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-rw-r--r--ising_scaling.tex21
1 files changed, 13 insertions, 8 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex
index 62495fc..2fa2528 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -584,7 +584,7 @@ use these coefficients to fix the unknown functions $G$ and $g$, the error in
the approximate functions and their derivatives can be evaluated by comparison
to their known values at the critical isotherm, or $\theta=1$.
-\begin{table}\label{tab:fits}
+\begin{table}
\begin{tabular}{l|lll}
\multicolumn1{c|}{$m$} & \multicolumn{1}{c}{$\mathcal F_-^{(m)}$} & \multicolumn{1}{c}{$\mathcal F_0^{(m)}$} & \multicolumn1c{$\mathcal F_+^{(m)}$} \\\hline
0 & \hphantom{$-$}0 & $-1.197\,733\,383\,797\ldots$ & \hphantom{$-$}0 \\
@@ -610,7 +610,7 @@ 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}
\end{table}
\begin{table}
@@ -723,9 +723,9 @@ to their known values at the critical isotherm, or $\theta=1$.
set xlabel '$n$'
set xrange [1.5:7.5]
- set ylabel '$|\Delta\mathcal F_0^{(m)}|$'
- set format y '$10^{%T}$'
set logscale y
+ set format y '$10^{%T}$'
+ set ylabel '$|\Delta\mathcal F_0^{(m)}|$'
set yrange [0.000002:0.003]
set style data linespoints
@@ -758,19 +758,21 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
\begin{gnuplot}[terminal=epslatex]
dat1 = 'data/glow_numeric.dat'
dat2 = 'data/glow_series_ours_0.dat'
- dat3 = 'data/glow_series_ours_9.dat'
+ dat3 = 'data/glow_series_ours_7.dat'
dat4 = 'data/glow_series_caselle.dat'
+ set xlabel '$m$'
+ set xrange [0:14.5]
+
set key top left Left reverse
set logscale y
- set xlabel '$m$'
set ylabel '$\mathcal F_-^{(m)}$'
set format y '$10^{%T}$'
- set xrange [0:14.5]
plot \
dat1 using 1:(abs($2)):3 title 'Numeric' with yerrorbars, \
dat2 using 1:(abs($2)) title 'This work ($n=2$)', \
+ dat3 using 1:(abs($2)) title 'This work ($n=7$)', \
dat4 using 1:(abs($2)) title 'Caselle \textit{et al.}'
\end{gnuplot}
\caption{
@@ -785,7 +787,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
\begin{gnuplot}[terminal=epslatex]
dat1 = 'data/glow_numeric.dat'
dat2 = 'data/glow_series_ours_0.dat'
- dat3 = 'data/glow_series_ours_9.dat'
+ dat3 = 'data/glow_series_ours_7.dat'
dat4 = 'data/glow_series_caselle.dat'
ratLast(x) = (back2 = back1, back1 = x, back1 / back2)
back1 = 0
@@ -799,6 +801,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
plot \
dat1 using (1/$1):(abs(ratLast($2))) title 'Numeric', \
dat2 using (1/$1):(abs(ratLast($2))) title 'This work ($n=2$)', \
+ dat3 using (1/$1):(abs(ratLast($2))) title 'This work ($n=7$)', \
dat4 using (1/$1):(abs(ratLast($2))) title 'Caselle \textit{et al.}'
\end{gnuplot}
\caption{
@@ -813,6 +816,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
\begin{gnuplot}[terminal=epslatex]
dat1 = 'data/ghigh_numeric.dat'
dat2 = 'data/ghigh_series_ours_2.dat'
+ dat3 = 'data/ghigh_series_ours_7.dat'
dat4 = 'data/ghigh_caselle.dat'
set key top left Left reverse
@@ -825,6 +829,7 @@ accurate to within $2\times10^{-3}$. This approximation for the scaling function
plot \
dat1 using 1:(abs($2)):3 title 'Numeric' with yerrorbars, \
dat2 using 1:(abs($2)) title 'This work ($n=2$)', \
+ dat3 using 1:(abs($2)) title 'This work ($n=7$)', \
dat4 using 1:(abs($2)) title 'Caselle \textit{et al.}'
\end{gnuplot}
\caption{