Ising transition driven by frustration in a 2D classical model with SU(2) symmetry

TL;DR

This study uses Monte Carlo simulations to demonstrate that frustration in a 2D classical Heisenberg model induces a finite-temperature Ising transition, with the transition's nature and critical temperature depending on the ratio of exchange couplings.

Contribution

It provides numerical evidence that frustration-driven effective symmetry breaking causes a 2D Ising transition in a classical SU(2) symmetric model.

Findings

Finite-temperature phase transition for J2/J1 > 1/2

Transition belongs to the 2D Ising universality class

Critical temperature approaches zero as J2/J1 approaches 1/2

Abstract

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for $J_2/J_1 > 1/2 $, thermal fluctuations give rise to an effective $Z_2$ symmetry leading to a {\it finite-temperature} phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that $T_c\to 0$ with an infinite slope when $J_2/J_1\to 1/2$.