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July 2015 Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus
B. Gois, C. Landim
Ann. Probab. 43(4): 2151-2203 (July 2015). DOI: 10.1214/14-AOP930

Abstract

We consider the Kawasaki dynamics at inverse temperature $\beta$ for the Ising lattice gas on a two-dimensional square of length $2L+1$ with periodic boundary conditions. We assume that initially the particles form a square of length $n$, which may increase, as well as $L$, with $\beta$. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.

Citation

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B. Gois. C. Landim. "Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus." Ann. Probab. 43 (4) 2151 - 2203, July 2015. https://doi.org/10.1214/14-AOP930

Information

Received: 1 May 2013; Revised: 1 February 2014; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1326.60137
MathSciNet: MR3353824
Digital Object Identifier: 10.1214/14-AOP930

Subjects:
Primary: 60K35, 82C22

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 4 • July 2015
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