O. Penrose, METASTABLE DECAY-RATES, ASYMPTOTIC EXPANSIONS, AND ANALYTIC CONTINUATION OF THERMODYNAMIC FUNCTIONS, Journal of statistical physics, 78(1-2), 1995, pp. 267-283
The grand potential P(z)/kT of the cluster model at fugacity z, neglec
ting interactions between clusters, is defined by a power series Sigma
(n) Q(n)z(n), where Q(n), which depends on the temperature T, is the '
'partition function'' of a cluster of size n. At low temperatures this
series has a finite radius of convergence z(s). Some theorems are pro
ved showing that if Q(n), considered as a function of n, is the Laplac
e transform of a function with suitable properties, then P(z) can be a
nalytically continued into the complex z plane cut along the real axis
from z(s) to +infinity and that (a) the imaginary part of P(z) on the
cut is (apart from a relatively unimportant prefactor) equal to the r
ate of nucleation of the corresponding metastable state, as given by B
ecker-Doring theory, and (b) the real part of P(z) on the cut is appro
ximately equal to the metastable grand potential as calculated by trun
cating the divergent power series at its smallest term.