Duality and Fisher zeros in the 2D Potts model on square lattice

TL;DR

This paper proposes a simple phenomenological expression for the free energy of the 2D Potts model on a square lattice, leveraging duality symmetry and critical exponents, with strong agreement with numerical data for q=3 and extensions to q>4.

Contribution

It introduces a new functional form for the free energy of the 2D Potts model that respects duality and critical properties, providing a unified description across different q values.

Findings

Excellent agreement with numerical data for q=3 at all temperatures.

The proposed scheme extends naturally to q>4 cases.

Discussion of the q=4 limit and its implications.

Abstract

A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent {\alpha} allow to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.