Phase Transitions with Discrete Symmetry Breaking in Antiferromagnetic Heisenberg Models on a Triangular Lattice

TL;DR

This paper investigates phase transitions with discrete symmetry breaking in antiferromagnetic Heisenberg models on a triangular lattice, revealing different transition types depending on symmetry and introducing a novel method linking spin systems to Potts models.

Contribution

It introduces a new approach connecting frustrated spin systems to Potts models with invisible states to analyze finite-temperature phase transitions.

Findings

First-order transition with threefold symmetry breaking (SO(3)×C3)

Second-order transition with twofold symmetry breaking (SO(3)×Z2)

Method linking spin models to Potts models with invisible states

Abstract

We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two cases in which a phase transition with discrete symmetry breaking occurs. The first is that the order parameter space is SO(3)$\times C_3$. In this case, a first-order phase transition, with threefold symmetry breaking, occurs. The second has the order parameter space SO(3)$\times Z_2$. In this case, a second-order phase transition occurs with twofold symmetry breaking. To investigate finite-temperature properties of these phase transitions from a microscopic viewpoint, we introduce a method to make the connection between continuous frustrated spin systems and the Potts model with invisible states.