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

Nir Schreiber, Reuven Cohen, Simi Haber, Gideon Amir, and Baruch Barzel

Phys. Rev. E 100, 052119 – Published 18 November 2019

Abstract

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 $q_{c} \leq 3$ . 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.