  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.
