On the Lowest Energy Nucleation Path in a Supersaturated Lattice Gas

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.