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

We study how thermal fluctuations affect the dynamics of vortices in the tw o-dimensional classical, ferromagnetic, anisotropic Heisenberg model depend ing on their additive or multiplicative character. Using a collective coord inate 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 coordinat e approach). This is a nontrivial result, as multiplicative and additive no ises usually modify the dynamics quite differently. We also carry out numer ical simulations of both versions of the model finding that they indeed giv e rise to very similar vortex dynamics. [S0163-1829(99)03917-X].