Droplet growth for three-dimensional Kawasaki dynamics

• Published in: Probability theory and related fields 2003-02, Vol.125 (2), p.153-194
• Main Authors: HOLLANDER, F. Den, NARDI, F. R, OLIVIERI, E, SCOPPOLA, E
• Format: Article
• Language: English
• Subjects: Computational methods in statistical physics and nonlinear dynamics; Critical point phenomena; Density; Droplets; Exact sciences and technology; Low temperature; Mathematics; Nucleation; Physics; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics
• ISSN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-002-0233-3

The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics at low temperature and low density. Let $\Lambda\subseteq{\mathbb Z}^3$ be a large finite box. Particles perform simple exclusion on $\Lambda$, but when they occupy neighboring sites they feel a binding energy $-U0$ is an activity parameter. Thus, the boundary of $\Lambda$ plays the role of an infinite gas reservoir with density $\rho$. We consider the regime where $\Delta\in (U,3U)$ and the initial configuration is such that $\Lambda$ is empty. For large $\beta$, the system wants to fill $\Lambda$ but is slow in doing so. We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and shape of the critical droplet\/ and the time of its creation in the limit as $\beta\to\infty$.