The spherical model of Berlin and Kac is applied to an antiferromagnetic interaction. The critical-field curve, magnetization-field curves, specific heats, and long-range order are calculated. The problem is translated into lattice-gas language, to afford a possible model for the solid—gas transition. Very unphysical behavior is found, and a probable reason is discussed. This is ascribed to a ``borrowing'' of spin from one sublattice by the other.
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Robert M. Mazo (1963) studied this question.
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