New data in table.

1 files changed, 77 insertions, 80 deletions

diff --git a/ising_scaling.tex b/ising_scaling.tex
index 2fa2528..7b5da7b 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -576,7 +576,7 @@ that the codimension of the fit is constant.
 We performed this procedure starting at $n=2$, or matching the scaling
 function at the low and high temperature zero field points to quadratic order,
 through $n=7$. The resulting fit coefficients can be found in Table
-\ref{tab:fits} without any sort of uncertainty, which is difficult to quantify
+\ref{tab:data} without any sort of uncertainty, which is difficult to quantify
 directly due to the truncation of series. However, precise results exist for
 the value of the scaling function at the critical isotherm, or equivalently for
 the series coefficients of the scaling function $\mathcal F_0$. Since we do not
@@ -610,110 +610,107 @@ to their known values at the critical isotherm, or $\theta=1$.
     \cite{Mangazeev_2008_Variational}. Those without are taken from Fonseca
     \textit{et al.}, and are assumed to be accurate to within their last digit
     \cite{Fonseca_2003_Ising}.
-  } \label{tab:fits}
+  } \label{tab:data}
 \end{table}
 
 \begin{table}
   \singlespacing
-  \begin{tabular}{c|llllllll}
+  \begin{tabular}{c|lllllll}
     \multicolumn{1}{c|}{$n$} &
      \multicolumn{1}{c}{$\theta_\mathrm{YL}$} &
-     \multicolumn{1}{c}{$A_\mathrm{YL}$} &
+     \multicolumn{1}{c}{$C_\mathrm{YL}$} &
      \multicolumn{1}{c}{$G_1$} &
      \multicolumn{1}{c}{$G_2$} &
      \multicolumn{1}{c}{$G_3$} &
      \multicolumn{1}{c}{$G_4$} &
-     \multicolumn{1}{c}{$G_5$} &
-     \multicolumn{1}{c}{$G_6$} \\
+     \multicolumn{1}{c}{$G_5$} \\
     \hline
       2 &
-      0.18041 &
-      2.1295 &
-      1.2447 &
-      0.49975 \\
+      0.198152 &
+      2.39338 &
+      1.52182 &
+      0.455868 \\
       3 &
-      0.19613 &
-      2.1999 &
-      1.2402 &
-      0.39028 \\
+      0.199048 &
+      2.25700 &
+      1.30767 &
+      0.396157 \\
       4 &
-      0.19563 &
-      2.2433 &
-      1.2964 &
-      0.37080 &
-      $-0.028926$ \\
+      0.198918 &
+      2.36150 &
+      1.46058 &
+      0.307198 &
+      \hphantom{$-$}0.0323334 \\
       5 &
-      0.19553 &
-      2.2321 &
-      1.2804 &
-      0.36318 &
-      $-0.028924$ & & \\
+      0.198100 &
+      2.43224 &
+      1.55298 &
+      0.362791 &
+      $-0.108393$ &
+      0.0228573 \\
       6 &
-      0.19737 &
-      2.3981 &
-      1.5091 &
-      0.39200 &
-      $-0.090023$ &
-      0.017233 & \\
+      0.197027 &
+      2.45864 &
+      1.59639 &
+      0.484865 &
+      $-0.119149$ &
+      0.0150607 \\
       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 &
-      $-0.0072455$ \\
+      0.196809 &
+      2.49636 &
+      1.65176 &
+      0.54349 &
+      $-0.141089$ &
+      0.00877823 &
+      $-0.00110698$ \\
       \hline
     \end{tabular}
-    \begin{tabular}{c|llllllll}
-        \hline
+    \begin{tabular}{c|llllll}
+      \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}{$h_7$} \\
+        \multicolumn{1}{c}{$g_1$} &
+        \multicolumn{1}{c}{$g_2$} &
+        \multicolumn{1}{c}{$g_3$} &
+        \multicolumn{1}{c}{$g_4$} &
+        \multicolumn{1}{c}{$g_5$} \\
       \hline
-        2 &
-        1.2114 \\
-        3 &
-      1.3498 &
-      $-0.014909$ \\
+      2 &
+        1.22182 &
+        $-0.0140696$ \\
+      3 &
+        1.33128 &
+        $-0.0144135$ &
+        $-0.000233014$ \\
       4 &
-      1.4490 &
-      $-0.10871$ & $-0.0031747$ \\
+        1.33106 &
+        $-0.0268822$ &
+        \hphantom{$-$}$0.0332121$ \\
       5 &
-      1.4719 &
-      $-0.11399$ & $-0.0031669$ & $8.8574\times10^{-7}$ \\
+        1.51661 &
+        $-0.248646$ &
+        \hphantom{$-$}$0.0513219$ &
+        $0.00433870$ \\
       6 &
-      1.4358 &
-      $-0.19533$ & 0.029301 & 0.0039906 & $-0.00011913$ \\
+        1.37654 &
+        $-0.236244$ &
+        $-0.00860939$ &
+        0.00204312 &
+        $-0.000954046$ \\
       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 & $-0.00026034$ \\
+        1.33161 &
+        $-0.252714$ &
+        $-0.0308462$ &
+        0.00491578 &
+        \hphantom{$-$}0.000264989 &
+        $-0.000210698$
   \end{tabular}
+  \caption{
+    Free parameters in the fit of the parametric coordinate transformation and
+    scaling form to known values of the scaling function series coefficients
+    for $\mathcal F_\pm$. The fit at stage $n$ matches those coefficients up to
+    and including order $n$.
+  } \label{tab:fits}
 \end{table}
 
 \begin{figure}
@@ -778,7 +775,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
   \caption{
     The series coefficients for the scaling function $\mathcal F_-$ as a
     function of polynomial order $m$. The numeric values are from Table
-    \ref{tab:fits}, and those of Caselle \textit{et al.} are from the most
+    \ref{tab:data}, and those of Caselle \textit{et al.} are from the most
     accurate scaling function listed in \cite{Caselle_2001_The}.
   } \label{fig:glow.series}
 \end{figure}
@@ -835,7 +832,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
   \caption{
     The series coefficients for the scaling function $\mathcal F_+$ as a
     function of polynomial order $m$. The numeric values are from Table
-    \ref{tab:fits}, and those of Caselle \textit{et al.} are from the most
+    \ref{tab:data}, and those of Caselle \textit{et al.} are from the most
     accurate scaling function listed in \cite{Caselle_2001_The}.
   }
 \end{figure}