Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise

TL;DR

This paper investigates how thermal fluctuations, modeled as additive or multiplicative noise, influence vortex dynamics in two-dimensional ferromagnetic systems, revealing that both noise types have similar effects.

Contribution

The study analytically and numerically demonstrates that multiplicative and additive noise produce comparable effects on vortex dynamics in 2D ferromagnets.

Findings

Both noise types lead to similar vortex behavior.

Analytical and numerical results are consistent.

Multiplicative noise effects can be approximated by additive noise.

Abstract

We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional classical, ferromagnetic, anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise both have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a non-trivial result, as multiplicative and additive noises usually modify the dynamics quite differently. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.