## Abstract

A lattice gas with non-conserved spin flip dynamics (of both non-Glauber and Glauber types) is considered at T ≪ T _{c}, 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.

Original language | English (US) |
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Pages (from-to) | 293-318 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 112 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1 2003 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Glauber dynamics
- Lattice gas
- Nucleation
- Preexponential