Nonequilibrium relaxation study of the anisotropic antiferromagnetic Heisenberg model on the triangular lattice

TL;DR

This study investigates how exchange anisotropy influences relaxation times and phase transitions in the classical antiferromagnetic Heisenberg model on a triangular lattice, revealing a complex phase diagram with a singular isotropic point.

Contribution

It provides the first detailed analysis of the anisotropic effects on relaxation and phase transitions, highlighting the singular nature of the isotropic Heisenberg point.

Findings

Critical temperatures decrease sharply with decreasing anisotropy.

The BKT critical region widens divergently as anisotropy approaches zero.

The phase diagram exhibits a sharp 'V shape' around the isotropic point.

Abstract

Effect of exchange anisotropy on the relaxation time of spin and vector chirality is studied for the antiferromagnetic classical Heisenberg model on the triangular lattice by using the nonequilibrium relaxation Monte Carlo method. We identify the Berezinskii-Kosterlitz-Thouless (BKT) transition and the chiral transition in a wide range of the anisotropy, even for very small anisotropy of $\sim$ 0.01%. As the anisotropy decreases, both the critical temperatures steeply decrease, while the BKT critical region becomes divergently wide. We elucidate a sharp "V shape" of the phase diagram around the isotropic Heisenberg point, which suggests that the isotropic case is exceptionally singular and the associated Z vortex transition will be isolated from the BKT and chiral transitions. We discuss the relevance of our results to peculiar behavior of the spin relaxation time observed experimentally in triangular antiferromagnets.