From 4c78908d322b491b2613ebad3c65e8761aa10e70 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 26 Oct 2021 12:33:22 +0200
Subject: Added some outlook talk.

---
 ising_scaling.tex | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

(limited to 'ising_scaling.tex')

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
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