Abstract
The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series∑ n Q n z n, whereQ n , which depends on the temperatureT, is the “partition function” of a cluster of sizen. At low temperatures this series has a finite radius of convergencez s . Some theorems are proved showing that ifQ n , considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz s to +∞ and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.
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Penrose, O. Metastable decay rates, asymptotic expansions, and analytic continuation of thermodynamic functions. J Stat Phys 78, 267–283 (1995). https://doi.org/10.1007/BF02183348
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DOI: https://doi.org/10.1007/BF02183348