Padé Approximation to Ferromagnet with Anisotropic Exchange Interaction

Abstract

The Heisenberg model, the Ising model and the x y model in ferromagnetism are treated within a unified scheme. The exchange interaction between nearest neighboring spins i and j is -( J /2)[ a σ i z σ j z + b (σ i x σ j x +σ i y σ j y )], where J is the exchange integral, σ i the Pauli spin operator of the i -th spin, and a and b are parameters varying from 0 to 1, respectively. The high temperature series for the susceptibilities of linear chain, simple quadratic and simple cubic lattices are calculated up to the seventh order of J / k T . Padé approximation is applied to find the Curie point and the power of the singularity of the susceptibility. In the case of a =1 the Curie point is almost constant in the region \(0{\leq}b{\lesssim}0.7\) for simple quadratic and \(0{\leq}b{\lesssim}0.8\) for simple cubic lattice, respectively, but the convergence of Padé approximation becomes worse as b approaching 1.