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

Gois, B ^[1] ; Landim, C. ^[2]
1. [1] Instituto Nacional de Matemática Pura e Aplicada
  
  Instituto Nacional de Matemática Pura e Aplicada
  
  Brasil
2. [2] University of Rouen
  
  University of Rouen
  
  Arrondissement de Rouen, Francia
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 2151-2203
Idioma: inglés
DOI: 10.1214/14-AOP930
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Resumen
- We consider the Kawasaki dynamics at inverse temperature β 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 β. 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.