We develop a general method to study inhomogeneous liquids in an external field using orthogonal polynomials tailored to the one-body density. The procedure makes integral equation calculations of these systems no more difficult than those of ordinary homogeneous molecular fluids. We apply this method to the ferromagnetic Heisenberg spin fluid in an external magnetic field using both the reference-hypernetted chain closure and a reference version of the Zerah-Hansen closure, with no further approximations. The calculation includes a mapping of the two-phase region for several values of the external magnetic field. Comparison with Monte Carlo simulation data shows the integral equation procedure yielding nearly exact results, in particular for nonzero external fields.

• Received 26 February 1998

DOI:https://doi.org/10.1103/PhysRevE.58.3478