  First-order phase transitions that proceed via nucleation of bubbles are
described by the homogeneous nucleation theory of Langer. The nucleation rate
is one of the most interesting parameters of these transitions. In previous
works we have computed nucleation rates with two different methods: (A)
employing coarse-grained potentials; (B) by means of a saddle-point
approximation, using dimensionally regularized field theory. In this article we
compare the results of the two approaches in order to test their reliability
and to determine the regions of applicability. We find a very good agreement.
