Novel phase transitions in XY Antiferromagnets on Plane Triangulations

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in XY antiferromagnets on various plane triangulations, revealing complex sequences of Ising and Kosterlitz-Thouless transitions with novel ordering behaviors.

Contribution

It uncovers new phase transition sequences in XY antiferromagnets on Union Jack and bisected-hexagonal lattices, contrasting with known behaviors on the triangular lattice.

Findings

Triangular lattice exhibits chiral and magnetic order transitions at different temperatures.

Union Jack and bisected-hexagonal lattices show sublattice quasi-long-range order before chiral order.

Some sublattice spins undergo Ising transitions between different ordered phases.

Abstract

Using Monte Carlo simulations and finite-size scaling, we investigate the XY antiferromagnet on the triangular, Union Jack and bisected-hexagonal lattices, and in each case find both Ising and Kosterlitz-Thouless transitions. As is well-known, on the triangular lattice, as the temperature decreases the system develops chiral order for temperatures $T < \Tc$, and then quasi-long-range magnetic order on its sublattices when $T < \Ts$, with $\Ts < \Tc$. The behavior $\Ts<\Tc$ is predicted by theoretical arguments due to Korshunov, based on the unbinding of kink-antikink pairs. On the Union Jack and bisected-hexagonal lattices, by contrast, we find that as $T$ decreases the magnetizations on some of the sublattices become quasi-long-range ordered at a temperature $\Ts > \Tc$, before chiral order develops. In some cases, the sublattice spins then undergo a second transition, of Ising type, separating two quasi-long-range ordered phases. On the Union Jack lattice, the magnetization on the degree-4 sublattice remains disordered until $\Tc$ and then undergoes an Ising transition to a quasi-long-range ordered phase.