The Potts model is generalized to include the effects of random fields. The model is solved by the mean-field approximation. The mean-field approximation is shown to be exact in one dimension in the infinite-state limit, which suggests the exactness of this approximation for the infinite-state model in any dimension. A simple domain-energy argument is shown to explain the behavior of the infinite-state model in the ground state.
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Hidetoshi Nishimori (1983) studied this question.
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