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 be a subset of the two dimensional lattice, a sufficiently large finite box. Particles perform simple exclusion on Lambda, but when they occupy neighboring sites they feel a binding energy U1<0 in the horizontal direction and U2<0 in the vertical direction; we assume U1 less than U2. Along each bond touching the boundary of Lambda from the outside, particles are created with rate rho exponentially small with beta and Delta and are annihilated with rate 1, where beta is the inverse temperature and Delta>0 is an activity parameter. Thus, the boundary of Lambda plays the role of an infinite gas reservoir with density rho. We take Delta in the interval (U1, U1+U2) 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 beta converging to infinity. 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.

Anisotropy effects in nucleation for conservative dynamics / Nardi, F.R; Olivieri, E.; Scoppola, E.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 119:(2005), pp. 539-595. [10.1007/s10955-004-3247-7]

Anisotropy effects in nucleation for conservative dynamics

NARDI, FRANCESCA ROMANA;
2005

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 be a subset of the two dimensional lattice, a sufficiently large finite box. Particles perform simple exclusion on Lambda, but when they occupy neighboring sites they feel a binding energy U1<0 in the horizontal direction and U2<0 in the vertical direction; we assume U1 less than U2. Along each bond touching the boundary of Lambda from the outside, particles are created with rate rho exponentially small with beta and Delta and are annihilated with rate 1, where beta is the inverse temperature and Delta>0 is an activity parameter. Thus, the boundary of Lambda plays the role of an infinite gas reservoir with density rho. We take Delta in the interval (U1, U1+U2) 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 beta converging to infinity. 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.
2005
119
539
595
Nardi, F.R; Olivieri, E.; Scoppola, E.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1078642
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