The Phase Diagram of an Anisotropic Potts Model

TL;DR

This paper explores the phase diagram of a three-dimensional anisotropic Potts model, combining analytical and Monte Carlo methods to identify six phases, including orbital ordering similar to that in LaMnO3.

Contribution

It provides a comprehensive mapping of the phase diagram for an anisotropic Potts model, revealing complex phase transitions and the occurrence of orbital ordering.

Findings

Six distinct phases identified

Two phase transitions meet at a triple point

Orbital ordering similar to LaMnO3 observed

Abstract

A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results. We find one region where there are two phase transitions with the lines meeting in a triple point. The orbital ordering that occurs in $LaMnO_3$ occurs as one of the ordered phases.