Binary mixtures prepared in an 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 takes 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.Comment: 6 pages, 9 figure