  We study analytically and numerically the decay of a metastable phase in
(2+1)-dimensional classical scalar field theory coupled to a heat bath, which
is equivalent to two-dimensional Euclidean quantum field theory at zero
temperature. By a numerical simulation we obtain the nucleation barrier as a
function of the parameters of the potential, and compare it to the theoretical
prediction from the bounce (critical bubble) calculation. We find the
nucleation barrier to be accurately predicted by theory using the bounce
configuration obtained from the tree-level (``classical'') effective action.
Within the range of parameters probed, we found that using the bounce derived
from the one-loop effective action requires an unnaturally large prefactor to
match the lattice results. Deviations from the tree-level prediction are seen
in the regime where loop corrections would be expected to become important.
