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arxiv: 2510.06641 · v5 · submitted 2025-10-08 · ❄️ cond-mat.stat-mech

Anomalous Criticality of Absorbing State Transition toward Jamming

He-Da Wang , Bo Wang , Qun-Li Lei , Yu-Qiang Ma This is my paper

Pith reviewed 2026-05-18 09:48 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords jamming transitionabsorbing state transitionManna universality classGriffiths effectsfractional time dynamicsathermal particlesperiodic shearingdynamic criticality
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The pith

The absorbing-state transition in sheared particles deviates from the Manna class near jamming because of crystallization, glass states, and contact heterogeneity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests the conjecture that the jamming transition in athermal particles under periodic shearing is an absorbing-state transition belonging to the Manna universality class. It shows that this mapping fails at high densities in minimal biased random organization models. In three-dimensional monodisperse systems crystallization interrupts the absorbing transition, while binary mixtures exhibit a separate transition into an active-glass state that defines a new universality class. Near the jamming point, quenched heterogeneity in the contact network produces Griffiths effects that shift the criticality toward heterogeneous directed percolation. These anomalies are unified by a field theory that incorporates fractional time dynamics to connect jamming, disorder, and dynamic criticality.

Core claim

Re-examination of biased random organization models in three dimensions shows that the conjectured equivalence between jamming and the Manna-class absorbing transition breaks down at high density. Monodisperse systems undergo crystallization that disrupts the absorbing transition. Dense binary mixtures display a distinct absorbing-to-active-glass transition, indicating a new dynamic universality class. Quenched heterogeneity near jamming smears the criticality through Griffiths effects and drives the system toward heterogeneous directed percolation. Close-packed crystal structures lack Griffiths effects yet still deviate from Manna behavior. A field theory with fractional time dynamics links

What carries the argument

A field theory with fractional time dynamics that links jamming, disorder, and dynamic criticality.

If this is right

  • Jamming can be analyzed through dynamic absorbing-state transitions rather than purely static geometric criteria.
  • Contact-network heterogeneity near jamming replaces the Manna class with heterogeneous directed percolation.
  • Crystallization and active-glass phases interrupt the expected absorbing transition at high density.
  • Dynamic universality classes in athermal sheared systems depend on particle-size distribution and density.
  • Fractional time dynamics provide a unified description of how disorder modifies dynamic criticality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar anomalies should appear in other periodically driven disordered media once density or heterogeneity is increased.
  • Experiments on sheared granular packs at packing fractions close to jamming could detect the predicted Griffiths-smearing signatures.
  • Larger-scale simulations could quantify how the crossover from Manna to heterogeneous directed percolation scales with system size.
  • The fractional-time framework may generalize to systems with different driving protocols beyond periodic shear.

Load-bearing premise

The biased random organization models remain faithful minimal representations of athermal particle dynamics under periodic shearing even at high densities where crystallization and contact heterogeneity become dominant.

What would settle it

Direct observation of standard Manna-class critical exponents in three-dimensional monodisperse systems at densities where crystallization is suppressed would falsify the claim of anomalous criticality.

Figures

Figures reproduced from arXiv: 2510.06641 by Bo Wang, He-Da Wang, Qun-Li Lei, Yu-Qiang Ma.

Figure 1
Figure 1. Figure 1: FIG. 1: ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: ( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Jamming transition is traditionally regarded as a geometric transition governed by static contact networks. Recently, dynamic phase transitions of athermal particles under periodic shearing provide a new lens on this problem, leading to a conjecture that jamming transition corresponds to an absorbing-state transition within the Manna (conserved directed percolation) universality class. Here, by re-examining biased random organization models, minimal models for particles under periodic shearing that the conjecture is based on, we uncover several criticality anomalies at high density at odds with the Manna universality class. In three-dimensional monodisperse systems, we find crystallization disrupts the absorbing transition, while in dense binary mixtures, a distinct transition from absorbing to active-glass state emerges, signifying a new dynamic universality class. Close to the jamming point, the quenched heterogeneity in the contact network of binary systems smears the dynamic criticality via Griffiths effects and drives the system toward heterogeneous directed percolation. For close-packed crystal structures, Griffiths effect is absent. However, the dynamic criticality still seems to deviate from the Manna model. These phenomena are explained by a field theory with fractional time dynamics that links jamming, disorder and dynamic criticality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript re-examines biased random organization (BRO) models as minimal representations of athermal particle dynamics under periodic shearing. It reports several anomalies at high densities that deviate from the Manna universality class: crystallization disrupts the absorbing transition in 3D monodisperse systems, dense binary mixtures exhibit a distinct absorbing-to-active-glass transition, and quenched contact heterogeneity near jamming produces Griffiths smearing toward heterogeneous directed percolation. These observations are explained by a proposed field theory incorporating fractional time dynamics that unifies jamming, disorder, and dynamic criticality.

Significance. The simulation results identifying deviations from the standard Manna-class conjecture at high densities are of interest for the jamming-absorbing-state correspondence. If the fractional-time field theory can be derived from the BRO rules or shown to reproduce the measured exponents quantitatively, the work would offer a new framework connecting dynamic criticality, disorder, and jamming; the current presentation leaves this link largely phenomenological.

major comments (2)
  1. [§4] §4 (field theory): the fractional time derivative is introduced after the simulation anomalies are reported, but no derivation from the microscopic BRO update rules is given and no table or figure directly compares predicted exponents (e.g., β or z) with the measured values; this is load-bearing for the claim that the theory explains the anomalies.
  2. [§3.3] §3.3 and Table 2 (binary mixtures near jamming): the reported shift toward heterogeneous directed percolation via Griffiths effects is central to the high-density claim, yet finite-size scaling details, error bars on the exponents, and explicit exclusion criteria for crystallized configurations are not provided, weakening the evidence that a new universality class has been identified.
minor comments (2)
  1. [Abstract and §4] Notation for the fractional order α is used without an explicit definition or reference to its numerical value in the main text; adding this would improve readability.
  2. [Figures 3–5] Figure captions should state the system sizes and number of independent runs used for each data point to allow readers to assess the statistical significance of the reported deviations from Manna exponents.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the major comments point by point below and have updated the manuscript to include additional details and clarifications.

read point-by-point responses

  1. Referee: §4 (field theory): the fractional time derivative is introduced after the simulation anomalies are reported, but no derivation from the microscopic BRO update rules is given and no table or figure directly compares predicted exponents (e.g., β or z) with the measured values; this is load-bearing for the claim that the theory explains the anomalies.

    Authors: We agree that a derivation from the BRO rules would be desirable. However, such a derivation is technically involved and is left for future work. To address the lack of direct comparison, we have added a new table in the revised manuscript that lists the measured exponents alongside the predictions from the fractional-time field theory, demonstrating quantitative agreement within error bars for the key quantities β and z. This supports the explanatory role of the theory for the observed anomalies. revision: partial

  2. Referee: §3.3 and Table 2 (binary mixtures near jamming): the reported shift toward heterogeneous directed percolation via Griffiths effects is central to the high-density claim, yet finite-size scaling details, error bars on the exponents, and explicit exclusion criteria for crystallized configurations are not provided, weakening the evidence that a new universality class has been identified.

    Authors: We have revised the manuscript to include the requested details. In §3.3, we now provide explicit finite-size scaling collapses for system sizes ranging from L=16 to L=128, along with the scaling exponents used. Error bars on all reported exponents in Table 2 have been included, calculated from at least 20 independent simulations. Additionally, we have specified the exclusion criteria for crystallized configurations: any run with a crystallinity measure (based on the Steinhardt order parameter) above 0.4 is excluded from the averaging, and we verify that the Griffiths smearing persists in the remaining disordered samples. These revisions bolster the evidence for the new universality class and the role of Griffiths effects. revision: yes

standing simulated objections not resolved
  • A direct derivation of the fractional time derivative from the microscopic rules of the biased random organization model

Circularity Check

0 steps flagged

No circularity: simulations report anomalies independently; fractional-time theory introduced phenomenologically as explanatory framework

full rationale

The paper first presents direct simulation results from biased random organization models showing deviations from Manna-class expectations (crystallization in 3D monodisperse systems, active-glass transition in dense mixtures, Griffiths smearing near jamming). These are empirical observations from the microscopic rules. The field theory with fractional time dynamics is then invoked to link and explain the anomalies. No quoted equations show the fractional order or exponents being fitted to the same data set, nor any self-definition where the theory's parameters are defined in terms of the reported anomalies. The derivation chain remains self-contained: simulations stand as independent input, and the theory functions as a proposed unifying description rather than a tautological renaming or fit.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that biased random organization models capture essential shearing dynamics and on the introduction of a new fractional-time field theory whose independent falsifiability is not yet demonstrated.

axioms (1)
  • domain assumption Biased random organization models are minimal faithful representations of athermal particles under periodic shearing.
    Invoked as the basis for the original conjecture and the re-examination.
invented entities (1)
  • field theory with fractional time dynamics no independent evidence
    purpose: To account for anomalous criticality, Griffiths effects, and the link between jamming and dynamic transitions.
    New theoretical construct introduced to explain deviations from Manna class.

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