Phase ordering and symmetries of the Potts model

TL;DR

This study investigates the phase ordering and symmetry breaking in the two-dimensional q-colours Potts model, revealing a critical q value around 4 that determines the system's ability to reach equilibrium at zero temperature.

Contribution

It proposes that for large enough q, the Potts model cannot break symmetries at zero temperature, extending understanding of phase ordering in this model.

Findings

For q<4, the system forms domains proportional to system size.

For q>4, the system relaxes to a non-equilibrium phase with higher energy.

Results align with previous findings by De Oliveira et al.

Abstract

We have studied the ordering of the q-colours Potts model in two dimensions on a square lattice. On the basis of our observations we propose that if q is large enough the system is not able to break global and local null magnetisation symmetries at zero temperature: when q<4 the system forms domains with a size proportional to the system size while for q>4 it relaxes towards a non-equilibrium phase with energy larger than the ground state energy, in agreement with the previous findings of De Oliveira et al. (M. J. de Oliveira, A. Petri, T. Tome, Europhys. Lett., 65, 20 (2004)).