The Heisenberg antiferromagnet on a triangular lattice: topological excitations

TL;DR

This paper analyzes topological defects in the classical Heisenberg antiferromagnet on a triangular lattice, revealing a crossover from spinwave-dominated behavior to Kosterlitz-Thouless type transition at higher temperatures.

Contribution

It provides an analytical reduction of the model's partition function to a Coulomb gas, elucidating the nature of topological excitations and phase crossover in the system.

Findings

Partition function reduces to a Coulomb gas model.

Correlation length shows crossover from spinwave to vortex-driven behavior.

Monte Carlo results support the predicted crossover.

Abstract

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of $Z_2$ type, consideration of the energy leads us to a description of the low--energy stationary points of the action in terms of $\pm$ vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2--dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spinwaves, while at higher temperatures we expect a crossover to a Kosterlitz--Thouless type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover.