Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties

TL;DR

This study uses Monte Carlo simulations to analyze the antiferromagnetic XY model on a triangular lattice, revealing two separate phase transitions with distinct critical behaviors: one related to chirality and the other to spin order.

Contribution

It provides detailed insights into the critical properties of the antiferromagnetic XY model, identifying a chiral transition in the Ising universality class and a non-Kosterlitz-Thouless spin transition.

Findings

Chiral transition follows 2D Ising universality class.

Spin transition exhibits non-KT criticality.

Two separate phase transitions occur at different temperatures.

Abstract

We study the antiferromagnetic {\it XY} model on a triangular lattice by extensive Monte Carlo simulations, focusing on its ordering and critical properties. Our result clearly shows that two separate transitions occur at two distinct temperatures, the one at a higher temperature is associated with a $Z_2$-symmetry breaking driven by the chirality, and the one at a lower temperature is associated with the onset of the quasi-long-range order of the {\it XY} spin. We carefully examine the critical properties of each transition to find that the criticality of the chiral transition is consistent with the standard two-dimensional Ising universality class, whereas that of the spin transition might differ from the conventional Kosterlitz-Thouless (KT) one. The observed non-KT nature of the spin criticality is consistent with the most recent simulation result on the fully-frustrated {\it XY} model on a square lattice.