Phase transition of ferro- and antiferromagnetic r-state Potts models by the Bethe approximation

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The temperature dependence of the order parameter, specific heat, entropy and susceptibility are estimated for degenerate antiferromagnetic Potts models (AFPMs) and ferromagnetic Potts models (FMP). The inverse transition temperature mod J mod /kBTc=ln(z/(z-r)) obtained for r-state AFPMs contradicts Wang and Wu's result (1973) of ln((z-2)/(z-r)), where J is the interaction parameter and z is the number of nearest-neighbouring sites. Disappearance of the order for r>z in the AFPM can be attributed to the large zero-point entropy.