[论文解读] Glass and jamming transitions in a random organization model

Leonardo Galliano, Ludovic Berthier|arXiv (Cornell University)|Mar 16, 2026

Material Dynamics and Properties被引用 0

一句话总结

该论文研究一个二维无 lattice 的随机组织模型以绘制其 phi-epsilon 相图，揭示在吸收态之前出现玻璃转变，以及在被动力学阻滞状态内的与制备过程相关的堵塞线，并在接近堵塞时显示出类似 Gardner 的特征。

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 $ε o 0$ 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.

研究动机与目标

• Disentangle amorphous phase transitions from absorbing-state transitions in a random organization model.
• Characterize how crowding and non-equilibrium kicks drive glassy dynamics and jamming.
• Investigate how preparation protocol affects the location of the jamming transition.
• Explore hyperuniformity and its dependence on phase (liquid, glass, jammed).
• Assess universality of jamming critical exponents and relation to energy-minimization results.

提出的方法

• Simulate a binary mixture of off-lattice particles with random organization dynamics where overlapping particles are kicked along the line of centers with amplitude drawn from [0, epsilon].
• Use center-of-mass conserving kicks to study hyperuniformity and non-equilibrium effects.
• Map the phase diagram in terms of packing fraction phi and kick amplitude epsilon identifying absorbing and active phases.
• Define phi_c(epsilon) as the absorbing transition line and analyze its dependence on preparation protocol (Z0) via controlled initial configurations.
• Employ annealing protocols to approach the epsilon -> 0 limit and extract a jamming density phi_J, demonstrating a continuous J-line dependent on preparation.
• Measure dynamic and structural quantities such as f(t), Delta^2(t), Fs(q,t), and Z(h) to characterize glassy and jammed states.

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)

实验结果

研究问题

• RQ1 How does the phase diagram in the (phi, epsilon) plane separate absorbing and active (glass-like) phases?
• RQ2 Is the jamming transition universal across preparation protocols, or is it protocol-dependent (i.e., a J-line)?
• RQ3 Do Gardner-like marginal stability signatures appear near jamming in a non-thermal random organization dynamics?
• RQ4 How does hyperuniformity manifest across liquid, glass, and jammed states, and is it controlled by the random organization dynamics or by the jammed structure itself?
• RQ5 Do the jamming critical exponents align with those from energy-minimized packings and mean-field replica theory?

主要发现

• There is a continuous line of absorbing transitions phi_c(epsilon) in the phi-epsilon plane separating an absorbing phase from an active phase.
• At small epsilon, the system enters a kinetically arrested glass before the absorbing transition, implying memory of preparation influences phi_c(epsilon).
• The end-point epsilon -> 0 defines a jamming transition phi_J that depends on the preparation protocol, forming a J-line rather than a unique point.
• Evidence of Gardner physics is observed near jamming through ergodicity breaking between copies (clones) of glass configurations as epsilon decreases, indicating a complex landscape.
• Critical exponents at jamming agree with energy-minimized packings and analytic mean-field replica theory predictions, supporting universality of jamming behavior across frameworks.
• Hyperuniformity emerges in different phases with distinct signatures, and the hyperuniformity at jamming is non-universal and not dictated by random organization dynamics.

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 ja