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

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.

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Cited by in corpus (5)

• Hydrodynamics in kinetically-constrained lattice-gas models
• The relation between the structure of blocked clusters and the relaxation dynamics in kinetically-constrained models
• Kinetically constrained model for gravity-driven granular flow and clogging
• Locality approach to the bootstrap percolation paradox
• Constraint relaxation leads to jamming