Self-Consistent Correlation Theory of Ferromagnetism

Abstract

The theory to be described here may be classified as a cluster theory of ferromagnetism. It is presently restricted to lattices with nearest-neighbor interactions and no external magnetic field, but is unrestricted in spin magnitude. A point of departure from previous cluster theories is that it represents the effect of the other spins of the lattice on the cluster as a temperature-dependent exchange coupling, rather than as a molecular field. A second departure is that a consistency condition is imposed on the spin-spin correlation functions of the cluster rather than on the spin averages as in previous methods. This allows the coupling between the cluster and its environment to be retained above the Curie point, making it a useful theory for the study of the high-temperature behavior of a magnetic system. The theory gives reasonable values for the Curie temperature for those lattices studied which have a transition, and predicts no transition for those lattices which are commonly believed not to order at finite temperatures. The theory, as it stands, is least useful at temperatures below the Curie point, since it predicts that the spontaneous magnetization attains its saturation value immediately below the Curie point. Results of calculations on the Heisenberg and Ising square and simple cubic lattices are presented. Only the spin-\textonehalf{} cases are considered.