First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in the ν-dimensional Potts model for ν >= 2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in the ν-dimensional Potts gauge model, ν >= 3, is obtained if the underlying gauge group is finite but large. (orig.)