The Curie–Weiss–Néel model of a ferrimagnet

Abstract

An analogue, for ferrimagnetism, of the Curie–Weiss model ferromagnet is introduced. The resulting structure, the Curie–Weiss–Néel model, is based on a two sublattice description in which spins of one magnitude occupy one sublattice and spins of another magnitude occupy the other. Attention is concentrated on the case in which spins on the different sublattices tend to align in an anti-parallel fashion. Many properties of the new model are similar to those of the Curie–Weiss ferromagnet. Artificially long-ranged interactions connect spins on the different sublattices. The complete thermodynamics can be obtained exactly by relatively elementary methods. The exact solution of the model is essentially identical with the appropriate mean field results (of Néel). Attention is given to the Néel point and associated critical phenomena. Many standard critical exponents are calculated and, of course, classical exponent values result. Novel features of critical phenomena in ferrimagnets are considered. These are associated with the fact that, theoretically, the staggered magnetization and staggered fields are important while, experimentally, the total magnetization and uniform fields are usually employed. It is shown that, within the present context, corresponding staggered and uniform properties have identical exponent values.