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| -rw-r--r-- | ising_scaling.tex | 12 |
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} |