Phase separation and critical percolation in bidimensional spin-exchange models

TL;DR

This paper investigates how binary mixtures undergoing phase separation in two dimensions pass through a critical percolation state during domain growth, using numerical simulations and scaling analysis.

Contribution

It demonstrates that the coarsening process in a spin-exchange model leads to a critical percolation state, with a detailed analysis of the associated growth dynamics.

Findings

System reaches a critical percolation state during phase separation.

The time dependence of the growing length is characterized.

Scaling analysis confirms the critical percolation transition.

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.