On the Lowest Energy Nucleation Path in a Supersaturated Lattice Gas

Document Type

Article

Publication Date

1-1-2003

Abstract

A lattice gas with non-conserved spin flip dynamics (of both non-Glauber and Glauber types) is considered at T ≪ Tc, the critical temperature. For arbitrary supersaturation, S, a general expression for the inverse of the nucleation rate along the lowest energy path is derived. The exponential part is identical to the one by Neves and Schonmann [Commun. Math. Phys. 137:20 (1991)]. The preexponential can be expressed in terms of elliptic theta-functions for small S, and in the limits, respectively, of S ≫ T/φ or S ≪ T/φ (-φ being the nearest-neighbor interaction energy), elementary versions of the general expression are further obtained. The preexponential has a smooth component, as well as small-scale modulations which are approximately periodic in the inverse supersaturation. For S ≪ T/φ, the smooth part is proportional to √S, in contrast to the zero-T limit where it is linear in S. The latter limit becomes apparent only at extremely low temperatures which are cubic in S.

Identifier

0038403537 (Scopus)

Publication Title

Journal of Statistical Physics

External Full Text Location

https://doi.org/10.1023/A:1023687822656

ISSN

00224715

First Page

293

Last Page

318

Issue

1-2

Volume

112

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