1305.4542 (B. Gois et al.)

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

B. Gois, C. Landim

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 $L^2\, \theta_\beta$ particles form almost always a square and that this square evolves as a Brownian motion when the temperature vanishes.

View original: http://arxiv.org/abs/1305.4542