High temperature series expansions for the anisotropic Heisenberg model

Abstract

High temperature series expansions have been calculated in terms of a general spin variable S, and anisotropy parameter eta , and and arbitrary lattice structure for the longitudinal version of the anisotropic Heisenberg model defined by the hamiltonian H_N=- Sigma _ijJ(S_izS_jz+ eta (S_i⁺S_j^-+S_i^-S_j⁺))- mu H Sigma _i=1^NS_iz where the initial sum extends over the set of nearest neighbour sites of a regular crystal lattice structure of N sites, situated in an external magnetic field H. This model contains the Ising model and the isotropic Heisenberg model at the points eta =0, and eta =¹/₂ respectively. The expansions of the partition function Z in zero field and the zero field susceptibility have been obtained through orders T^-7 and T^-6 respectively.