  We present a lattice method to compute bubble nucleation rates at radiatively
induced first order phase transitions, in high temperature, weakly coupled
field theories, nonperturbatively. A generalization of Langer's approach, it
makes no recourse to saddle point expansions and includes completely the
dynamical prefactor. We test the technique by applying it to the electroweak
phase transition in the minimal standard model, at an unphysically small Higgs
mass which gives a reasonably strong phase transition (lambda/g^2 =0.036, which
corresponds to m(Higgs)/m(W) = 0.54 at tree level but does not correspond to a
positive physical Higgs mass when radiative effects of the top quark are
included), and compare the results to older perturbative and other estimates.
While two loop perturbation theory slightly under-estimates the strength of the
transition measured by the latent heat, it over-estimates the amount of
supercooling by a factor of 2.
