High-Temperature Critical Indices for the Classical Anisotropic Heisenberg Model

High-temperature series expansions for the spin-spin correlation function of the classical anisotropic Heinsenberg model are calculated for various lattices and anisotropies through order $T^{-8\mathrm{}}$ (close-packed lattices) and $T^{-9\mathrm{}}$ (loose-packed lattices). These series are combined and then extrapolated to give the high-temperature critical indices $\gamma$ (susceptibility), $\nu$ (correlation range), and $\alpha$ (specific heat) as functions of anisotropy. Our results are consistent with the hypothesis that the critical indices change only 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.