Critical Equalities for Potts Models

We apply a simple analytical criterion for locating critical temperatures to Potts models on square and triangular lattices. In the self-dual case, i.e. on the square lattice we reproduce known exact values of the critical temperature and derive the internal energy of the model at the critical point. For the Potts model on the triangular lattice we obtain very good numerical estimate of the critical temperature and also of the internal energy at the critical point.