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| -rw-r--r-- | ising_scaling.tex | 179 |
1 files changed, 176 insertions, 3 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex index e1b8589..bed9db3 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -1,7 +1,7 @@ \documentclass[ aps, pre, - reprint, + preprint, longbibliography, floatfix ]{revtex4-2} @@ -474,10 +474,183 @@ When analytically continued to complex $\theta$, \eqref{eq:2d.real.Fc} has branc \end{equation} analytic for all $\theta\in\mathbb C$ outside the Langer branch cuts. - - \subsection{Fitting} +The scaling function has a number of free parameters: the position $\theta_c$ of the abrupt transition, prefactors in front of singular functions from the abrupt transition and the Yang--Lee point, the coefficients in the analytic part of $\mathcal F$, and the coefficients in the undetermined function $h$. + +\begin{table} + \begin{tabular}{c|ccccccccc} + & \multicolumn{9}{c}{$n$} \\ + & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\ + \hline + $\theta_c$ & + 1.19022 & + 1.24954 & + 1.24954 & + 1.27419 & + 1.28016 & + 1.31927 & + 1.32612 & + 1.33347 & + \\ + $A_c$ & + 0.100228 & + 0.0720104 & + 0.0809725 & + 0.0561657 & + 0.0530319 & + 0.0377424 & + 0.0353443 & + 0.0328499 & + \\ + $A_{\mathrm{YL}}$ & + 2.3876 & + 2.37518 & + 2.46094 & + 2.45696 & + 2.47971 & + 2.4754 & + 2.47666 & + 2.4769 & + \\ + $F_0$ & + 1.07383 & + 1.14375 & + 1.16003 & + 1.23109 & + 1.25496 & + 1.31044 & + 1.32179 & + 1.33327 & + \\ + $F_1$ & + 1.99663 & + 2.14753 & + 2.15397 & + 2.30314 & + 2.34538 & + 2.46209 & + 2.48527 & + 2.50906 & + \\ + $F_2$ & + 0.228235 & + 0.226794 & + 0.240421 & + 0.218875 & + 0.228138 & + 0.224167 & + 0.231472 & + 0.232317 & + \\ + $h_0$ & + 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 & + \\ + $h_3/10^{-3}$ & & + $-0.300336$ & + $-1.11915$ & + $-1.68817$ & + $-2.06784$ & + $-2.55373$ & + $-2.6766$ & + $-2.79303$ & + \\ + $h_4/10^{-4}$ & & & + $2.59026$ & + $4.92004$ & + $6.6988$ & + $8.39954$ & + $8.83288$ & + $9.25784$ & + \\ + $h_5/10^{-4}$ & & & + $-0.578821$ & + $-1.50074$ & + $-2.55766$ & + $-3.15364$ & + $-3.30063$ & + $-3.4621$ & + \\ + $h_6/10^{-4}$ & & & & + $0.350651$ & + $0.965437$ & + $1.24302$ & + $1.29961$ & + $1.36707$ & + \\ + $h_7/10^{-5}$ & & & & + $-0.617004$ & + $-3.5398$ & + $-5.06226$ & + $-5.40426$ & + $-5.70884$ & + \\ + $h_8/10^{-5}$ & & & & & + $0.978241$ & + $1.90968$ & + $2.22565$ & + $2.40644$ & + \\ + $h_9/10^{-6}$ & & & & & + $-1.76567$ & + $-6.25434$ & + $-8.84571$ & + $-10.1167$ & + \\ + $h_{10}/10^{-6}$ & & & & & & + $1.51279$ & + $3.12976$ & + $4.0249$ & + \\ + $h_{11}/10^{-7}$ & & & & & & + $-2.17053$ & + $-9.37655$ & + $-14.7593$ & + \\ + $h_{12}/10^{-7}$ & & & & & & & + $2.0809$ & + $4.687$ & + \\ + $h_{13}/10^{-8}$ & & & & & & & + $-2.83978$ & + $-12.363$ & + \\ + $h_{14}/10^{-8}$ & & & & & & & & + $2.39528$ & + \\ + $h_{15}/10^{-9}$ & & & & & & & & + $-2.99667$ & + \\ + \end{tabular} +\end{table} + \subsection{Comparison} \section{The three-dimensional Ising model} |