A Modified Spherical Model of a First-Order Phase Transition

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Abstract
It is shown that the addition of a weak anisotropy field to the spherical model produces a very complete and realistic mathematical picture of a first-order phase transition. In contrast to the conventional spherical model of a ferromagnet (or lattice gas), the modified model exhibits phase separation in the flat two-phase region of the magnetization curve (or isotherm). The magnetization curve has an analytic continuation into the two-phase region which may be identified with a homogeneous metastable state. The new model is not exactly soluble but lends itself easily to a diagram renormalization technique. Except in the immediate neighborhood of the critical point, this technique gives rigorous results.