Results of Monte Carlo studies of the q-state Potts model on a square lattice with antiferromagnetic nearest-neighbor coupling and ferromagnetic next-nearest-neighbor coupling are presented for $q>~3$. The three-state Potts model shows a variety of unusual transitions whereas for $q>~4$, we find two first-order phase transitions separated by a broken sublattice symmetry state.
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Grest et al. (1981) studied this question.
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