Integral equation approach for XY spin fluids in an external magnetic field

We develop an integral equation approach to study anisotropic fluids with planar spins in the presence of an external field. As a result, the integral equation calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The method proposed is applied to the investigation of coexistence phase properties of ferromagnetic XY spin fluids in a magnetic field. The soft mean spherical approximation is used for the closure relation connecting the orientationally dependent two-particle direct and total correlation functions. The Lovett-Mou-Bu-Wertheim and Born-Green-Yvon equations are employed to describe the one-particle orientational distribution. The phase diagrams are obtained in the whole range of varying the external field for a wide class of XY spin fluid models with various ratios of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of changing the screening radii of the interaction potentials is also considered. Different types of the phase diagram topology are identified. They are characterized by the existence of critical, tricritical, critical end, and triple points related to transitions between gas, liquid, para- and ferro-magnetic states, accompanied by different external field dependencies of critical temperatures and densities corresponding to the gas-liquid transition. Under special van Laar conditions, an unsymmetrical tricritical point is found additionally. This complexity with respect to simple liquids is explained by coupling between spin and spatial degrees of freedom. As is demonstrated, the integral equation approach leads to accurate predictions of the complicated phase diagram behavior which coincide well with those evaluated by the cumbersome Gibbs ensemble simulation and multiple-histogram reweighing techniques. (author)