Glass and jamming transitions in a random organization model

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 $(φ,ε)$ phase diagram, where $φ$ is the packing fraction and $ε$ 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 $φ$, 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 $ε\to 0$ 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.

Figures (7)

• Figure 1: (a) Phase diagram showing the absorbing phase with no activity, the diffusive active liquid and the kinetically-arrested active glass. (b) Mean-squared displacement and (c) self-intermediate scattering function at fixed $\phi=0.8$ and different $\epsilon$ revealing glassy slowing down. (d) Corresponding structural relaxation time $\tau_\alpha$ as a function of $1/\epsilon$.
• Figure 2: (a) The critical line $\phi_c(\epsilon)$ between the active glass and absorbing states obtained using different sets of initial conditions parametrized by the reduced pressure $Z_0$ depends continuously on $Z_0$, because the active glass retains memory of its preparation. (b) The jamming packing fraction $\phi_J$, Eq. (\ref{['eq:phij']}), obtained under random organization dynamics also depends on $Z_0$, and is therefore not universal.
• Figure 3: (a-c) Time evolution of the mean-squared distances $\tilde{\Delta}^2(t)$ from Eq. (\ref{['eq:msdgardner']}) and $\tilde{\Delta}^2_{ab}(t)$ from Eq. (\ref{['eq:msdabgardner']}) for (a) $\epsilon=0.15$, (b) $\epsilon=0.1$, and (c) $\epsilon=0.015$. The distance between copies becomes much larger than the distance each copy travels at low $\epsilon$, indicating ergodicity breaking. (d) The long-time plateau values gradually split when $\epsilon$ decreases, revealing a Gardner crossover near $\epsilon \approx 0.11$ (dashed line) and the emergence of Gardner physics on the approach to jamming at $\epsilon \to 0$.
• Figure 4: (a) Average number of neighbors $Z(h)$ within a gap $h$. The extended plateau close to $Z = 4$ (dashed line) reveals a close approach to isostaticity and to the jamming critical point. (b) Evolution of the fraction of rattlers $f_r$ for different definitions $h$ of contacts. We select $h^\star = 5 \times 10^{-10}$ (dashed line) to define contacts and remove rattlers. (c) The excess contact number $\tilde{Z}(h)-\tilde{Z}(h^\star)$, Eq. (\ref{['eq:zh']}), is well-described by the mean-field exponent $\gamma = 0.41269\cdots$ (blue), but differs from the value $\gamma=0.58$ (red) reported in Ref. wilken2023dynamical for a similar model.
• Figure 5: Compressibility in active diffusive liquid measured at $(\phi=0.65,\epsilon=0.6)$, with quadratic hyperuniform scaling at low $q$ (dashed line).