  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.
