Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

TL;DR

This paper investigates an attractive East model using real-space RG, revealing a two-stage coarsening process and non-monotonic relaxation times, which align with colloidal system behaviors.

Contribution

It introduces a two-stage coarsening mechanism in an attractive kinetically constrained model and verifies it through numerical simulations.

Findings

Two nonuniversal dynamic exponents predicted by RG.

Model exhibits a two-stage coarsening process.

Relaxation time varies non-monotonically with attraction strength.

Abstract

We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we find that the characteristic relaxation time of the model is a non-monotonic function of attraction strength, again in agreement with numerical results.