Metastability in Two Dimensions and the Effective Potential

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.