Critical antiferromagnetic square-lattice Potts model

The critical temperature of the antiferromagnetic q-state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated. As with the ferromagnetic model, the transition is continuous for q≼4, and its first-order (i. e. has latent heat) for q>4. However, only for q≼3 can the critical temperature be real. For the isotropic model the criticality condition is exp(J/kT) = -1 + (4-q)½.