Emergent O(n) Symmetry in a series of three-dimensional Potts Models

TL;DR

This paper investigates a 3D Potts model with mixed interactions, revealing an emergent O(n) symmetry at criticality and complex phase transitions, using Monte Carlo simulations and finite-size scaling.

Contribution

It demonstrates the emergence of O(n) symmetry in a 3D Potts model with mixed interactions, providing new insights into phase transitions and symmetry in such systems.

Findings

Second-order phase transition in the universality class of 3D O(n)

Emergence of O(n) symmetry at criticality

First-order transition to a different ordered phase for q=4 and 5

Abstract

We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the 3D O(n) model with n=q-1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q=4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T=0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.