Metastability in a lattice gas with strong anisotropic interactions under Kawasaki dynamics
نویسندگان
چکیده
In this paper we analyze metastability and nucleation in the context of a local version Kawasaki dynamics for two-dimensional strongly anisotropic Ising lattice gas at very low temperature. Let $\Lambda\subset\mathbb{Z}^2$ be finite box. Particles perform simple exclusion on $\Lambda$, but when they occupy neighboring sites feel binding energy $-U_1<0$ horizontal direction $-U_2<0$ vertical one. Thus is conservative inside volume $\Lambda$. Along each bond touching boundary $\Lambda$ from outside to inside, particles are created with rate $\rho=e^{-\Delta\beta}$, while along outside, annihilated $1$, where $\beta$ inverse temperature $\Delta>0$ an activity parameter. Thus, plays role infinite reservoir density $\rho$. We consider parameter regime $U_1>2U_2$ also known as regime. take $\Delta\in{(U_1,U_1+U_2)}$ prove that empty (respectively full) configuration metastable stable) configuration. asymptotic corresponding limit large $\beta$. investigate how transition full takes place. particular, estimate probability, expectation distribution time stable Moreover, identify size \emph{critical droplets}, well some their properties. observe different behavior weakly regimes. find \emph{Wulff shape}, i.e., shape minimizing droplet fixed volume, not relevant pattern.
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2021
ISSN: ['1083-6489']
DOI: https://doi.org/10.1214/21-ejp701