{"id":"fed64f6c-ff12-48a9-be2a-37bb2f281343","arxiv_id":"1908.08820","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Avalanches in the elastic regime of Lennard-Jones glasses are power-law distributed with exponent about 1 in both 2D and 3D, matching mean-field predictions for marginally stable amorphous solids.","lead":"This paper simulates glasses being squeezed at tiny strains and finds that small rearrangements inside them follow a universal power-law size distribution, matching the law predicted for 'marginally stable' glasses. The result suggests ordinary glasses are intrinsically dissipative even at very small deformations, and that true elasticity disappears in the thermodynamic limit.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Tables S1-S2 violate the paper's own α=(2−τ)df/d scaling check, implying τ≈1.2–1.3 for poorly annealed glasses and undercutting the collapse-derived τ≈1.","rationale":"Assessing the paper in good faith, the reported observation of τ≈1 in the elastic regime is the key evidence for marginal stability. The reader's concern about transferring the infinite-dimensional mean-field result to finite-dimensional LJ glasses is legitimate, but it only matters if the measured τ is reliable. The more fundamental problem is that the paper's own consistency check fails: the scaling relation α=(2−τ)df/d, which follows directly from Eq. (4), is not satisfied by the tabulated α and df/d values. The implied τ from these tables ranges from 1.1 to 1.28 for the poorly annealed systems, in tension with the collapsed τ≈1.0. This suggests the universal exponent is an artifact of the collapse procedure, or that the scaling form with a single τ is inadequate. Either way, the identification of the avalanche exponent with the Franz–Spigler value is not supported by the internal evidence. The concrete re-analysis proposed above would settle whether the inconsistency is real. Because the current manuscript does not address this inconsistency, the conditional verdict should be maintained but with the explicit requirement to resolve it; if the re-analysis confirms Tini-dependent τ>1, the central claim would be rejected. I therefore see the reader's CONDITIONAL verdict as appropriate, with our concern sharpening the condition rather than changing the verdict category.","tokens_in":12688,"tokens_out":20263,"duration_ms":174944,"concrete_test":"From the deposited data (OSF U6PYF), recompute for each Tini and dimension the cutoff S_c (Eq. 6) and the mean avalanche size ⟨S⟩ using the same avalanche lists and fitting range; obtain df/d and α by power-law fits with bootstrap errors. Then test α=(2−τ)df/d using the quoted τ, and also re-fit the collapsed master curve per thermal history with τ left free. If the per-history τ values from the collapse agree with 2−α/(df/d) and scatter above 1 for the least stable states, the universal τ=1 claim fails. Additionally, perform the scaling collapse using ⟨S⟩ versus S_c as the scaling variable; if α≠df/d, the two collapses cannot both be of comparable quality, and the choice would reveal which exponent is biased.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The scaling form of Eq. (4), R(S,N) ∼ N^b χ^{-τ} f(χ) with χ = S/S_c and S_c ∼ N^{df/d}, implies the consistency relation α = (2−τ) df/d for the mean-size exponent α (the paper cites Lin et al. for this). The text claims τ≈1 and therefore α=df/d, citing Fig. 4(d) as confirmation. However, the tabulated fit parameters in Tables S1 and S2 do not satisfy this relation within error. For example, in 3D at Tini=0.87, α=0.172±0.008 while df/d=0.24±0.02; in 2D at Tini=1.0, α=0.19±0.01 vs df/d=0.225±0.008. Inverting the relation gives τ = 2 − α/(df/d) = 1.28±0.07 (3D Tini=0.87), 1.16±0.06 (2D Tini=1.0), and similar values >1 for the other poorly annealed states, all several sigma above the reported collapsed exponent τ=0.98–1.01. Only the most stable states (e.g., 3D Tini=0.479) yield τ≈1. Since the central claim requires a universal τ=1 matching Franz–Spigler, this internal inconsistency is load-bearing: it indicates either systematic bias in the multi-history collapse, an incorrect treatment of the cutoff, or a true Tini-dependence of τ that is hidden by the collapse. The paper's assertion that Fig. 4(d) confirms α=df/d is therefore contradicted by its own parameter tables.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies athermal quasistatic shear in two- and three-dimensional Lennard-Jones glasses, focusing on avalanche statistics in the elastic regime (strain intervals up to 0.02, well below yielding). For several system sizes and thermal histories, the authors measure the avalanche number density R(S,N,T_ini) and propose a scaling form with system-size-dependent cutoff S_c ~ N^{d_f/d} and amplitude N^b. They report a universal avalanche exponent τ ≈ 1 in both 2D (0.98 ± 0.01) and 3D (1.01 ± 0.01), compatible with the Franz–Spigler mean-field prediction for marginally stable systems. They further report energy-balance scaling b + 2d_f/d = 1, a mean-size exponent α that they claim equals d_f/d, and a pseudo-gap exponent θ that evolves from an initial value near 1/2 to a plateau correlated with α. The authors interpret the results as evidence that marginal stability is systematic in the thermodynamic limit, despite the common view that such behavior is restricted to jammed systems with short-range repulsions.","tokens_in":13083,"tokens_out":11066,"duration_ms":108992,"significance":"If the central claim holds, the paper would significantly extend the phenomenology of marginal stability from jammed soft spheres in infinite dimensions to finite-dimensional, high-density Lennard-Jones glasses with attractions, suggesting a universal avalanche exponent in the elastic regime. The manuscript is strengthened by direct numerical evidence, a scaling collapse, an energy-balance check (Fig. 3), and internal consistency checks relating exponents (Figs. 4 and 5). The data availability statement permits independent verification. However, the central claim rests on the validity of the scaling collapse and on the transfer of the mean-field prediction to this system class; the latter is an assumption that the authors acknowledge, and the former is challenged by an inconsistency in the reported fit parameters, as detailed in the major comments.","major_comments":[{"comment":"The tabulated exponents do not satisfy the consistency relation that the paper relies on. For 3D, T_ini = 0.87, the table gives d_f/d = 0.24 ± 0.02 and α = 0.172 ± 0.008. Using the relation α = (2 − τ) d_f/d quoted in the text, one obtains τ = 2 − α/(d_f/d) = 1.28 ± 0.07, several standard deviations above the collapsed value τ = 1.01 ± 0.01. For 2D, T_ini = 1.0, the analogous calculation gives τ = 1.16 ± 0.06. Only the most stable states (e.g., 3D T_ini = 0.479) are consistent with τ ≈ 1. The text claims that Fig. 4(d) confirms α = d_f/d, but the paper's own fit tables contradict this. This is a load-bearing issue: either the collapse-derived τ is biased by the choice of cutoff function or fitting range, or the reported α values do not correspond to the mean size defined in Eqs. (1)–(2), or the relation α = (2 − τ) d_f/d is misapplied. Please resolve this discrepancy explicitly.","section":"Tables S1-S2 and Fig. 4(d)"},{"comment":"The scaling form (4) directly implies ⟨S⟩ = η/M ∼ N^{d_f/d} for any τ < 2, because M ~ N^{b+d_f/d} and η ~ N^{b+2d_f/d}. The text instead cites Lin et al. for α = (2 − τ) d_f/d and then reduces it to α = d_f/d when τ ≈ 1. These two statements are inconsistent with each other under the paper's own definitions. The relation α = (2 − τ) d_f/d may apply to a different observable (for instance the total dissipated energy per unit strain rather than the mean avalanche size), but as written the manuscript does not define whether α in Fig. 4 and Tables S1-S2 is the exponent of ⟨S⟩ or of another moment. This matters because the paper presents Fig. 4(d) as a consistency check; please derive the relation used, state precisely which observable α governs, and reconcile it with Eq. (4).","section":"Eqs. (4)–(5) and the relation α = (2−τ) d_f/d"}],"minor_comments":[{"comment":"Equation (7) has a typesetting issue: the terms 'Nγ−1' and 'Nγ−1ρ−1' are ambiguous. They should be written as N^{-1} and N^{-1} ρ^{-1} respectively, or with explicit parentheses, so that the energy-balance identity is readable.","section":"Eq. (7)"},{"comment":"The caption states 'The dashed line shows the avalanche exponent −1 predicted by mean field theory (7) near the ground state.' It is unclear whether this line is a fit to the collapsed data or the predicted slope drawn for comparison; please clarify the role of the line in the figure.","section":"Fig. 1 caption"},{"comment":"The avalanche size definition S = N(ΔU + Δγ τ_θ / ρ) uses a threshold S > 0.01 without stating the units. Since the system uses reduced units, please specify the unit convention and confirm that the chosen threshold does not affect the reported exponents, beyond the statement that thresholds from 0.01 to 0.1 give 'qualitatively similar results'.","section":"Methods / Eq. (10)"},{"comment":"The text says the parameters are fitted from Fig. 2 and then 'both for 2D and 3D systems', but the fit parameters are given in Tables S1 and S2, not in the main text. Please refer to the tables at first mention and include the fit ranges used for the power-law fits in Fig. 2.","section":"Scaling analysis text"}],"recommendation":"major_revision","confidential_remarks":"The manuscript presents an interesting and potentially important result, and the numerical effort appears significant. However, the internal inconsistency between Tables S1-S2 and the claimed consistency relations (α vs d_f/d) is serious because it directly bears on the universality of τ ≈ 1. The authors should be asked to revisit the scaling analysis, report the derivation of the α relation, and either show that the deviations are within large finite-size corrections or revise the claim. I am not recommending rejection because the central proposition is defensible and the issue might be fixable with a careful re-analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nWhat you should know: This paper reports a careful AQS simulation study of avalanche statistics in the elastic regime (γ≤0.02) of 2D and 3D Lennard-Jones glasses over several thermal histories and system sizes. The headline finding is a power-law avalanche size distribution with exponent τ≈1 (0.98±0.01 in 2D, 1.01±0.01 in 3D), compatible with the Franz–Spigler mean-field prediction for marginally stable jammed spheres. If correct, this would extend marginal stability from near-jamming finite-range packings to ordinary dense glasses, which is a significant claim.\n\nWhat is genuinely good: The study is systematic—multiple sizes, thermal histories, two dimensions—and the raw distributions are shown. The scaling relations b+2df/d=1 and α=df/d are checked against the data, and the energy-balance argument for b+2df/d=1 is sound. Data are deposited. The distinction between elastic-regime and steady-state avalanche exponents is clearly drawn and is physically interesting.\n\nWhere I think the paper is soft: The stress-test concern is on point. The paper's own Tables S1 and S2 do not satisfy the scaling relation α=(2−τ)df/d that the text invokes. For the poorly annealed states, the tabulated α and df/d imply τ≈1.2–1.3, several σ above the reported universal τ≈1. Only the most stable states (e.g., 3D Tini=0.479) give α≈df/d and hence τ≈1. The collapse in Fig. 1 uses exponents fitted from the same data, so it can mask a systematic Tini-dependence of τ. This is load-bearing because the central claim is universality. The transfer of the infinite-dimensional mean-field result to finite-dimensional attractive systems is also an assumption, though the authors acknowledge it is surprising. The pseudo-gap analysis (θ plateau dependent on Tini) is suggestive but not directly validated against the model of Lin–Wyart beyond exponent matching.\n\nWho this is for: People working on avalanches, marginal stability, and yielding in glasses. It deserves a serious referee, but the referee should ask for a re-analysis of the scaling that either reconciles the tabulated exponent values or weakens the universality claim to only well-annealed systems. My recommendation: send to peer review, but treat the central claim as conditional pending that check.\n\nSincerely,\n\n[You]","headline":"Systematic numerical study of elastic-regime avalanches in Lennard-Jones glasses claims universal τ≈1, but the paper's own tables show α and df/d are inconsistent with τ≈1 for poorly annealed states, leaving the marginal-stability conclusion unproven.","tokens_in":13647,"tokens_out":4534,"would_cite":false,"duration_ms":38203,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Even deep in the elastic regime, amorphous solids deform through scale-free avalanches with a universal exponent τ ≈ 1, the mean-field signature of marginal stability.","keywords":["amorphous solids","elastic avalanches","marginal stability","athermal quasistatic shear","avalanche exponent","Lennard-Jones glasses","pseudo-gap","finite-size scaling"],"falsifier":"Measure the elastic-regime avalanche distribution in a qualitatively different glass former, e.g. a polymer glass or a metallic-glass model, using the same athermal quasistatic protocol; a value of $\\tau$ clearly different from 1 would falsify the claim of a universal marginal-stability signature. Alternatively, check the zero-strain pseudo-gap prediction directly: if the first-avalanche strain in a deeply annealed sample does not scale as $N^{-2/3}$, the extreme-value link to $\\theta = 1/2$ fails.","tokens_in":12427,"feed_emoji":"⚡","tokens_out":10827,"duration_ms":95506,"temperature":0.7,"pith_summary":"Nearly all studies of plasticity in glasses focus on large strains near or past yielding. This paper instead characterises what happens at strains far below yielding, in the nominally elastic part of the stress–strain curve, where energy drops are small but frequent. It finds that in two- and three-dimensional Lennard-Jones glasses the avalanche number density is a power law with exponent $\\tau \\approx 1$ ($0.98\\pm0.01$ in 2D, $1.01\\pm0.01$ in 3D), matching the mean-field prediction for marginally stable amorphous packings. After rescaling by system size and thermal history, all distributions collapse onto a single master curve, and the exponents obey three scaling relations that tie avalanches, dissipation, and the pseudo-gap in low-lying excitations together. The authors conclude that marginal stability is systematic in the thermodynamic limit and that the amorphous solid is intrinsically dissipative, so the apparent elastic regime is a finite-size effect.","feed_headline":"Tiny pre-yield slips in glasses follow a universal power law","feed_subtitle":"In 2D and 3D Lennard-Jones glasses, the avalanche exponent is ≈1, matching mean-field theory for marginally stable solids.","key_machinery":"The load-bearing object is the avalanche number density $R(S,N,T_{\\mathrm{ini}})$, defined as the number of energy-drop avalanches of size $S$ per unit avalanche size and per unit strain. The argument is carried by a scaling ansatz that factors out system-size and thermal-history dependences: $S_c \\sim \\xi_1 N^{d_f/d}$ and $R \\sim \\xi_2 N^b \\chi^{-\\tau} f(\\chi)$, so that the exponent $\\tau$ is extracted from a data collapse. Three identities anchor the interpretation: energy balance gives $b + 2d_f/d = 1$; extreme-value statistics of the strain to the first plastic event gives $\\langle \\epsilon_\\gamma \\rangle \\sim N^{-1/(1+\\theta)}$, yielding $\\theta \\approx 1/2$; and the elasto-plastic relation $\\alpha = \\theta/(1+\\theta)$ links the mean-avalanche-size exponent $\\alpha$ to the pseudo-gap exponent $\\theta$.","core_discovery":"The central claim is that amorphous solids respond to arbitrarily small shear strain through scale-free avalanche activity whose statistics are those of a marginally stable phase, not the localized, history-dependent events usually assumed for the elastic regime. In athermal quasistatic simple shear over strain interval $\\gamma \\in [0, 0.02]$, well below the yield strain, the avalanche number density obeys $R(S,N,T_{\\mathrm{ini}}) \\sim \\xi_2 N^b \\chi^{-\\tau} f(\\chi)$ with $\\chi = S/S_c$, $S_c \\sim \\xi_1 N^{d_f/d}$, and $\\tau = 0.98\\pm0.01$ (2D) and $1.01\\pm0.01$ (3D). The same scaling is compatible with the mean-field result that local minima in a hierarchical energy landscape are marginally stable, and with predictions of an elasto-plastic model in which marginal stability appears as a pseudo-gap with exponent $\\theta \\approx 1/2$ at zero strain. The paper further shows that the scalar exponents satisfy $b + 2d_f/d = 1$, $d_f/d = \\alpha$, and $\\alpha = \\theta/(1+\\theta)$, where $\\alpha$ governs the subextensive growth of the mean avalanche size with $N$. From the limit ordering $N\\to\\infty$ versus $\\gamma\\to0$ it infers that the thermodynamic-limit solid is intrinsically dissipative.","pith_inferences":["If the $\\tau \\approx 1$ law is universal, acoustic-emission or micro-mechanical experiments on metallic glasses in the pre-yield regime should observe the same exponent, giving a laboratory test beyond simulation.","The clean decrease of $\\alpha$ and $\\theta_{\\mathrm{plateau}}$ with annealing leaves open the possibility of a sharp ductile-to-brittle transition at a finite preparation temperature; testing this would require ultrastable samples at larger sizes than those studied here.","The master-curve collapse implies that avalanche statistics in the thermodynamic limit can be extrapolated from small systems once $\\xi_1$, $\\xi_2$, and $d_f/d$ are known, which could make experimental finite-sample data predictive."],"forward_implications":["Elastic avalanches belong to a universality class distinct from steady plastic flow: $\\tau \\approx 1$ here versus the larger exponents found in stationary shearing, so transient and steady-state plasticity must be analysed separately.","The energy-balance identity $b + 2d_f/d = 1$ holds in the elastic regime, providing a consistency check for any future simulation or experiment that measures avalanche cutoffs.","The pseudo-gap exponent starts at a universal $\\theta \\approx 1/2$ for the first event and falls to a thermal-history-dependent plateau, linking the brittle-to-ductile behaviour of a glass to its preparation.","In the thermodynamic limit the amorphous solid is intrinsically dissipative: taking $N\\to\\infty$ before $\\gamma\\to0$ leaves a finite dissipation per unit strain, so the purely elastic regime is a finite-size artefact."],"supporting_citations":[{"why":"Supplies the mean-field prediction $\\tau=1$ for avalanches in marginally stable packings that the simulations are testing.","marker":"(7)"},{"why":"Provides the elasto-plastic pseudo-gap description and the predicted $\\theta=1/2$ used to interpret first-event and plateau statistics.","marker":"(20)"},{"why":"Gives the energy-balance scaling relation $b+2d_f/d=1$ in plastic flow that the paper verifies for elastic avalanches.","marker":"(23)"},{"why":"Supplies the extreme-value-statistics argument linking the first-avalanche strain exponent to $\\theta$.","marker":"(33)"},{"why":"An independent report of a similar avalanche exponent in the elastic regime that supports universality.","marker":"(24)"},{"why":"A prior claim that elastic-regime plasticity is localized and size-independent, which the paper's subextensive scaling directly addresses.","marker":"(14)"}],"fun_headline_variants":["Universal power law governs tiny pre-yield slips in glasses","Even in elastic regime, glasses show scale-free avalanches","Marginal stability uncovered in pre-yield avalanche statistics","Pre-yield slips in glasses obey universal power law"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The interpretation assumes that the mean-field result for marginally stable jammed packings in infinite dimensions transfers to dense, attractive Lennard-Jones glasses; if that transfer fails, the measured exponent $\\tau \\approx 1$ could have a different cause.","fun_headline_variants_meta":{"raw":{"variants":["Universal power law governs tiny pre-yield slips in glasses","Even in elastic regime, glasses show scale-free avalanches","Marginal stability uncovered in pre-yield avalanche statistics","Pre-yield slips in glasses obey universal power law"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000598,"raw_usage":{"total_tokens":2868,"prompt_tokens":1089,"completion_tokens":1779,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":705,"completion_tokens_details":{"reasoning_tokens":1723}},"tokens_in":705,"tokens_out":1779,"duration_ms":14073,"temperature":1.0,"reasoning_tokens":1723,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:28:33.174128+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the elastic-regime avalanche distribution in a qualitatively different glass former, e.g. a polymer glass or a metallic-glass model, using the same athermal quasistatic protocol; a value of $\\tau$ clearly different from 1 would falsify the claim of a universal marginal-stability signature. Alternatively, check the zero-strain pseudo-gap prediction directly: if the first-avalanche strain in a deeply annealed sample does not scale as $N^{-2/3}$, the extreme-value link to $\\theta = 1/2$ fails.","supporting_citations":[],"review_version":1}