Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields

Real time thermalization and relaxation phenomena are studied in the low energy density phase of the 2+1 dimensional classical O(2) symmetric scalar theory by solving numerically its dynamics. The near-equilibrium decay rate of on-shell waves and the power law governing the large time asymptotics of the off-shell relaxation agree with the analytic results based on linear response theory. The realisation of the Mermin-Wagner theorem is also studied in the final equilibrium ensemble.