Nucleation Pattern at Low Temperature for Local Kawasaki Dynamics in Two Dimensions

A. Gaudilliere, E. Olivieri, Elisabetta Scoppola

2005, v.11, №4, 553-628

ABSTRACT

We study the first transition between metastability and stability for a two-dimensional Ising lattice gas evolving at low temperature under a local version of the Kawasaki conservative dynamics. We describe geometrically the configurations along paths typically followed during the transition, and show that the whole evolution goes with high probability from quasi-squares' to larger quasi-squares'. Moreover, along these paths, between two successive quasi-squares', the fluctuations in the dimensions of the clusters are bounded: if an $l\times L$ rectangle, with $l \leq L$, circumscribes one of these clusters then we have $L-l \leq 1+2\sqrt{L}$. Finally we show that fluctuations of this order cannot be neglected: such fluctuations occur with a probability non-exponentially small' in the inverse temperature $\beta$. This nucleation process thus substantially differs from that which takes place under the Glauber dynamics, especially in its supercritical part.

Keywords: metastability,conservative dynamics,Kawasaki dynamics,nucleation