Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

TL;DR

This study uses Monte Carlo simulations to analyze the classical Heisenberg antiferromagnet on a triangular lattice, revealing two distinct temperature regimes characterized by different dominant excitations and behaviors.

Contribution

It provides a detailed numerical investigation of topological excitations and their influence on physical quantities across temperature regimes in the Heisenberg antiferromagnet.

Findings

Identification of two temperature regimes with different dominant excitations.

Agreement of low-temperature behavior with nonlinear sigma model predictions.

Observation of a narrow crossover region around T_{th}  approximately 0.28.

Abstract

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$.