First-order phase transitions that proceed via nucleation of bubbles are de
scribed by the homogeneous nucleation theory of Langer. The nucleation rate
is one of the most interesting parameters of these transitions, In previou
s works we have computed nucleation rates with two different methods. (A) e
mploying coarse-grained potentials; (B) by means of a saddle-point approxim
ation, using dimensionally regularized field theory. In this Letter we comp
are the results of the two approaches in order to test their reliability an
d to determine the regions of applicability, We find a very good agreement.
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