Fluctuation effects in the spherical model

A general investigation is made of the spherical model for arbitrary dispersion of the volume integrals and lattice symmetry. It is shown that in this case a phase transition takes place to a structure that in general is not commensurate with the crystal lattice and is not destroyed by a magnetic field. The spontaneous and longitudinal magnetic moments and critical temperature are found as functions of the magnetic field. In addition, the physical meaning of the “sticking” of the saddle point is clarified. With a view to establishing the part played by fluctuations, the spherical model is considered for magnets with long but finite interaction range. In this model, the temperature and magnetic field regions in which fluctuation effects are important are determined, and it is shown that outside these regions the critical exponents are equal to the exponents found in mean field theory. A magnet with two inequivalent magnetic sublattices is investigated. It is shown that, depending on the radii of the exchange integrals, phases that are anomalous from the point of view of mean field theory can arise in such a system in the critical region.