  A nonperturbative correction to the thermal nucleation rate of critical
bubbles in a first order phase transition is estimated. The correction
originates from large-amplitude fluctuations which may be present before the
transition occurs. Using a simple model of a scalar field in a double-well
potential, we present a method to obtain a corrected potential which
incorporates the free-energy density available from large-amplitude
fluctuations, which is not included in the usual perturbative calculation. For
weaker phase transitions, the nucleation rate can be much larger than the rate
calculated via perturbation theory. As an application of our method, we show
how nonperturbative corrections can both qualitatively and quantitatively
explain anomalously high nucleation rates observed in 2-d numerical
simulations.
