Phase transitions of antiferromagnetic Potts models are investigated by cactus approximations and Monte Carlo simulations. These models show phase transitions associated with highly degenerate ground states. By the simulations for system cubic lattice, a Kosterlitz-Thouless phase has been found below kT/|J| ≃ 1.25 for the three-state Potts model, while a longrange ordering consisting of two sublattices has appeared below kT|J| ≃ 0.7 for the four-state Potts model.
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Ikuo Ono (1986) studied this question.