Phase separation and critical percolation in bidimensional spin-exchange models

Abstract

Binary mixtures prepared in a homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first take a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases