Unbiased Estimation of Corrections to Scaling by Partial Differential Approximants

Abstract

High-temperature series for two bcc lattice models which interpolate between the Gaussian (or free-field) model and the $S=\frac{1}{2}$ Ising model are analyzed by partial differential approximants. Series to order 21 in both $x\propto \frac{1}{T}$ and the interpolation parameter, $y$, yield unbiased estimates for the correction-to-scaling exponent, $\theta =0.54\mathrm{}\pm 5$, and the susceptibility exponent, $\gamma =1.2385\mathrm{}\pm 15$. The results are universal and agree tolerably with field-theoretic estimates and well with biased, one-variable analyses of general spin Ising models.