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diff --git a/ising_scaling.tex b/ising_scaling.tex index 668ba63..50de498 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -927,7 +927,18 @@ the ratio. \section{Outlook} -The successful smooth description of the Ising free energy produced in part by analytically continuing the singular imaginary part of the metastable free energy inspires an extension of this work: a smooth function that captures the universal scaling \emph{through the coexistence line and into the metastable phase}. Indeed, the tools exist to produce this: by writing $t=R(1-\theta^2)(1-(\theta/\theta_m)^2)$ for some $\theta_m>\theta_0$, the invariant scaling combination +We have introduced explicit approximate functions forms for the two-dimensional +Ising universal scaling function in the relevant variables. These functions are +smooth to all orders, include the correct singularities, and appear to converge +exponentially to the function as they are fixed to larger polynomial order. + +The successful smooth description of the Ising free energy produced in part by +analytically continuing the singular imaginary part of the metastable free +energy inspires an extension of this work: a smooth function that captures the +universal scaling \emph{through the coexistence line and into the metastable +phase}. Indeed, the tools exist to produce this: by writing +$t=R(1-\theta^2)(1-(\theta/\theta_m)^2)$ for some $\theta_m>\theta_0$, the +invariant scaling combination \begin{acknowledgments} The authors would like to thank Tom Lubensky, Andrea Liu, and Randy Kamien |