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, χ(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∝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≤1. It is concluded that the exponent θ characterizing the leading irrelevant corrections to scaling lies in the range θ=1.35±0.25. This supports the validity of Nienhuis’s conjecture θ=(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≲y≲0.6 and the appearance of an effective exponent, ${\gamma }_{\mathrm{eff}\mathrm{\simeq }1.9}$ to 2.0, is discussed and related to work on the λ${\mathrm{cphi}}^4$ model.