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REVIEW 4 major objections 3 minor 109 references

Yielding versus random organization: convex absorbing transitions in soft matter

T0 review · 4 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper argues that the reversible-irreversible transition in cyclically sheared suspensions and the yielding transition in yield-stress fluids are two realizations of a single absorbing phase transition, evidenced by a shared parametric

desk verdict The master-curve comparison between the RIT and yielding is real and worth refereeing, but the LR-CDP anchor for the α-ROM rests on an effective-transport mapping that is partly circular. read the letter →

arxiv 2606.23914 v2 pith:LRI4YM2K submitted 2026-06-22 cond-mat.soft cond-mat.stat-mech

Tristan Jocteur , Kirsten Martens , Eric Bertin , Romain Mari This is my paper · ORCID
classification cond-mat.softcond-mat.stat-mech
keywords absorbingphasetransitionsreversible-irreversibletransitionyieldinglong-rangeinteractionsrandomorganizationmodelelastoplasticmodelsconserveddirectedpercolationHebraud-Lequeux
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that two seemingly different soft-matter transitions—the reversible-irreversible transition of cyclically sheared suspensions and the yielding transition of yield-stress fluids—are governed by the same underlying absorbing phase transition once long-range interactions are tuned. It compares generalized versions of the two models, varying the decay exponent of long-range interactions, and finds that although the critical exponents differ at the same interaction range, they collapse onto a shared master curve when plotted parametrically against the order-parameter exponent β. The paper then argues that this master curve is covered by two known frameworks: long-range conserved directed percolation for the concave regime (β < 1) and a generalized Hebraud-Lequeux model for the convex regime (β > 1). A sympathetic reader would care because this would extend the universality-class picture of absorbing transitions to the convex, mechanically noisy transitions that are common in soft matter.

What carries the argument

The central device is the parametric exponent plot: instead of plotting critical exponents against the interaction-range exponent α, the paper plots them against the order-parameter exponent β. This removes the model-specific relation between α and the physics, revealing a common master curve. The two theoretical anchors are the LR-CDP field equations, which add fractional long-range transport to the conserved density and activity fields, and the generalized Hebraud-Lequeux model, a mean-field description in which local variables diffuse—normally or anomalously—under self-consistent noise until they cross a threshold, with diffusion coefficient proportional to the mean activity. For the α-RO

What would settle it

A decisive test: in the α-ROM, measure the correlation-length exponent ν⊥ directly (not via hyperscaling) and compute β_LR-CDP(d_f + ν⊥^{-1}); if it disagrees with the measured β beyond error bars in the concave regime, the LR-CDP assignment lacks support. Alternatively, simulate an α-ROM variant in which long-range noise and long-range transport are tuned independently; if the master curve breaks when the noise exponent is varied with transport fixed, the collapse is accidental.

Watch

Extended reading notes

Core claim

The central claim is that convex absorbing transitions—where the order parameter rises with exponent β > 1, fluctuations vanish, avalanches are non-compact, and hyperuniformity is lost—are not a separate exotic family but the same transition as ordinary concave ones, seen through the wrong parameter. Concretely, the α-ROM (a model of cyclically sheared suspensions with long-range hydrodynamic-like noise) and the α-Picard model (an elastoplastic model of yield-stress fluids with long-range elastic stress redistribution) produce different critical exponents at the same interaction-range exponent α, yet their exponents collapse onto one master curve when plotted as functions of β. The concave l

Load-bearing premise

The load-bearing premise is that an effective transport exponent α' = d_f + ν⊥^{-1}, built from the model's own fractal dimension and correlation-length exponents via a depinning scaling relation that the α-ROM does not actually satisfy, can stand in for the true interaction range when comparing the α-ROM to long-range conserved directed percolation.

Editorial extensions

If this is right

  • The reversible-irreversible transition and yielding are unified: for a given β, all measured critical exponents—activity mean and fluctuations, avalanche statistics, and fractal dimensions—match between the two models.
  • The crossover between concave and convex transitions, at β = 1, coincides in each model with the crossover from diverging to vanishing fluctuations and from compact to non-compact avalanches, so a single criterion separates the two regimes.
  • The concave side of the master curve is accounted for by long-range conserved directed percolation, meaning that the α-ROM behaves as if it had an effective long-range transport exponent even though its actual transport is short-range.
  • The convex side is accounted for by the generalized Hebraud-Lequeux model, whose prediction β = μ links the order-parameter exponent to the Lévy exponent of the mediated noise.
  • Hyperuniformity is lost for convex transitions: the structure factor of the conserved field develops a non-monotonic low-q behavior in the α-ROM and a vanishing hyperuniformity exponent in the α-Picard model, with zero modes extending the α-dependent regime up to α = 6.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The master-curve collapse invites the conjecture that a coarse-grained mapping connects the two models, analogous to the known mapping between disordered elastic interfaces and sandpiles; if such a mapping exists, it should predict the effective transport exponent rather than fit it.
  • A direct experimental test is available: measure the activity exponent β and the fluctuation exponent γ' in a cyclically sheared suspension and in a yield-stress fluid; both should fall on the same parametric curve even though their microscopic interaction ranges are not directly comparable.
  • If the Hebraud-Lequeux branch is exact, then any soft-matter system whose activity is created by noise near a threshold—foams, emulsions, granular packs—should fall on the same convex branch, which is testable by measuring the order-parameter exponent and its fluctuations in such systems.
  • The paper leaves open whether the zero-mode-dominated class it tentatively calls CDP-0 is real; this could be settled by simulating the α-Picard model at α > 6 and checking whether the hyperuniformity exponent follows the predicted zero-mode behavior rather than the LR-CDP saturation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper compares two minimal models of athermal soft-matter absorbing transitions—the α-ROM for cyclically sheared suspensions and the α-Picard elastoplastic model for yield-stress fluids—by tuning the decay exponent α of their long-range interaction kernels. It documents a continuous evolution of the order-parameter exponent β, the fluctuation exponent γ′, the avalanche exponents, and hyperuniformity as α varies, with a crossover at β=1. Parametric plots of exponents versus β are claimed to reveal a shared master curve for β>0.64, with the concave branch assigned to long-range conserved directed percolation (LR-CDP) and the convex branch assigned to a generalized Hebraud-Lequeux model with Lévy noise. The paper concludes that the reversible-irreversible transition and the yielding transition may be two physical realizations of a common absorbing transition.

Significance. If the master curve and the two-branch assignment are correct, this is a substantial step toward unifying two important classes of driven soft matter; it gives concrete, falsifiable criteria (exponent collapse, hyperuniformity crossover, noise statistics) and identifies candidate universality classes. The model definitions are precise, the numerical protocols are standard, and the authors are unusually explicit about the limitations of their arguments, including the admitted loophole in the effective α′ mapping. The main weakness is that the central quantitative evidence is presented without error bars and with one partially self-consistent mapping, so the significance is real but the support is not yet definitive.

major comments (4)
  1. [Sec. 4.1, Fig. 8(b)] The identification of the α-ROM with LR-CDP is not independently established. The effective transport exponent α′ is defined through α′=d_f+ν⊥^{-1}, using the depinning tilt-symmetry relation ν⊥^{-1}=α−d_f, which the paper itself states is not satisfied by the α-ROM. Moreover, ν⊥ is not measured directly but obtained from the hyperscaling relation γ′=dν⊥−2β (Eq. 10), i.e. from the same β and γ′ that are later used in the comparison. The agreement between β_LR-CDP(α′) and the measured β in Fig. 8(b) is therefore a self-consistency check of scaling relations, not an independent test of the LR-CDP mapping. The paper acknowledges this loophole in Sec. 5. To support the central claim that the concave regime of the α-ROM belongs to the LR-CDP class, an independent determination of ν⊥ (e.g., finite-size scaling of the correlation length) and a test of statistical tilt symmetry in the α-ROM, or
  2. [Figs. 2–6, 8–10] Critical exponents are reported without error bars or fitting details. The master-curve collapse in Fig. 6 is the central quantitative result, and Fig. 6 itself shows visible discrepancies for τ, τ′, and τ″ at intermediate β. Without uncertainties on these points and on the LR-CDP/HL comparison curves, the claim of a shared master curve for β>0.64 cannot be distinguished from systematic deviations. Please provide tables or error bars for all exponents, specify fitting ranges and finite-size scaling procedures, and state the statistical uncertainty of the collapse (e.g., scatter around a common parametric curve).
  3. [Sec. 4.2, Fig. 8(a)] The identification of the convex regime with the generalized Hebraud-Lequeux model depends on the mean-field relation µ=d/α for the Lévy noise exponent. The paper explicitly states that no analytical prediction for µ beyond mean field is available (Sec. 4.2.1). The µ-HL data in Figs. 9 and 8(a) are generated with µ as an input parameter; the link to the α-ROM and α-Picard models is therefore through an unmeasured exponent. Without a direct measurement of p(δξ) in the two models, or a robustness test of the master-curve agreement under alternative µ(α) assignments, the claim that generalized HL 'visits the entire part of the master curve associated with convex transition' is a statement about the HL model rather than about the physical models. This is load-bearing for the unified-description conclusion.
  4. [Appendix A] The LR-CDP exponents used as the concave-branch anchor are measured in a newly introduced LR-ROM model, but the appendix provides no simulation details: no system size, no lattice/off-lattice specification, no finite-size scaling analysis, no uncertainty estimates, and no explicit fitting procedure for β and γ′. The main text only states that the jump probability decays as ~1/|Δr|^{α′}. Given that these new exponents are central to the LR-CDP identification, their numerical determination should be documented at the same level as the other models, or the figure should be presented as preliminary pending a dedicated study.
minor comments (3)
  1. [Abstract and Sec. 4] The abstract refers to 'Long-Range Directed Percolation' while the body and the rest of the paper use 'Long-Range Conserved Directed Percolation' (LR-CDP). Please make the terminology consistent.
  2. [Fig. 7(c)] The linearized-theory prediction line in Fig. 7(c) is described only in the text. Please add the explicit prediction S_σ(q)∼q^{α−4} for 1<α<6 and q^2 for α≥6 to the caption, and indicate where the comparison is expected to fail.
  3. [Sec. 2.1.2 and Eq. (17)] The symbol A is used both for mean activity and for the prefactor in the noise distribution p(δξ)∼A/|δξ|^{1+µ}. This can be confusing; consider a different symbol for the prefactor.

Circularity Check

1 steps flagged · score 4.0 of 10

Master-curve comparison is independent, but the LR-CDP identification for the α-ROM leans on an effective α′ built from the model's own exponents via relations the model does not satisfy.

  1. fitted input called prediction [Sec. 5 (Discussion), with construction in Sec. 4.1 and Fig. 8(b); uses Eq. (10) hyperscaling]
    "This tentative scenario is suggested by the scaling relation ν−1⊥=α−df [67], which although not satisfied in the α-ROM, allows for the definition of an effective value αeff. Once plugged into the long-range CDP class, αeff predicts the correct value of the exponent β (i.e., the one measured in the α-ROM) as long as β≤1."

    The effective transport exponent α′ is not measured or derived from the α-ROM's dynamics; it is constructed as α′=d_f+ν⊥^{-1} using the depinning tilt-symmetry relation ν⊥^{-1}=α−d_f, which the paper admits the α-ROM does not satisfy. Moreover ν⊥ is not measured independently: it is obtained through the hyperscaling relation γ′=dν⊥−2β from the same α-ROM β and γ′ that Fig. 8(b) later 'predicts' via β_LR-CDP(α′). The agreement is therefore a self-consistency check on the model's own exponents rather than an independent confirmation of the LR-CDP class. The paper itself concedes a loophole cannot be excluded. If the effective-mapping premise fails, the placement of the α-ROM's concave regime in LR-CDP loses its theoretical anchor; the empirical master-curve collapse survives, but the univers

full rationale

Most of the paper is a direct comparison of measured critical exponents and avalanche statistics of two model families, and the parametric master curve (Fig. 6) is an empirical finding that does not reduce to any fit. The α-Picard data, the α-ROM data, and the new LR-ROM simulations are independent numerical outputs, so using them to test scaling ideas is not circular in itself. The main circularity concern is confined to the LR-CDP assignment for the α-ROM: the effective exponent α′ is assembled from the α-ROM's own d_f and from ν⊥ inferred via hyperscaling from the same β and γ′ that the LR-CDP curve is then used to reproduce, under a scaling relation the paper states is not satisfied. This makes Fig. 8(b) partly a self-consistency test, as the paper itself acknowledges ('a loophole cannot be excluded'). That acknowledged circular step is load-bearing for the universality-class identification but not for the central master-curve comparison, so the overall circularity score is moderate.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

No new microscopic entities (particles, forces, fields, dimensions) are introduced. The tentative 'CDP-0' label for a possible universality class (Sec. 3.6) is a classification label, not a new entity. The effective transport exponent α' is an invented mapping parameter, listed above as a free parameter.

free parameters (4)
  • α (interaction decay exponent)
    Control parameter of both generalized models, tuned over α∈(0,4] for α-ROM and α∈(1,6] for α-Picard. All crossover claims are functions of this free knob.
  • Effective transport exponent α' (α_eff) for α-ROM = varies; defined via α'=d_f+ν⊥^{-1}
    Constructed from the α-ROM's own measured d_f and ν⊥ (the latter via hyperscaling), using the depinning scaling relation ν⊥^{-1}=α-d_f that the paper admits the model does not satisfy. Used to map α-ROM onto LR-CDP for β≤1 (Sec. 4.1).
  • Critical points ϕ_c,α and Σ_Y,α = model- and α-dependent
    Reduced control parameters ε are defined relative to numerically fitted critical points; all reported exponents depend on these fits, though this is standard APT practice.
  • Noise exponent µ in Lévy-Hebraud-Lequeux model = 0<µ<2, varied as input
    µ is an input controlling fractional diffusion in Eqs. (23)-(24); the relation µ=d/α is the mean-field estimate, and the paper states there is no analytical prediction beyond mean-field (Sec. 4.2.1).
assumptions (7)
  • domain assumption CDP universality class describes short-range APTs with a conserved field; β≈0.64 in 2D, hyperuniform critical state.
    Used as the baseline/limit for both models when α is large (Secs. 3.1, 3.6).
  • domain assumption Long-range propagator in α-ROM: G(r)=c(1+r²)^{-α} with Gaussian displacements.
    Model definition from [47] by the same group; the noise-statistics conclusions (Gaussian for α<d/2, Lévy for α>d/2) follow from this form (Secs. 2.1.2, 4.2.1).
  • domain assumption Generalized Eshelby propagator with zero modes: G̃^{E,α}_{q_x,q_y}=-b_α q_x² q_y²/|q|^{6-α}.
    Defines the α-Picard model; zero modes shift the short-range limit to α=6 and motivate the tentative CDP-0 class (Secs. 2.2.2, 3.6).
  • ad hoc to paper Mediated noise distribution p(δξ)~A/|δξ|^{1+µ} with µ=d/α for α>d/2.
    Mean-field result from the authors' prior work [47]; the paper states there is no analytical prediction for µ beyond mean-field (Sec. 4.2.1). The HL comparison for the convex regime rests on this form.
  • domain assumption Hyperscaling γ'=dν⊥-2β and statistical tilt symmetry relation ν⊥^{-1}=α-d_f.
    Used to relate exponents and to define α_eff; the tilt-symmetry relation is explicitly stated to be violated by the α-ROM (Secs. 3.2, 4.1, 5).
  • domain assumption LR-CDP field equations (15)-(16) with fractional derivative transport describe long-range conserved APTs.
    Taken from Hinrichsen 2007 and Janssen-Stenull 2008; used as the framework for the concave regime, with the α-ROM mapped to it via α_eff (Sec. 4.1).
  • domain assumption Hebraud-Lequeux mean-field self-consistency D=κA for activity-induced diffusion.
    Standard HL assumption from [75]; determines β=2 for Gaussian noise and β=µ for Lévy noise (Sec. 4.2).

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Pith. "Pith review of Yielding versus random organization: convex absorbing transitions in soft matter." pith.science (2026). https://pith.science/paper/LRI4YM2K

@misc{pith2026260623914,
  author       = {Pith},
  title        = {Pith review of: Yielding versus random organization: convex absorbing transitions in soft matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LRI4YM2K}},
  note         = {Machine review of arXiv:2606.23914}
}
abstract

We compare two different soft matter models, a generalized Random Organization Model (ROM) describing the stroboscopic dynamics of cyclically sheared suspensions, and an elastoplastic model describing the mesoscale dynamics of a yield-stress fluid under imposed stress. Both show absorbing phase transitions, sharing a peculiar mechanism: activity induces an internal noise which is transmitted over large distances by long-ranged mediated interactions, either hydrodynamic or elastic, which results in non-local creation of activity. They also both show convex transitions (i.e., the exponent $\beta >1$), in stark contrast with usual absorbing phase transitions, like (Conserved) Directed Percolation, which are concave ($\beta <1$). We further compare the dependence of the critical properties (activity mean value and fluctuations, avalanche statistics, low-wavenumber structure factor) on the decay exponent $\alpha$ of long-range interactions in both models, finding a qualitatively similar scenario. A smooth crossover is observed as a function of $\alpha$ between a concave transition regime for short-range interactions, with diverging fluctuations and compact avalanches, and a convex transition regime, with vanishing fluctuations and non-compact avalanches, for longer-range interactions. Although for a given range exponent $\alpha$, the values of critical exponents for both models differ, a good agreement between the models is found by parametrically plotting the different critical exponents as a function of the exponent $\beta$ of the mean activity. In this parametric representation, the concave regime is consistent with the behavior of the Long-Range Conserved Directed Percolation class, while the convex regime can be accounted for by a mean-field-type scenario with anomalous diffusion close to an absorbing boundary, inspired by the H\'ebraud-Lequeux model for the yielding transition.

Figures

Figures reproduced from arXiv: 2606.23914 by the authors.

Figure 1
Figure 1. Similarities between the reversible-irreversible transition (RIT) of cyclically sheared suspensions and the yielding transition of yield stress fluids. Top: RIT. (a) A suspension of neutrally buoyant particles is cyclically sheared in a cylindrical Couette cell, and the particle positions are observed stroboscopically, once per cycle. If no interparticle contact occurs during the shear cycle, the particles follow re… view at source ↗
Figure 2
Figure 2. Critical exponent β characterizing the mean activity ⟨A⟩ ∼ ε β as a function of the power-law decay exponent α of the propagator, where ε is the distance to the critical point. (a) α-ROM, with ε = (ϕ − ϕc,α)/ϕc,α. Data originally from [47]. (b) α-Picard model, with ε = (Σ − ΣY,α)/ΣY,α. Data originally from [17]. The critical behavior of the α-ROM depends on the exponent α characterizing long-range interactions, as s… view at source ↗
Figure 3
Figure 3. Critical exponent γ ′ characterizing the variance of the activity ⟨(A − ⟨A⟩) 2 ⟩ ∼ ε−γ ′ as a function of the power-law decay exponent α of the propagator. (a) α-ROM, with ε = (ϕ − ϕc,α)/ϕc,α. Data originally from [47]. (b) α-Picard model, with ε = (Σ − ΣY,α)/ΣY,α. Data originally from [17]. correlation length, since the variance of activity fluctuations still diverges with respect to the mean value ⟨A⟩ of activity,… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Critical exponents of avalanche statistics versus the power-law decay exponent α of the propagator. Top: fractal dimension df , exponent χ and dynamical exponent z characterizing the cut-off of avalanche distributions, for the α-ROM model (a) (data originally from [48]…
Figure 5
Figure 5. Figure 5: Plots of β − 1, γ ′ and df − d (data from Figs. 2, 3 and 4) showing that the values β = 1, γ ′ = 0 and df = d (here, d = 2) occur for very close values of α ≈ α ∗, suggesting that the common value α ∗ separates two markedly different behaviors. (a) α-ROM, (b) α-Picard …
Figure 6
Figure 6. Figure 6: Parametric plots of the exponents as a function of the exponent β, showing a rather good collapse of data from different models. (a) γ ′ , (b) τ, (c) τ ′ , (d) τ ′′, (e) df , (f) χ, (g) z. α, as seen in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Spatial correlation of the conserved field in Fourier space. (a) Structure factor S(q) in the α-ROM. Data originally from [47]. (b) Fourier correlation Sσ(q) of the stress field in the α-Picard model. Fits to power laws Sσ(q) ∼ q η are shown in dashed lines. (c) Expone…
Figure 8
Figure 8. Figure 8: (a) Parametric plot of γ ′ versus β in the α-ROM and α-Picard models as in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Evolution with the noise exponent µ of (a) the order parameter exponent β (data originally from [47]) and (b) the fluctuations exponent γ ′ , in the L´evy-H´ebraud-Lequeux model. Dots: numerical resolution of the suspension L´evy-H´ebraud-Lequeux model given by Eq. (24…
Figure 10
Figure 10. Figure 10: Long-range conserved directed percolation (LR-CDP) exponents as function of the power-law transport exponent α ′ . (a) Order parameter exponent β. (b) Order parameter fluctuations exponent γ ′ . References [1] Haye Hinrichsen. Nonequilibrium Critical Phenomena and Pha…

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.