Ising fluids in an external magnetic field: an integral equation   approach
  The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field $H$ for a wide class of Ising fluid models with various ratios $R$ for the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths $z_1$ and $z_2$, corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in $R$ as well as in $z_1$ and $z_2$ can lead to different topologies of the phase diagrams. In particular, depending on the value of $R$, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing $H$. The para-ferro magnetic transition is also affected by changes in $R$ and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For $H \to \infty$, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated, that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when $z_1$ and $z_2$ are large). In the Kac limit $z_1,z_2 \to +0$, both approaches tend to nearly the same results. 
I.P. Omelyan, I. M. Mryglod, R. Folk, and W. Fenz