Spatial correlations in the relaxation of the Kob-Andersen model

TL;DR

This paper investigates spatial correlations and heterogeneities in the Kob-Andersen glassy model, revealing how dynamic correlation lengths grow with density and characterizing cluster sizes that influence slow dynamics.

Contribution

It provides a detailed analysis of spatio-temporal correlations and introduces a double-exponential law describing correlation length growth with density.

Findings

Dynamic correlation lengths increase with density.

Trapping time and cooperativity lengths are characterized.

Distribution of persistent clusters relates to slow dynamics.

Abstract

We describe spatio-temporal correlations and heterogeneities in a kinetically constrained glassy model, the Kob-Andersen model. The kinetic constraints of the model alone induce the existence of dynamic correlation lengths, that increase as the density $\rho$ increases, in a way compatible with a double-exponential law. We characterize in detail the trapping time correlation length, the cooperativity length, and the distribution of persistent clusters of particles. This last quantity is related to the typical size of blocked clusters that slow down the dynamics for a given density.