Added Jim's braggy paragraph.

1 files changed, 10 insertions, 0 deletions

diff --git a/ising_scaling.tex b/ising_scaling.tex
index d91e5ca..1fdacc3 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -90,6 +90,16 @@ their simplest form. Then, the arbitrary analytic functions that compose those
 coordinates are approximated by truncated polynomials whose coefficients are
 fixed by matching the series expansions of the universal function.
 
+For the two-dimensional Ising model, his method produces scaling functions
+accurate to within $10^{-4}$ using just the values of the first three
+derivatives of the function evaluated at two points, e.g., critical amplitudes
+of the magnetization, susceptibility, and first generalized susceptibility.
+With six derivatives, it is accurate to about $10^{-7}$. We hope that with some
+refinement, this idea might be used to establish accurate scaling functions for
+critical behavior in other universality classes, doing for scaling functions
+what advances in conformal bootstrap did for critical exponents
+\cite{Gliozzi_2014_Critical}.
+
 \section{Universal scaling functions}
 
 A renormalization group analysis predicts that certain thermodynamic functions