On Ising droplets

Abstract

One of the fundamental goals of statistical mechanics is to understand the macroscopic effects induced by the random forces acting at the microscopic level. Some satisfactory results are now available for the Ising model at equilibrium in the phase coexistence regime in any dimension: it is rigorously proved that the most likely shapes of the macroscopic droplets of one pure phase floating in the other pure phase are close to the Wulff crystal of the model. However, the dynamical processes leading to the emergence of a droplet are far from being understood. We formulate a classical conjecture: the scaling limit of the Glauber microscopic dynamics should be an anisotropic motion by mean curvature.