Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

Abstract

The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an $\mathrm{exp}(\ensuremath{-}A{s}^{4}+B{s}^{2})$ spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Pad\'e-Borel method to yield the critical indices $\ensuremath{\gamma}=1.241\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\eta}=0.02\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\nu}=0.63\ifmmode\pm\else\textpm\fi{}0.01$, and ${\ensuremath{\Delta}}_{1}=0.49\ifmmode\pm\else\textpm\fi{}0.01$.