Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the two-dimensional anisotropic classical Heisenberg model with XY symmetry there are nonplanar vortices which exhibit a localized structure of the z components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.