Phase diagram in a continuum model of the classical Heisenberg ferromagnet: mean spherical approximation

The continuum Heisenberg model of spin fluid is considered. The pair correlation functions and the single-particle distribution function of ferromagnetic state are obtained by the self-consistent solution of the Ornstein–Zernike and the Lovett equations in the mean spherical approximation. On the basis of the analytical solution the phase diagram is calculated and compared with the available Monte Carlo results for the same model. The agreement between theory and simulation is quite satisfactory, especially for the liquid–gas coexistence line. The MSA suggests that only ordered states are involved in the gas–liquid transition near the gas–liquid critical point. This result confirms the Monte Carlo prediction about the existence of a magnetic critical point.