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@@ -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