Glass and jamming transitions in a random organization model

TL;DR

This study investigates the phase transitions in a 2D off-lattice particle model, revealing complex behaviors near jamming and glass transitions, and demonstrating similarities with thermal systems despite non-equilibrium dynamics.

Contribution

It introduces a detailed numerical analysis of the phase diagram, connecting jamming, glass, and absorbing transitions, and compares findings with mean-field theory and other approaches.

Findings

Identification of a non-equilibrium glass transition preceding the absorbing transition.

Jamming transition location varies with preparation protocol and is not unique.

Critical exponents at jamming agree with mean-field replica theory and energy minimization.

Abstract

We study a two-dimensional, off-lattice particle model introduced to describe absorbing phase transitions in driven non-Brownian suspensions. We numerically explore the $(\phi,\epsilon)$ phase diagram, where $\phi$ is the packing fraction and $\epsilon$ controls the amplitude of particle jumps. We use a binary mixture to suppress crystallization, which allows us to disentangle the model's distinct phase transitions between amorphous states. At large $\phi$, we find that the approach to the absorbing transition is preceded by a non-equilibrium glass transition to a non-diffusive amorphous state. This dynamic arrest makes the location of the critical absorbing transitions protocol-dependent. The $\epsilon \to 0$ end-point of the transition line defines a jamming transition whose location is shown to vary continuously with the preparation protocol, and cannot serve as a unique definition of random close packing. Near jamming, we observe a complex landscape and marginal stability, reminiscent of Gardner phases found in thermal glasses. The critical exponents characterizing packings at the jamming transition numerically agree with alternative approaches based on energy minimization, and with analytic predictions from mean-field replica theory. We analyze hyperuniformity in fluid and glass phases, where it emerges with qualitatively distinct signatures, and show that random organization dynamics does not determine the hyperuniformity observed in jammed packings, which is found to be non-universal. Our results show that random organization models share deep physical similarities with thermal soft-particle systems undergoing glass and jamming transitions, with little impact of the non-equilibrium nature of the microscopic dynamics on emerging physical properties.