An approximation to the partition function of the standard Potts model is constructed by considering only the dominant tree-like configurations. This approximation gives a good representation of the positions of the non-physical singularities obtained from low-temperature series, and it is also possible to relate the behaviour of the approximations to the order of the Potts model transitions. It is found that for the two-dimensional lattices studied the transition is first-order for q>4, whereas for the three-dimensional lattices it is first-order when q>2.
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Enting et al. (1975) studied this question.
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