Phase separation and critical percolation in bidimensional spin-exchange models

Abstract

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.

6 pages, 9 figures

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• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Domain-area distribution anomaly in segregating multicomponent superfluids
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance