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Droplet growth for three-dimensional Kawasaki dynamics
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  • Published: February 2003

Droplet growth for three-dimensional Kawasaki dynamics

  • F. den Hollander1,
  • F.R. Nardi1,
  • E. Olivieri2 &
  • …
  • E. Scoppola3 

Probability Theory and Related Fields volume 125, pages 153–194 (2003)Cite this article

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Abstract

 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 $-U<0$ that slows down their dissociation. Along each bond touching the boundary of $\Lambda$ 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 $\D>0$ 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 $\beta\to\infty$.

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Authors and Affiliations

  1. EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands., , , , , , NL

    F. den Hollander & F.R. Nardi

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Rome, Italy, , , , , , IT

    E. Olivieri

  3. Dipartimento di Matematica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy and Istituto Nazionale di Fisica della Materia, Unità di Roma 1, Rome, Italy, , , , , , IT

    E. Scoppola

Authors
  1. F. den Hollander
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  2. F.R. Nardi
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  3. E. Olivieri
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  4. E. Scoppola
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Additional information

Received: 23 February 2002 / Revised version: 24 June 2002 / Published online: 24 October 2002

Mathematics Subject Classification (2000): 60K35, 82B43, 82C43, 82C80

Key words or phrases: Lattice gas – Kawasaki dynamics – Metastability – Critical droplet – Large deviations – Discrete isoperimetric inequalities

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den Hollander, F., Nardi, F., Olivieri, E. et al. Droplet growth for three-dimensional Kawasaki dynamics. Probab Theory Relat Fields 125, 153–194 (2003). https://doi.org/10.1007/s00440-002-0233-3

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  • Issue Date: February 2003

  • DOI: https://doi.org/10.1007/s00440-002-0233-3

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Keywords

  • Binding Energy
  • Local Version
  • Activity Parameter
  • Initial Configuration
  • Inverse Temperature
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