  We present a consistent calculation of bubble-nucleation rates in theories of
two scalar fields. Our approach is based on the notion of a coarse-grained free
energy that incorporates the effects of fluctuations with momenta above a given
scale k. We establish the reliability of the method for a variety of two-scalar
models and confirm the conclusions of previous studies in one-field theories:
Langer's theory of homogeneous nucleation is applicable as long as the
expansion around the semiclassical saddle point associated with tunnelling is
convergent. This expansion breaks down when the exponential suppression of the
rate by the saddle-point action becomes comparable to the pre-exponential
factor associated with fluctuations around the saddle point. We reconfirm that
Langer's theory is not applicable to the case of weakly first-oder phase
transitions. We also find that the same is true in general for radiatively
induced first-order phase transitions. We discuss the relevance of our results
for the electroweak phase transition and the metastability bound on the
Higgs-boson mass.
