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

Abstract

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.