Two-dimensional Ising-like systems: Corrections to scaling in the Klauder and double-Gaussian models.

Abstract

Partial-differential approximants are used to study the critical behavior of the susceptibility, \ensuremath{\chi}(x,y), of the Klauder and double-Gaussian scalar spin, or O(1) models on a square lattice using two-variable series to order ${x}^{21}$ where x\ensuremath{\propto}J/${k}_{B}$T while y serves to interpolate analytically from the Gaussian or free-field model at y=0 to the standard spin-(1/2) Ising model at y=1. The pure Ising critical point at y=1 appears to be the only non-Gaussian multisingularity in the range 0<y\ensuremath{\le}1. It is concluded that the exponent \ensuremath{\theta} characterizing the leading irrelevant corrections to scaling lies in the range \ensuremath{\theta}=1.35\ifmmode\pm\else\textpm\fi{}0.25. This supports the validity of Nienhuis's conjecture \ensuremath{\theta}=(4/3) but it is argued that, contrary to normal expectations, this (rational) value entails only logarithmic corrections to pure Ising critical behavior. The existence of strong crossover effects for 0.1\ensuremath{\lesssim}y\ensuremath{\lesssim}0.6 and the appearance of an effective exponent, ${\ensuremath{\gamma}}_{\mathrm{eff}\mathrm{\ensuremath{\simeq}}1.9}$ to 2.0, is discussed and related to work on the \ensuremath{\lambda}${\mathrm{cphi}}^{4}$ model.