  The stability and dynamics of a free magnetic polaron are studied by Monte
Carlo simulation of a classical two-dimensional Heisenberg model coupled to a
single electron. We compare our results to the earlier mean-field analysis of
the stability of the polaron, finding qualitative similarity but quantitative
differences. The dynamical simulations give estimates of the temperature
dependence of the polaron diffusion, as well as a crossover to a tunnelling
regime.
