Change in the Order of a Phase Transition in the 2D Potts Model with Equivalent Neighbours

TL;DR

This paper investigates how increasing the interaction range in a 2D Potts model with three states can change the phase transition from second-order to first-order by analyzing partition function zeros.

Contribution

It identifies the specific number of interacting neighbors that causes a change in the phase transition order in the 2D q=3 Potts model.

Findings

Increasing interaction range alters the phase transition order.

Partition function zeros reveal the critical interaction range.

Transition changes from second-order to first-order at a specific neighbor count.

Abstract

Two dimensional Potts model is a classical example where the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbours interaction, when the number of states $q$ is less than or equal to 4, the second-order phase transition is observed, while for $q>4$ the first-order phase transition occurs. Recent research shows that even when the number of states is fixed, increasing the interaction range allows one to reach the point where the order of the phase transition changes. We focus on a $q=3$ 2D Potts model and, from the analysis of the partition function zeros, locate the number of interacting neighbours that change the order of the phase transition.