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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-28 09:18:21 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-10-28 09:18:21 +0200
commit641557954eba488630fda8905bfbcfbe3d73bad9 (patch)
treec39f3ebde4d3f547088ceba9f9f26172a010a56e
parent2acb7414c60879238fa4afbd58eb55a834a470b2 (diff)
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Added Schofield coordinate plot.
-rw-r--r--ising_scaling.tex34
1 files changed, 34 insertions, 0 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex
index 3f11729..919049e 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -332,6 +332,40 @@ the low-temperature zero-field (phase coexistence) line.
In practice the infinite series in \eqref{eq:schofield.funcs} cannot be
entirely fixed, and it will be truncated at finite order.
+\begin{figure}
+ \begin{gnuplot}[terminal=epslatex]
+ t0 = 1.36261
+ g0 = 0.438453
+ g1 = -0.0531270
+ g2 = -0.00391478
+ g3 = -0.000408016
+ g4 = 0.0000262629
+ g5 = -0.00000109745
+
+ g(t) = (1-(t/t0)**2)*(g0*t + g1*t**3 + g2*t**5 + g3*t**7 + g4*t**9 + g5*t**11)
+
+ set xlabel '$u_t$'
+ set ylabel '$u_h$'
+ set key left bottom reverse title '\raisebox{1em}{$R$}'
+
+ set xzeroaxis
+ set yzeroaxis
+
+ set parametric
+ set trange [-t0:t0]
+
+ plot \
+ (1-t**2),g(t) title '$1$', \
+ 2*(1-t**2),2*g(t) title '$2$', \
+ 4*(1-t**2),4*g(t) title '$4$'
+ \end{gnuplot}
+ \caption{
+ Example of the parametric coordinates. Lines are of constant $R$ from
+ $-\theta_0$ to $\theta_0$ for $g(\theta)$ taken from the $n=6$ entry of
+ Table \ref{tab:fits}.
+ } \label{fig:schofield}
+\end{figure}
+
One can now see the convenience of these coordinates. Both invariant scaling
combinations depend only on $\theta$, as
\begin{align}