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-rw-r--r--ising_scaling.tex49
1 files changed, 28 insertions, 21 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex
index bfa67fb..161a4e6 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -480,15 +480,16 @@ analytic for all $\theta\in\mathbb C$ outside the Langer branch cuts.
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}
+ \begin{tabular}{c|cccccccccc}
& \multicolumn{9}{c}{$n$} \\
- & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\
+ & 0 & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\
\hline\hline
- $n_-$ & 2 & 3 & 3 & 4 & 5 & 6 & 6 & 6 \\
- $n_0$ & 1 & 2 & 3 & 4 & 4 & 5 & 7 & 8 \\
- $n_+$ & 2 & 2 & 4 & 4 & 6 & 6 & 6 & 8
+ $n_-$ & 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 &
@@ -499,6 +500,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
1.33347 &
\\
$A_c$ &
+ 0.0982351 &
0.100228 &
0.0720104 &
0.0809725 &
@@ -509,6 +511,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
0.0328499 &
\\
$A_{\mathrm{YL}}$ &
+ 2.38365 &
2.3876 &
2.37518 &
2.46094 &
@@ -519,6 +522,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
2.4769 &
\\
$F_0$ &
+ 1.07666 &
1.07383 &
1.14375 &
1.16003 &
@@ -529,6 +533,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
1.33327 &
\\
$F_1$ &
+ 2.00381 &
1.99663 &
2.14753 &
2.15397 &
@@ -539,6 +544,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
2.50906 &
\\
$F_2$ &
+ 0.228234 &
0.228235 &
0.226794 &
0.240421 &
@@ -549,6 +555,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
0.232317 &
\\
$h_0$ &
+ 1.19426 &
1.19078 &
1.2259 &
1.18183 &
@@ -558,7 +565,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
1.21605 &
1.21825 &
\\
- $h_1/10^{-2}$ &
+ $h_1/10^{-2}$ & &
$0.0377284$ &
$-1.32208$ &
$-1.98552$ &
@@ -568,7 +575,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
$-5.53426$ &
$-5.79592$ &
\\
- $h_2/10^{-3}$ &
+ $h_2/10^{-3}$ & &
&
1.68015 &
3.72445 &
@@ -578,7 +585,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
9.31123 &
9.7244 &
\\
- $h_3/10^{-3}$ & &
+ $h_3/10^{-3}$ & & &
$-0.300336$ &
$-1.11915$ &
$-1.68817$ &
@@ -587,7 +594,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
$-2.6766$ &
$-2.79303$ &
\\
- $h_4/10^{-4}$ & & &
+ $h_4/10^{-4}$ & & & &
$2.59026$ &
$4.92004$ &
$6.6988$ &
@@ -595,7 +602,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
$8.83288$ &
$9.25784$ &
\\
- $h_5/10^{-4}$ & & &
+ $h_5/10^{-4}$ & & & &
$-0.578821$ &
$-1.50074$ &
$-2.55766$ &
@@ -603,54 +610,54 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
$-3.30063$ &
$-3.4621$ &
\\
- $h_6/10^{-4}$ & & & &
+ $h_6/10^{-4}$ & & & & &
$0.350651$ &
$0.965437$ &
$1.24302$ &
$1.29961$ &
$1.36707$ &
\\
- $h_7/10^{-5}$ & & & &
+ $h_7/10^{-5}$ & & & & &
$-0.617004$ &
$-3.5398$ &
$-5.06226$ &
$-5.40426$ &
$-5.70884$ &
\\
- $h_8/10^{-5}$ & & & & &
+ $h_8/10^{-5}$ & & & & & &
$0.978241$ &
$1.90968$ &
$2.22565$ &
$2.40644$ &
\\
- $h_9/10^{-6}$ & & & & &
+ $h_9/10^{-6}$ & & & & & &
$-1.76567$ &
$-6.25434$ &
$-8.84571$ &
$-10.1167$ &
\\
- $h_{10}/10^{-6}$ & & & & & &
+ $h_{10}/10^{-6}$ & & & & & & &
$1.51279$ &
$3.12976$ &
$4.0249$ &
\\
- $h_{11}/10^{-7}$ & & & & & &
+ $h_{11}/10^{-7}$ & & & & & & &
$-2.17053$ &
$-9.37655$ &
$-14.7593$ &
\\
- $h_{12}/10^{-7}$ & & & & & & &
+ $h_{12}/10^{-7}$ & & & & & & & &
$2.0809$ &
$4.687$ &
\\
- $h_{13}/10^{-8}$ & & & & & & &
+ $h_{13}/10^{-8}$ & & & & & & & &
$-2.83978$ &
$-12.363$ &
\\
- $h_{14}/10^{-8}$ & & & & & & & &
+ $h_{14}/10^{-8}$ & & & & & & & & &
$2.39528$ &
\\
- $h_{15}/10^{-9}$ & & & & & & & &
+ $h_{15}/10^{-9}$ & & & & & & & & &
$-2.99667$ &
\\
\end{tabular}
@@ -718,7 +725,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of
set xlabel '$1/n$'
set xrange [0:0.55]
set ylabel '$\mathcal F_n/\mathcal F_{n-1}$'
- set yrange [0:10]
+ set yrange [0:15]
plot \
dat1 using (1/$1):(abs(ratLast($2))) title 'Numeric', \