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-rw-r--r--ising_scaling.tex12
1 files changed, 8 insertions, 4 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex
index 210f63c..1933983 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -26,7 +26,7 @@ linkcolor=purple
\begin{document}
-\title{Smooth and global Ising universal scaling functions}
+\title{Precision approximation of the universal scaling functions for the 2D Ising model in an external field}
\author{Jaron Kent-Dobias}
\affiliation{Laboratoire de Physique de l'Ecole Normale Supérieure, Paris, France}
@@ -133,10 +133,14 @@ $\Delta=\beta\delta=\frac{15}8$ will appear often. The flow equations are
truncated here, but in general all terms allowed by the symmetries of the
parameters are present on their righthand side. By making a near-identity
transformation to the coordinates and the free energy of the form
-\begin{equation}
+\begin{align}
\label{eq:AnalyticCOV}
-u_t(t,h)=t+\cdots, ~~~~u_h(t, h)=h+\cdots,~~~\mathrm{and}~u_f(f,u_t,u_h)\propto f(t,h)-f_a(t,h),
-\end{equation}
+ u_t(t,h)=t+\cdots
+ &&
+ u_h(t, h)=h+\cdots
+ &&
+ u_f(f,u_t,u_h)\propto f(t,h)-f_a(t,h),
+\end{align}
one can bring
the flow equations into the agreed upon simplest normal form
\begin{align} \label{eq:flow}