Long-range order for antiferromagnetic Potts models

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Abstract
Long-range order for the three-state antiferromagnetic Potts model may appear at zero temperature as an instability with respect to boundary conditions. It is studied using an approximate correspondence, reminiscent of duality, which links this model with the ferromagnetic Ising model at a particular temperature. The basic idea is to represent entropy constraints in the former in terms of energy increase in the latter. The correspondence can be made exact by modifying the Ising model. The (non)existence of long-range order is then linked to the location of the critical temperature of the modified Ising model with respect to the particular value given by the correspondence.