Vortex dynamics in the classical two-dimensional antiferromagnetic XY model

Abstract We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry by explicitly calculating the dynamic correlation functions S αα ( q , w ), α = x, y, z . In addition to the spin waves we find also topological excitations, namely vortices which cause a Kosterlitz-Thouless phase transition at T KT . Our main interest is focused on the free vortices just above T KT where we developed a phenomenology based on a dilute gas of noninteracting vortices. With this ansatz we find central peaks in S αα ( q , w ) which are at different positions in q -space depending on whether the static vortex structure or the deviations from it due to a finite velocity dominates the correlations. We compare these results with a combined Monte Carlo Molecular Dynamics simulation on a 100 × 100 square lattice. We find a good agreement between our theory and the simulations and we obtain from this comparison explicit values for the vortex correlation length and the vortex average velocity.