We have investigated the phase behavior of the ferromagnetic Heisenberg fluid using two versions of density-functional theory, viz., the mean-field and modified mean-field approximations. In the latter, configurations in the average of the perturbative part of the energy are weighted by the zero-density approximation of the pair distribution function. This is known to yield an improved description of the phase diagram of dipolar fluids. Both theories predict, in addition to isotropic liquid and vapor phases, a ferromagnetically ordered liquid phase at moderate to high (fluid) densities. The topology of the phase diagram depends sensitively on the relative strengths of the isotropic and anisotropic parts of the intermolecular potential. For weakly anisotropic potentials, the order disorder transition is always continuous and terminates at a critical endpoint on (the liquid side of) the liquid-vapor coexistence curve. Increasing the anisotropy above a certain threshold drives the transition first order at low temperatures, thus leading to the appearance of a tricritical point and a ferromagnetic liquid-isotropic liquid-vapor triple point. For strongly anisotropic potentials, ordinary liquid-vapor phase separation is preempted by a direct (condensation-ordering) transition between a low-density disordered phase and a ferromagnetic liquid that becomes continuous at a tricritical point. Results are in agreement with earlier theoretical work and, moreover, are compatible with recent Monte Carlo simulations of the same system. These provide evidence of a magnetic critical point (with the Curie line ending at a critical endpoint on the vapor side of the liquid-vapor coexistence curve). Owing to finite size effects, however, the existence of a tricritical point cannot be ruled out. The latter is predicted, for the same model, by both theories. In this context, we looked for coexistence between orientationally ordered fluid phases in generalized Heisenberg models and found it, within mean-field theory, for a class of fluids characterized by soft repulsive isotropic interactions, in addition to the hard-core and ferromagnetic Heisenberg potentials.

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Journal Phys. Rev. E
Tavares, J. M, Telo da Gama, M. M, Teixeira, P. I. C, Weis, J. J, & Nijmeijer, M. J. P. (1995). Phase diagram and critical behavior of the ferromagnetic Heisenberg fluid from density-functional theory. Phys. Rev. E, 52, 1915–1929.