Corrections to Scaling and Crossover in Two-Dimensional Ising and Scalar-Spin Systems

Abstract

Two-dimensional criticality is studied in the Klauder and double-Gaussian $O\mathrm{}\left(1\right)\mathrm{}$ models which interpolate from a Gaussian model at $y=0\mathrm{}$ to the $S=\frac{1}{2}$ Ising model at $y=1\mathrm{}$. Despite strong crossover effects for $0<y\lesssim 0.6$, partial differential approximants for the two-variable susceptibility series indicate criticality of Ising type for all $y>\mathrm{}0\mathrm{}$ and yield a correction exponent $\theta =1.35\mathrm{}\pm 0.25$. The conjecture $\theta =\frac{4}{3}$ in the absence of a related critical operator, and the observation ${\gamma }_{\mathrm{eff}}\simeq 2.0$ in the Klauder, double-Gaussian, and $\lambda {\varphi }^4$ models, are discussed.