Jamming in Hierarchical Networks

TL;DR

This study investigates jamming phenomena in hierarchical networks using the Biroli-Mezard model, revealing that dynamical jamming occurs even without an ideal glass transition, with jams disappearing when hopping is permitted.

Contribution

It provides the first detailed analysis of jamming and dynamical behavior in hierarchical networks within the Biroli-Mezard lattice glass model framework.

Findings

Dynamical jamming occurs in hierarchical networks without an ideal glass transition.

Jams exhibit diverging time-scales but do not necessarily diverge at high packing fractions.

Allowing hopping in simulations generally removes jams.

Abstract

We study the Biroli-Mezard model for lattice glasses on a number of hierarchical networks. These networks combine certain lattice-like features with a recursive structure that makes them suitable for exact renormalization group studies and provide an alternative to the mean-field approach. In our numerical simulations here, we first explore their equilibrium properties with the Wang-Landau algorithm. Then, we investigate their dynamical behavior using a grand-canonical annealing algorithm. We find that the dynamics readily falls out of equilibrium and jams in many of our networks with certain constraints on the neighborhood occupation imposed by the Biroli-Mezard model, even in cases where exact results indicate that no ideal glass transition exists. But while we find that time-scales for the jams diverge, our simulations cannot ascertain such a divergence for a packing fraction distinctly above random close packing. In cases where we allow hopping in our dynamical simulations, the jams on these networks generally disappear.