High-Temperature Critical Indices for the Classical Anisotropic Heisenberg Model

Abstract

Using the vertex renormalized form of the technique developed by Englert,¹ high‐temperature series expansions for the spin‐spin correlation function of the classical anisotropic Heisenberg model are calculated for various lattices and anisotropies through order T⁻⁸ (close‐packed lattices) and T⁻⁹ (loose‐packed lattices). These series are combined and then extrapolated to give the high‐temperature critical indices γ (zero‐field susceptibility), ν (correlation range), and α (specific heat) as functions of anisotropy. The results are consistent with the hypothesis that the critical indices only change when there is a change in the symmetry of the system, e.g., in interpolating between the Ising and isotropic Heisenberg models, indices remain Ising‐like until the system becomes isotropic, at which point they appear to change discontinuously. Previous results for the limiting cases are confirmed and extended. Series for the limiting cases (spin‐infinity Ising, XY and isotropic Heisenberg models) as well as for the spin‐½ Ising model² have been derived for the B‐site spinel lattice. Analysis of these series shows that the anomalies in the critical indices, reported on the basis of six‐term expansions,³ disappear with the use of longer series.