Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

TL;DR

This paper introduces a new efficient numerical algorithm to accurately compute finite-density corrections to the critical jamming density in large-scale kinetically-constrained models, surpassing previous simulation sizes.

Contribution

A novel memory-efficient algorithm for large-scale simulations of kinetically-constrained models, enabling precise calculation of finite-density corrections.

Findings

Finite-density corrections are not finite-size effects.

System sizes exceeding 10^7 x 10^7 were simulated.

Average seed sites for critical droplets exceed 1.

Abstract

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10^7x10^7, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.