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REVIEW 3 major objections 6 minor 47 references

Avalanches in the Random Organization Model with long-range interactions

T0 review · 3 major / 6 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read At the reversible-irreversible transition, long-range fluid interactions turn avalanches from compact to sparse as their fractal dimension crosses space dimension.

desk verdict Solid computational paper that finally gives avalanche statistics for the α-ROM and shows df crossing d near α≈1.5; the geometric claim is well supported by the collapses, with only the usual caveats about inherited φc and single reactivation protocol. read the letter →

arxiv 2603.18909 v1 pith:67XUJRQF submitted 2026-03-19 cond-mat.soft

T. Jocteur , K. Martens , R. Mari , E. Bertin This is my paper · ORCID
classification cond-mat.soft
keywords absorbingphasetransitionreversible-irreversibleRandomOrganizationModelavalancheslong-rangeinteractionsfractaldimensionconserveddirectedpercolationshearedsuspensions
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

Cyclically sheared suspensions sit at an absorbing phase transition: below a critical strain they eventually settle into reversible motion; above it they keep colliding forever. Earlier work tracked only global activity or waiting times. This paper instead measures the intermittent bursts of activity at criticality in a Random Organization Model that includes long-range hydrodynamic kicks decaying as a tunable power of distance. The bursts are scale-free avalanches whose size, duration and number of particles obey power laws whose exponents depend continuously on the interaction range. The decisive geometric fact is that the fractal dimension of an avalanche crosses the spatial dimension near a characteristic range: short-range kicks produce compact avalanches that re-activate the same particles many times, while long-range kicks produce sparse, non-compact avalanches. That geometric switch also organises the non-monotonic drift of the power-law exponents and the internal cluster statistics. The result supplies a concrete dynamical probe that experiments on oscillatory suspensions can use to read out the effective range of fluid-mediated interactions.

What carries the argument

The α-ROM: a stroboscopic particle model in which active (overlapping) particles receive random kicks and also induce random displacements of distant passive particles through a coarse-grained power-law kernel G(r)∼r^{-2α}. Avalanches are defined as temporally connected bursts of activity between successive absorbing states, reactivated by single-particle random kicks.

What would settle it

Measure the fractal dimension of activity bursts in a two-dimensional oscillatory suspension while systematically changing the effective interaction range (for example by changing solvent viscosity or particle size); if df never crosses 2, or if the power-law exponents stay independent of range, the central claim fails.

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Extended reading notes

Core claim

At the absorbing critical point of the mediated Random Organization Model, avalanche size, duration and participation number are power-law distributed with exponents that vary continuously with the interaction-decay exponent α. The avalanche fractal dimension df crosses the spatial dimension d=2 near α*≈1.5, so avalanches are compact (df>d) for short-range interactions and non-compact (df<d) for long-range interactions; the same crossover organises the non-monotonic behaviour of the power-law exponents and the cluster statistics inside avalanches.

Load-bearing premise

The packing fraction is set exactly at the previously measured critical density for each interaction range, and the single-particle reactivation protocol used to keep the system alive does not change the reported avalanche cutoff exponents.

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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

3 major / 6 minor

Summary. The manuscript studies intermittent avalanche dynamics at the reversible–irreversible (absorbing) transition of a two-dimensional Random Organization Model with fluid-mediated long-range interactions (α-ROM). Activity is coarse-grained onto a grid and passive particles receive additive Gaussian kicks whose variance is set by a power-law propagator G(r)∼(1+r²)^−α. At the α-dependent critical packing fraction ϕc, avalanches are generated by repeated single-particle random reactivation. Finite-size collapses of P(S), P(T) and P(N) for L=256–2048 yield α-dependent power-law and cutoff exponents (Table I, Figs. 1–4, 10–12). The central geometric claim is that the avalanche fractal dimension df crosses the spatial dimension d=2 near α*≈1.5, so that avalanches are compact (df>d) for short-range interactions and non-compact/sparse (df<d) for long-range ones (Fig. 5). Conditional averages, a depinning-style scaling check β=ν⊥(d−df+z), and power-law cluster statistics inside avalanches are also reported.

Significance. If the reported α-dependence of the avalanche exponents and the compact-to-sparse crossover at α*≈1.5 hold, the work supplies a concrete dynamical probe of interaction-range effects at absorbing transitions that goes beyond the static exponents of the authors’ prior study. The multi-size finite-size collapses, compensated plots, space-time visualizations, and successful check of the large-avalanche scaling relation are genuine strengths and make the geometric claim falsifiable. The α-ROM is a minimal, tunable setting that links the reversible–irreversible transition in sheared suspensions to long-range depinning and conserved directed percolation, and it opens a clear route to experimental comparison (Brownian or sedimentation reactivation). The sequential use of ϕc(α) and static exponents from the companion paper is ordinary and does not undermine novelty of the avalanche analysis.

major comments (3)
  1. [§III.B] §III.B: All avalanche distributions are measured after fixing ϕ exactly at the α-dependent critical values ϕc(α) taken from the authors’ static study [25], with no independent re-determination or off-criticality scan in the present work. Because the cutoff exponents df, z, χ (and therefore the claimed crossing df=d near α*≈1.5) are extracted from finite-size collapses that assume criticality, even a small systematic offset in ϕc could bias the reported geometry. A short sensitivity check (e.g., distributions at ϕc±δϕ for one or two α) or an explicit statement of the uncertainty on ϕc would make the central claim more secure.
  2. [§III.B, §III.E] §III.B and §III.E: Avalanches are generated exclusively by a single-particle random-reactivation protocol. The text correctly notes (citing yielding work [36]) that absolute values of df and z can depend on the reactivation rule while scaling relations may be preserved, yet no second protocol is tested. Given that the geometric distinction compact vs sparse rests on the absolute value of df relative to d=2, at least a brief comparison (or a stronger argument why the single-particle rule is representative of the experimental reactivation mechanisms mentioned) is needed before the α* crossover can be regarded as protocol-independent.
  3. [§III.E, Eq. (6), Fig. 7] §III.E, Eq. (6) and Fig. 7: The test of the depinning scaling relation uses ν⊥ estimated from the hyperscaling formula ν⊥=d−1(2β+γ′) with static exponents taken from [25]. For long-range interactions (especially α≲1.5, where the authors themselves report departure from LR-CDP), hyperscaling is not guaranteed. The main geometric claim does not rely on this test, but the claim that “Eq. (6) is very well followed” should be qualified by an explicit discussion of possible hyperscaling violation, or by an independent estimate of ν⊥.
minor comments (6)
  1. [Table I, Fig. 4] Table I and Fig. 4: No uncertainties are quoted on the fitted exponents. Even rough error bars from the quality of the collapses (or from jackknife over system sizes) would help the reader judge how sharply df crosses d=2.
  2. [§II.B, Eq. (3)] §II.B, Eq. (3): The piecewise choice of the prefactor c (constant for α>1, L-dependent for α<1) is stated but not motivated beyond numerical convenience; a one-sentence physical or normalization argument would help.
  3. [§III.F] §III.F: The cluster graph connectivity threshold √3·2 is introduced without discussion of robustness. A brief remark that the power-law exponents are stable under modest changes of the threshold would strengthen the cluster section.
  4. [Figs. 1–3, 10–12] Figs. 1–3 and 10–12: Compensated plots are useful; adding the fitted exponent value directly on each panel (as done for clusters in Fig. 8) would improve readability.
  5. [Abstract, Introduction] Abstract and Introduction: “kin depinning” appears to be a typographical remnant of “akin to depinning”; please correct.
  6. [§I] §I: A short pointer to the experimental reactivation mechanisms (Brownian motion, sedimentation) already appears in §III.B; moving a sentence of that discussion into the introduction would better motivate the avalanche focus for a soft-matter audience.

Circularity Check

1 steps flagged · score 2.0 of 10

Ordinary sequential self-citation for ϕc(α) and static exponents from the authors’ prior α-ROM study; avalanche power-laws, cutoffs and df(α) are independently measured from new simulations.

  1. self citation load bearing [§III.B (Definitions of avalanches…) and §III.E (Scaling relations)]
    "we thus set the packing fraction ϕ to its (α-dependent) critical value ϕc. … We estimate the value of ν⊥ assuming hyperscaling ν⊥=d-1(2β+γ′), where β and γ′ are the order parameter and order parameter fluctuations exponents, respectively, the values of which were numerically evaluated in [25]."

    Criticality (and therefore the claim that the measured power-laws are critical) is fixed by importing ϕc(α) and the static exponents β, γ′ from the authors’ own prior simulation study of the same model. The avalanche distributions and df(α) are new data, so the loop is only partial; the self-citation is load-bearing for the premise “at the absorbing phase transition” but does not definitionally force the reported avalanche exponents.

full rationale

The paper’s central results—power-law distributions P(S), P(T), P(N) with α-dependent exponents, the crossing of df through d=2 near α*≈1.5, and the compact-to-sparse geometric change—are obtained by direct finite-size collapses of avalanche histograms generated at criticality under a fixed single-particle reactivation protocol (Figs. 1–3, 5–6, Table I, §III.B–C). These measurements do not reduce by construction to any fitted constant or prior static exponent. The only self-citations that enter the derivation chain are (i) the α-dependent critical packing fractions ϕc(α) taken from the authors’ earlier static study [25] so that the system can be placed at criticality, and (ii) the static exponents β, γ′ (again from [25]) used solely to construct ν⊥ for a consistency check of the depinning scaling relation (Fig. 7). Neither step forces the reported avalanche exponents or the df-crossing claim; both are ordinary sequential science. No self-definitional loop, no fitted-input-called-prediction, and no uniqueness theorem imported from the authors appear. Score 2 reflects the mild load-bearing character of the ϕc self-citation while recognizing that the avalanche statistics themselves remain independent content.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claim is a numerical observation inside a defined stochastic particle model. Load-bearing inputs are: (i) the α-ROM dynamics and coarse-grained kernel taken from prior work, (ii) the identification of the reversible-irreversible transition with an absorbing critical point at ϕ=ϕc(α), (iii) the single-particle reactivation protocol that generates the avalanche ensemble, and (iv) visual finite-size collapse used to extract exponents. No new physical entity is postulated; free parameters are discrete simulation choices and the continuous interaction exponent α.

free parameters (5)
  • interaction decay exponent α = scanned set {0.5,1.25,1.5,1.75,2,3}
    Scanned over the discrete set {0.5, 1.25, 1.5, 1.75, 2, 3}; the reported continuous variation of exponents and the location α*≈1.5 of the df=d crossing depend on this choice of range.
  • propagator prefactor c = 0.25 or 0.25 L^{2α−2}
    Set by hand to c=0.25 (α>1) or c=0.25 L^{2α−2} (α<1) to ensure convergence of the convolution; enters the definition of passive displacements.
  • critical packing fractions ϕc(α) = α-dependent values from Ref. [25]
    Taken from the authors’ previous static study and used to place every run at criticality; mis-location of ϕc would cut off or inflate the power laws.
  • cutoff exponents df, z, χ (collapse tuning) = Table I values
    Chosen to produce the best visual data collapse of P(S), P(T), P(N); they are the reported fractal, dynamical and participation cutoffs.
  • cluster graph connectivity threshold = 2√3
    Spatio-temporal cells are linked if Euclidean distance ≤2√3; this ad-hoc cutoff defines what counts as a cluster.
assumptions (5)
  • domain assumption The stroboscopic reversible-irreversible transition in cyclically sheared suspensions is in the same universality class as the absorbing transition of the (α-)ROM.
    Stated in the introduction and §II; underpins the claim that avalanche results speak to real suspensions.
  • domain assumption Long-range hydrodynamic kicks on passive particles can be represented by an additive, uncorrelated Gaussian displacement whose variance is a coarse-grained convolution with G(r)∼r^{−2α}.
    §II.B; the coarse-graining and uncorrelated-variance assumptions are taken from [25] and are not re-derived.
  • domain assumption Avalanche exponents extracted under single-particle random reactivation obey the same scaling relations as under other reactivation protocols (by analogy with yielding).
    §III.A cites [36]; only the scaling combination df−z is argued to be protocol-independent, not each exponent separately.
  • domain assumption Hyperscaling ν⊥=d^{−1}(2β+γ′) holds and may be used to test the depinning relation β=ν⊥(d−df+z).
    §III.E; used to construct Fig. 7 from static exponents of [25].
  • standard math Standard finite-size scaling forms for avalanche distributions at an absorbing critical point (power law times cutoff function of S/L^{df}, etc.).
    Eq. (5); conventional in depinning and absorbing-state literature.
invented entities (2)
  • α-ROM (mediated Random Organization Model)
    purpose: Minimal particle model that continuously interpolates short-range ROM and long-range mean-field-like absorbing transitions via the kernel exponent α.
    Introduced in the authors’ prior work [24,25] and used here as the simulation platform; not independently evidenced outside that model family, but it is a defined computational object rather than a new physical particle.
  • coarse-grained activity-field propagator G(r)=c/(1+r²)^α
    purpose: Numerically efficient surrogate for particle-pair long-range kicks; enables large-L avalanche statistics.
    §II.B; the paper asserts that the discrepancy with exact pair interactions is irrelevant for critical properties, without a direct side-by-side test in this work.

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Pith. "Pith review of Avalanches in the Random Organization Model with long-range interactions." pith.science (2026). https://pith.science/paper/67XUJRQF

@misc{pith2026260318909,
  author       = {Pith},
  title        = {Pith review of: Avalanches in the Random Organization Model with long-range interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67XUJRQF}},
  note         = {Machine review of arXiv:2603.18909}
}
abstract

Oscillatory sheared suspensions, when observed stroboscopically, exhibit a reversible-irreversible transition as a function of the strain amplitude, which is a kind of absorbing phase transition. So far studies of this transition focused on global quantities, e.g. quantifying the irreversibility on one side of the transition or the time to reach a reversible state on the other side. Here, motivated by the kin depinning transition, we focus on the intermittent dynamics near the transition. We perform simulations of a modified Random Organization Model (ROM), a minimal particle model which we recently adapted to take into account the generic presence of long-range interactions mediated by the fluid, taking the power-law-decay exponent $\alpha$ as an additional control parameter of the model. We show that at the absorbing phase transition, this model displays power-law-distributed avalanches. We characterize the avalanche statistics in terms of avalanche size, duration and number of particles involved, and we determine the associated exponents. By varying the exponent $\alpha$, the fractal dimension of avalanches crosses space dimension $d$, inducing a qualitative change of the spatial structure of avalanches, from compact avalanches when interactions have a short range, to sparse avalanches when interactions are long-ranged. Finally, we characterize the clusters within the avalanches, which we also find power-law distributed.

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Reviewed July 13, 2026 · model on record in the stance chip above.