Application of the Projected Dynamics Method to an Anisotropic Heisenberg Model

TL;DR

This paper applies the Projected Dynamics method to an anisotropic Heisenberg model with continuous spins, enabling analysis of metastable decay and lifetime estimation, extending its use beyond discrete spin systems.

Contribution

It adapts the Projected Dynamics method for continuous-spin Heisenberg models with anisotropy, providing a new approach to study metastability in such systems.

Findings

Successful application of the method to anisotropic Heisenberg models

Method enables estimation of metastable lifetimes

Framework for extrapolating results from small to large systems

Abstract

The Projected Dynamics method was originally developed to study metastable decay in ferromagnetic discrete spin models. Here, we apply it to a classical, continuous Heisenberg model with anisotropic ferromagnetic interactions, which evolves under a Monte Carlo dynamic. The anisotropy is sufficiently large to allow comparison with the Ising model. We describe the Projected Dynamics method and how to apply it to this continuous-spin system. We also discuss how to extract metastable lifetimes and how to extrapolate from small systems to larger systems.