A model for amorphous ferromagnets consisting of a gas of hard spheres each having a spin mu =+or-1 and interacting with a long-range Kac potential gamma nu K( gamma mod r mod ) in nu dimensions, is considered in the long-range gamma to 0+limit. The resulting free energy is a combination of the classical van der Waals and Curie-Weiss (or mean-field) expressions. Isotherms in the pure gas phase have a cusp for a range of temperatures, reflecting the transition from gas to magnetic gas, with standard mean-field exponents. The transition point on the critical isotherm is a higher-order critical point with non-classical exponents.
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Frankel et al. (1975) studied this question.
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