Exchange interaction model of ferromagnetism

Abstract

The Schrödinger exchange operator for arbitrary spin has been used to form an interaction Hamiltonian for a nearest-neighbor model of ferromagnetism. Through use of the cluster expansion method and new group theoretic results in conjunction with the diagrammatic method, eight terms in the high temperature series for the zero-field partition function and the low-field susceptibility are obtained for arbitrary spin and general crystal lattice. Critical parameters are estimated from these series by means of various ratio tests and Padé approximants. For the cubic lattices the Curie temperature Tc and the critical index γ are given by kBTC/J = 0.547(q - 1.6)(Y-1 + 0.21) and γ = 0.48 + 2.16 Y-1 for S > 1/2; = 1.41 ± 0.02 for S = 1/2, respectively, where Y = 2S + 1. Comparison of these results with those appropriate to the Heisenberg model as well as to experimental values is made. The concept of multipolar ordering is also discussed. It is shown that for the present model all of the 2S "independent" multipolar phase transitions are exactly degenerate with the usual dipolar transition.