Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

TL;DR

This paper uses the self-consistent harmonic approximation to analyze static and dynamic behaviors of the 2D easy-axis Heisenberg model, comparing analytical results with numerical simulations to understand spin wave and topological excitation contributions.

Contribution

It introduces a combined analytical and numerical approach to study static and dynamic properties of the 2D easy-axis Heisenberg model, highlighting the validity range of the SCHA.

Findings

Spin waves dominate static and dynamic features below the transition temperature.

SCHA accurately predicts static properties and low-temperature dynamics.

Topological excitations are negligible far below the transition temperature.

Abstract

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.