 2.50906 & - \\ - $F_2$ & - 0.228234 & - 0.228235 & - 0.226794 & - 0.240421 & - 0.218875 & - 0.228138 & - 0.224167 & - 0.231472 & - 0.232317 & - \\ - $h_0$ & - 1.19426 & - 1.19078 & - 1.2259 & - 1.18183 & - 1.20578 & - 1.19878 & - 1.21439 & - 1.21605 & - 1.21825 & - \\ - $h_1/10^{-2}$ & & - $0.0377284$ & - $-1.32208$ & - $-1.98552$ & - $-3.4617$ & - $-4.05948$ & - $-5.27306$ & - $-5.53426$ & - $-5.79592$ & - \\ - $h_2/10^{-3}$ & & - & - 1.68015 & - 3.72445 & - 5.89419 & - 7.03625 & - 8.88373 & - 9.31123 & - 9.7244 & - \\ - $h_3/10^{-3}$ & & & - $-0.300336$ & - $-1.11915$ & - $-1.68817$ & - $-2.06784$ & - $-2.55373$ & - $-2.6766$ & - $-2.79303$ & - \\ - $h_4/10^{-4}$ & & & & - $2.59026$ & - $4.92004$ & - $6.6988$ & - $8.39954$ & - $8.83288$ & - $9.25784$ & - \\ - $h_5/10^{-4}$ & & & & - $-0.578821$ & - $-1.50074$ & - $-2.55766$ & - $-3.15364$ & - $-3.30063$ & - $-3.4621$ & - \\ - $h_6/10^{-4}$ & & & & & - $0.350651$ & - $0.965437$ & - $1.24302$ & - $1.29961$ & - $1.36707$ & - \\ - $h_7/10^{-5}$ & & & & & - $-0.617004$ & - $-3.5398$ & - $-5.06226$ & - $-5.40426$ & - $-5.70884$ & - \\ - $h_8/10^{-5}$ & & & & & & - $0.978241$ & - $1.90968$ & - $2.22565$ & - $2.40644$ & - \\ - $h_9/10^{-6}$ & & & & & & - $-1.76567$ & - $-6.25434$ & - $-8.84571$ & - $-10.1167$ & - \\ - $h_{10}/10^{-6}$ & & & & & & & - $1.51279$ & - $3.12976$ & - $4.0249$ & - \\ - $h_{11}/10^{-7}$ & & & & & & & - $-2.17053$ & - $-9.37655$ & - $-14.7593$ & - \\ - $h_{12}/10^{-7}$ & & & & & & & & - $2.0809$ & - $4.687$ & - \\ - $h_{13}/10^{-8}$ & & & & & & & & - $-2.83978$ & - $-12.363$ & - \\ - $h_{14}/10^{-8}$ & & & & & & & & & - $2.39528$ & - \\ - $h_{15}/10^{-9}$ & & & & & & & & & - $-2.99667$ & - \\ + \singlespacing + \begin{tabular}{c|llllllll} + \multicolumn{1}{c|}{$n$} & + \multicolumn{1}{c}{$\theta_\mathrm{YL}$} & + \multicolumn{1}{c}{$A_\mathrm{YL}$} & + \multicolumn{1}{c}{$F_1$} & + \multicolumn{1}{c}{$F_2$} & + \multicolumn{1}{c}{$F_3$} & + \multicolumn{1}{c}{$F_4$} & + \multicolumn{1}{c}{$F_5$} & + \multicolumn{1}{c}{$F_6$} \\ + \hline + 2 & + 0.18041 & + 2.1295 & + 1.2447 & + 0.49975 \\ + 3 & + 0.19613 & + 2.1999 & + 1.2402 & + 0.39028 \\ + 4 & + 0.19563 & + 2.2433 & + 1.2964 & + 0.37080 & + $-0.028926$ \\ + 5 & + 0.19553 & + 2.2321 & + 1.2804 & + 0.36318 & + $-0.028924$ & & \\ + 6 & + 0.19737 & + 2.3981 & + 1.5091 & + 0.39200 & + $-0.090023$ & + 0.017233 & \\ + 7 & + 0.19730 & + 2.4229 & + 1.5454 & + 0.41320 & + $-0.12161$ & + 0.026346 & \\ + 8 & + 0.19655 & + 2.5513 & + 1.7323 & + 0.59677 & + $-0.29521$ & + 0.078509 & + $-0.0072514$ \\ + 9 & + 1.3754 & + 0.19652 & + 2.5482 & + 1.7278 & + 0.60278 & + $-0.28737$ & + 0.072411 & + $-0.0072455$ \\ + \hline + \end{tabular} + \begin{tabular}{c|llllllll} + \hline + $n$ & + \multicolumn{1}{c}{$\theta_0$} & + \multicolumn{1}{c}{$h_1$} & + \multicolumn{1}{c}{$h_2$} & + \multicolumn{1}{c}{$h_3$} & + \multicolumn{1}{c}{$h_4$} & + \multicolumn{1}{c}{$h_5$} & + \multicolumn{1}{c}{$h_6$} & + \multicolumn{1}{c}{$h_7$} \\ + \hline + 2 & + 1.2114 \\ + 3 & + 1.3498 & + $-0.014909$ \\ + 4 & + 1.4490 & + $-0.10871$ & $-0.0031747$ \\ + 5 & + 1.4719 & + $-0.11399$ & $-0.0031669$ & $8.8574\times10^{-7}$ \\ + 6 & + 1.4358 & + $-0.19533$ & 0.029301 & 0.0039906 & $-0.00011913$ \\ + 7 & + 1.4324 & + $-0.22077$ & 0.036245 & 0.010120 & $-0.0011434$ & 0.00010095 \\ + 8 & + 1.3710 & + $-0.35150$ & 0.0050232 & 0.053659 & $-0.019806$ & 0.0033531 & $-0.00026034$ \\ \end{tabular} \end{table} |