On the susceptibility of a ferromagnetic above the Curie point

Abstract

Series expansions for the susceptibility of a ferromagnetic at high temperatures are examined in detail to estimate the curvature of the reciprocal of the susceptibility immediately above the Curie point. For an Ising model with spin ½ a substantial number of terms of the series are available, and the series is well behaved (i. e. the coefficients vary smoothly). The asymptotic behaviour of the coefficients can be conjectured with fair confidence, and a closed formula can be derived based on this conjecture. For an Ising model with spin greater than ½ fewer terms of the series are available, but the series is still well behaved, and an extra­polation can again be undertaken fairly confidently. For the Heisenberg model with spin ½ the behaviour of the coefficients is considerably more erratic and the predictions are more tentative. It is concluded generally that the curvature of the reciprocal susceptibility depends primarily on the lattice structure and little on the type of interaction; that there is little variation between the different types of two-dimensional, and different types of three-dimensional lattice, although there is a marked difference between two- and three-dimensional lattices. The experimental curve of Weiss & Forrer for nickel is examined, and it is found that the data can be fitted quite well by the extrapolation formula for a three-dimensional lattice. It is thus possible to account for the experimental results assuming only short-range interatomic forces.