Anisotropy Effects in Nucleation for Conservative Dynamics

We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the twodimensional it anisotropic Ising lattice gas at very low temperature. Let LsubsetZ² be a sufficiently large finite box. Particles perform simple exclusion on L, 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 U₁ges U₂. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e^Db and are annihilated with rate 1, where b is the inverse temperature and D>0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Din (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 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.