Vortices in the classical two-dimensional anisotropic Heisenberg model

The structure and dynamics of vortex spin configurations are considered for a two-dimensional classical Heisenberg model with easy-plane anisotropy. Using both approximate analytic methods based on a continuum description and direct numerical simulations on a discrete lattice, two types of static vortices (planar and out-of-plane) are identified. Planar (out-of-plane) vortices are stable below (above) a critical anisotropy. The structure of moving vortices is calculated approximately in a continuum limit. Vortex-vortex interactions are investigated numerically. A phenomenology for dynamic structure factors is developed based on a dilute gas of mobile vortices above the Kosterlitz-Thouless transition. This yields a central peak scattering whose form is compared with the results of a large-scale Monte Carlo–molecular-dynamics simulation.