Unusual changeover in the transition nature of local-interaction Potts models

A combinatorial approach is used to study the critical behavior of a q-state Potts model with a round-the-face interaction. Using this approach, it is shown that the model exhibits a first order transition for q > 3. A second order transition is numerically detected for q = 2. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer q(c) <= 3. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is q(c) = 4. A lower bound on the first order critical temperature is additionally derived.