Pair-Product Model of Heisenberg Ferromagnets

A model is proposed which is similar in character to the Heisenberg ferromagnets in the vicinity of Curie points. Its mathematical structure resembles the Ising model. This model is convenient for investigating magnetic transitions. In one dimension, this model can be treated exactly: it is shown that there occurs no phase transition. The following results are obtained for the two or three dimensional cases: in anisotropic ferromagnets, as the transverse components becomes larger, the Curie point becomes lower; as the number of nearest neighbours becomes larger, the Curie point becomes higher and the anisotropy-dependence smaller. The theory is extended to the cases with higher spin values. In addition, the cross section of critical scattering is calculated using the Bethe approximation for the pair-product model. Finally, the singularity of the susceptibilities in the vicinity of the Curie point is discussed using the Padé approximation for the pair-product model.