From 431064bdd6cc2b479066f0f17ec0eb70d8976af1 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 29 Jul 2021 17:50:13 +0200
Subject: Added table.

---
 ising_scaling.tex | 179 +++++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 176 insertions(+), 3 deletions(-)

(limited to 'ising_scaling.tex')

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}
-- 
cgit v1.2.3-54-g00ecf

