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

TL;DR

This paper investigates the critical behavior of a $q$-state Potts model with round-the-face interaction, revealing a changeover from second to first order transitions at a critical $q_c \

Contribution

It introduces a combinatorial approach to analyze a Potts model with local face interactions, showing a different transition order changeover than standard models.

Findings

First order transition for $q>3$

Second order transition detected at $q=2$

Transition changeover at $q_c \

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.