Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus

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.

Published at http://dx.doi.org/10.1214/14-AOP930 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Condenser physics applied to Markov chains - A brief introduction to potential theory

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