Onsager reaction-field approximation for a ferromagnet with a single-ion anisotropy

Abstract

The Onsager reaction-field approximation is extended to the case of a Heisenberg ferromagnet with a uniaxial single-ion second-order anisotropy. For a paramagnetic phase of a three-dimensional ferromagnet with classical vector spins, the critical temperature of the ferromagnetic transition, susceptibility, pair longitudinal and transverse spin correlation functions, and the magnetic contribution to heat capacity have been calculated with allowance for Onsager corrections for the reaction field. It is shown that the critical exponents of the susceptibility, heat capacity, and correlation radius for an anisotropic ferromagnet in this approximation coincide with the critical exponents of the spherical model. The effect of Onsager corrections on the critical temperature of the transition of a ferromagnet with a d-dimensional hypercubic lattice has been analyzed to show that the corrections from the Onsager reaction field vanish in the limit of an infinite dimensionality of space.