Padé Approximation to Ferromagnet with Anisotropic Exchange Interaction

Department of Physics, Tokyo Metropolitan University

The Heisenberg model, the Ising model and the xy model in ferromagnetism are treated within a unified scheme. The exchange interaction between nearest neighboring spins i and j is -(J/2)[aσizσjz+bixσjxiyσjy)], where J is the exchange integral, σi 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/kT. 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. ©1967 The Physical Society of Japan

DOI: 10.1143/JPSJ.23.516

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