We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the two-dimensional it anisotropic Ising lattice gas at very low temperature. Let Lambda subset of Z(2) be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy -U-1< 0 in the horizontal direction and U-2< 0 in the vertical direction; we assume U-1>= U-2. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e(-Delta beta) and are annihilated with rate 1, where beta is the inverse temperature and Delta > 0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Delta is an element of (U-1,U-1+U-2) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.
Nardi, F., Olivieri, E., Scoppola, E. (2005). Anisotropy effects in nucleation for conservative dynamics. JOURNAL OF STATISTICAL PHYSICS, 119(2009/04/03 00:00:00.000), 539-595 [10.1007/s10955-004-3247-7].
Anisotropy effects in nucleation for conservative dynamics
OLIVIERI, ENZO;
2005-01-01
Abstract
We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the two-dimensional it anisotropic Ising lattice gas at very low temperature. Let Lambda subset of Z(2) be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy -U-1< 0 in the horizontal direction and U-2< 0 in the vertical direction; we assume U-1>= U-2. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e(-Delta beta) and are annihilated with rate 1, where beta is the inverse temperature and Delta > 0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Delta is an element of (U-1,U-1+U-2) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.