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

A. Gaudilliere, E. Olivieri, Elisabetta Scoppola

2005, v.11, Issue 4, 553-628


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


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