The Region of Validity of Homogeneous Nucleation Theory
arXiv:hep-ph/9808263 · doi:10.1016/S0370-2693(99)01158-2
Abstract
We examine the region of validity of Langer's picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k. The nucleation rate I = A_k exp(-S_k) is exponentially suppressed by the action S_k of the saddle-point configuration that dominates tunnelling. The factor A_k includes a fluctuation determinant around this saddle point. Both S_k and A_k depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor A_k compensates the exponential suppression exp(-S_k). In these regions the standard nucleation picture breaks down. We give an approximate expression for A_k in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory.
8 pages, 4 figures. v2: Final version with extended discussion
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