Ferromagnetic Potts models with multi-site interaction

Nir Schreiber, Reuven Cohen, Simi Haber

Published 2017-09-25Version 1

We provide a bound on the critical point of the $q$ states Potts models with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q<4$ the system exhibits a second order phase transition, and when $q>4$ the transition is first order. The $q=4$ model is borderline. When the transition if first order, the critical bound can be improved and related to the finite size correlation length. These two results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four site interaction model using the Wang-Landau entropic sampling method for $q=3,4,5$. In particular, the $q=4$ model shows an ambiguous finite size pseudo-critical behaviour.