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.
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