Liquid-vapor interfaces in XY-spin fluids: An inhomogeneous anisotropic integral-equation approach

An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the Ornstein-Zernike equation for the orientationally dependent two-particle correlation functions. Using the proposed inhomogeneous angle-harmonics expansion formalism we show that these integral equations can be reduced to a much simpler form similar to that inherent for a system of isotropic fluids. The interfacial orientationally dependent direct correlation function can be consistently constructed by means of a nonlinear interpolation via its values obtained in the coexisting anisotropic bulk phases. A soft mean spherical approximation is employed for the closure relation. This has allowed us to solve the complicated integral equations in the situation when both spatial inhomogeneity and orientational anisotropy are present simultaneously. The approach introduced is applied to an XY fluid model with ferromagnetic spin interactions. As a result, the density-orientation and magnetization profiles at the liquid-vapor interfaces are calculated in a wide range of temperatures up to subcritical regions. The influence of the external field on the microscopic structure of the interfaces and the surface tension is also analyzed in detail.