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The 32-vertex model on a triangular lattice is solved exactly in two special cases. In one case the model is reducible to a three-spin Ising model and has the exponents alpha = alpha '= 2 / 3 . The other soluble case is the free-fermion model which exhibits the Ising behaviour but may possess multiple transitions.
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Sacco et al. (1975) studied this question.
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