Violation of a universal changeover in two-dimensional Potts models

We present a novel combinatorial approach which allows the determination of the critical temperature and the phase transition order of Potts models with multi-site interaction. Applying this approach to the hexagonal lattice, it is demonstrated that Potts models with local, range independent interaction may changeover from a continuous to a discontinuous phase transition, at a marginal value q_c≤3. Our theory is substantiated by Monte-Carlo simulations. In particular, it is numerically indicated that the system undergoes a first order transition for q=3. The latter is in agreement with a further prediction of q_c≤2, established under a mild assumption related to the asymptotic growth of hexagonal lattice animals. Our findings are in contrast to known cases where q_c=4 which were believed to represent a universal
phenomenon. Thus, the universality of q_c=4 is violated.