{"id":"e95ace43-8a0c-4db8-8743-ff44cf5cef2e","arxiv_id":"2508.09617","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Non-overdamped relaxation turns 2D long-range elastic interface depinning into a stick-slip coexistence regime, while in 1D and short-range cases it produces anomalous ballistic avalanches.","lead":"By simulating driven disordered interfaces with a relaxation phase, the authors find a coexistence of pinned and flowing states in two-dimensional systems with long-range forces. In one dimension and for short-range forces, they instead find large 'ballistic' avalanches that change the usual power-law statistics.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed k_c=0.11 transition in 2D long-range elasticity is not established: the S_max divergence rests on a finite-size extrapolation without a full scaling collapse, so the coexistence regime may be a finite-size artifact.","rationale":"The paper's most distinctive and load-bearing claim is the coexistence regime in 2D long-range systems, which hinges on the existence of a finite critical stiffness k_c. The reader's verdict flagged both the representativeness of the slow-dissipation model and the finite-size extrapolation of k_c. I focus on the latter because it is testable within the paper's own framework and, if wrong, invalidates the central phase diagram. The current evidence consists of S_max data at four system sizes with no scaling collapse, no error bars, and no code/data to permit independent reanalysis. The qualitative behavior below k_c—system-spanning avalanches coexisting with a decreasing cutoff—is precisely what one expects from finite-size rounding, making the thermodynamic interpretation insecure. A proper finite-size collapse, or a measurement of the system-spanning avalanche probability versus L, would settle this. I agree with the reader's CONDITIONAL verdict; adding this test as an explicit condition is appropriate. I do not raise the relaxation-model faithfulness concern as the primary attack because it is a modeling assumption that the authors themselves hedge, while the finite-size issue threatens the internal validity of the numerical result.","tokens_in":9985,"tokens_out":5124,"duration_ms":55104,"concrete_test":"Reanalyze the S_max data of Fig. 2b for the 2D long-range model at Theta=0.5 by performing a finite-size scaling collapse: S_max(kp,L) = L^gamma * F((kp-k_c)L^{1/nu}), fitting k_c, gamma, and nu simultaneously using all L = 200, 400, 600, 800. If no collapse with k_c > 0 is found—e.g., if the best fit yields k_c = 0 or the collapse quality is poor—the divergence is a finite-size crossover, not a true phase transition. Additionally, measure the probability of system-spanning avalanches (S > L^D) as a function of L at kp = 0.08 and 0.12; if this probability decays with L for kp < k_c, the coexistence regime is a finite-size artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central novel claim is a finite-k_c stick-slip transition in 2D long-range elasticity, with k_c = 0.11 (Table I). The evidence (Fig. 2b,c) is a power-law divergence of S_max = <S^2>/<S> as kp -> k_c, extrapolated from L = 200, 400, 600, 800. No finite-size scaling collapse is shown; the reported exponents (sigma = 1.95(5), k_c) depend on the assumed functional form. For kp < k_c, the authors state that 'the cutoff decreases again, but large-scale system-size events start to be present'—a classic signature of finite-size rounding of a transition that may actually sit at kp = 0 or drift with L. With a long-range kernel and periodic boundary conditions, finite-size corrections are strong. Without a collapse of S_max as a function of (kp-k_c)L^{1/nu}, the data do not distinguish a true thermodynamic transition from a crossover controlled by system size. If the divergence is a finite-size artifact, the 2D coexistence phase and the accompanying anomalous exponents collapse, undermining the paper's strongest claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper investigates driven elastic disordered interfaces beyond the overdamped limit, using a cellular-automaton model with a relaxation phase that models non-overdamped effects such as inertia or viscoelasticity. In the slow-dissipation case with relaxation strength Theta=0.5, the authors report that in 2D with long-range elasticity, there is a critical stiffness k_c≈0.11 below which pinned and flowing states coexist, while in 1D long-range and in short-range 1D/2D systems no such coexistence occurs. Instead, those systems show a pronounced bump in the avalanche size distribution and large avalanches that expand ballistically. The paper reports modified roughness, cutoff, and avalanche-size exponents and suggests experimental signatures. The Theta=0 baseline reproduces known depinning exponents, which serves as an internal check.","tokens_in":10268,"tokens_out":7893,"duration_ms":86573,"significance":"If the central claims hold, the paper would significantly expand the phenomenology of non-overdamped depinning beyond mean-field models: dimensionality and interaction range would determine whether a true stick-slip coexistence regime exists, and avalanches in the non-coexistence regimes would be governed by different critical exponents. The model is clearly specified, the baseline Theta=0 check is strong, and the roughness exponent is verified by two independent methods. However, the most novel claim—the finite-k_c transition in 2D long-range elasticity—rests on finite-size extrapolations without a full scaling collapse, and the qualitative conclusions are tied to a single relaxation strength. The paper is potentially important but needs additional evidence before the central claims can be accepted.","major_comments":[{"comment":"The central claim of a finite-k_c stick-slip transition in 2D long-range elasticity is not established by the evidence shown. The divergence S_max ~ (k0-k_c)^(-sigma) is inferred from L=200,400,600,800 without a finite-size scaling collapse; no fit ranges, goodness-of-fit, or uncertainty for k_c=0.11 are reported. The observation that for k0<k_c 'the cutoff decreases again, but large-scale system-size events start to be present' is a classic signature of finite-size rounding of a transition that may actually sit at k0=0 or drift with L. Please provide a scaling collapse of S_max (and ideally P(S)) as a function of (k0-k_c)L^(1/nu), and explicitly address whether the apparent k_c extrapolates to a nonzero value in the thermodynamic limit.","section":"Results, Fig. 2(b,c), Table I"},{"comment":"The finite-dimensional conclusions are obtained for a single relaxation strength, Theta=0.5, and the two limiting relaxation prescriptions are not checked against each other in the regimes where coexistence is claimed. The text states that the exponents 'explicitly depend on Theta', but no finite-dimensional data at another Theta are provided, and for the 2D long-range case the fast-dissipation behavior is only speculation. Since the slow-dissipation rule (Phi(tau)=1 during the entire avalanche) is a load-bearing modeling assumption, at least one additional value of Theta and a discussion of the fast-dissipation limit in 2D long-range are needed to support the paper's claim that these are general non-overdamped phenomena rather than an artifact of this parameter choice.","section":"Model, Slow dissipation"},{"comment":"The definition of the coexistence regime relies on a qualitative reading of P(S) and F(w). For k0<k_c, the text describes a decreasing cutoff coexisting with system-size events; to make the claim falsifiable, a quantitative order parameter is needed, e.g. the fraction of events with S > L^2/2 or the amplitude of the quasi-periodic oscillations in F(w), together with its L dependence. This would also distinguish genuine coexistence from finite-size nucleation effects. This point is related to the finite-size issue in Fig. 2, but I list it separately because the bimodal shape itself is claimed as evidence.","section":"Fig. 1(b,d), Results"}],"minor_comments":[{"comment":"Eq. (3) is referenced in the text but not displayed, and Eqs. (5)-(6) use a confusing notation mixing the generation index and the relaxation time tau. Please renumber and define all symbols consistently.","section":"Model, Eqs. (3)-(6)"},{"comment":"In the 2D long-range column, sigma=2.0 for depinning and 1.95(5) for Theta=0.5 are not significantly different; the text states that 'both r and a are significantly larger'. Clarify which exponents actually change and adjust the wording accordingly.","section":"Table I and text"},{"comment":"There are typos and inconsistent notations: 'relazation' in the Introduction, 'Sax' versus 'Smax', and 'D' used for both spatial dimension and system size. The captions of Fig. 2(b,c) should include legends and define k_c in panel (c).","section":"General"},{"comment":"The 'flat-bump protocol' used to prepare flat initial profiles is not defined. Please explain the protocol or provide a reference.","section":"Supplementary Material, Fig. S6"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the paper is well-suited to the journal and the baseline checks are encouraging, but the central 2D coexistence transition needs a proper finite-size scaling analysis and the robustness in Theta should be documented before publication. Without these additions, I cannot support acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things before you read it. The paper claims that slow relaxation beyond the overdamped limit changes the phase diagram of driven disordered interfaces in a way that depends on dimension and interaction range: 2D long-range elasticity gives a coexistence regime between pinned and flowing states with a finite critical stiffness k_c ≈ 0.11, while 1D long-range and short-range (1D and 2D) show no coexistence but a pronounced bump of large, ballistically expanding avalanches. Second, the evidence for the 2D transition is numerical and mostly clean, but the finite-size analysis is not as airtight as the abstract suggests.\n\nWhat's genuinely new: prior coexistence results were only for fully connected or mean-field models. This is a first serious finite-dimensional look, and the 1D/short-range ballistic bump is not something I've seen in the depinning literature. The model is well specified, and the Θ=0 baseline reproduces known depinning exponents, which is a good internal check. The supplementary also cross-checks the roughness exponent via avalanche geometry, so the reported numbers have more support than a single method would give.\n\nSoft spots. The main one is the 2D long-range k_c. S_max is shown to diverge near k_c=0.11 for L=200,400,600,800, but there's no finite-size scaling collapse, and the statement that below k_c the cutoff decreases while system-size events appear is exactly the fingerprint of a rounded transition. Without a proper collapse in (k_c-k0)L^{1/ν}, a skeptical reader can't tell whether k_c is truly finite or drifts to zero. The F(w) oscillations that support coexistence are only shown for L=100 and 200, which isn't huge. Also, only Θ=0.5 is used; no scan, no code/data, and exponents have one-sigma errors without a fully described fitting procedure. These are not fatal, but they make k_c=0.11 a conditional number.\n\nI'm less worried than the stress-test note about the coexistence being entirely artificial: the bimodal distribution and the F(w) oscillations are qualitatively distinct from depinning and persist as L grows from 100 to 200. But the note is right that the quantitative k_c needs stronger backing.\n\nThis paper is for people working on depinning, friction, and avalanche statistics. It deserves a serious referee, and I'd recommend sending it out rather than desk rejecting. The referee should ask for a finite-size collapse, a Theta scan, and better data availability. I'd bring it to a reading group—it will generate good discussion about what counts as a transition in these driven disordered systems.","headline":"A genuinely new numerical result on non-overdamped avalanche statistics, but the 2D coexistence transition needs a finite-size collapse before I'd trust k_c≈0.11.","tokens_in":10757,"tokens_out":4713,"would_cite":true,"duration_ms":43625,"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":"Relaxation after each instability changes avalanche criticality, and in 2D long-range systems it creates a coexistence regime between pinned and flowing states.","keywords":["depinning transition","avalanche statistics","non-overdamped dynamics","slow dissipation","stick-slip coexistence","long-range elasticity","critical exponents","driven disordered systems"],"falsifier":"Measure avalanche size distributions and the global force $F(w)$ in a displacement-controlled simulation of a 2D long-range interface with $L>800$ and $\\Theta$ tuned below 0.5: if $S_{\\max}$ stops diverging at $k_c=0.11$, or if a pronounced bump appears in the fast-dissipation 1D case (where the paper predicts none), the claimed coexistence transition and dimensional dichotomy would be ruled out. The experimental counterpart is a quasi-2D frictional interface loaded by a spring of controllable stiffness: the predicted bimodal histogram and quasi-periodic force drops should appear only below a","tokens_in":9835,"feed_emoji":"⚡","tokens_out":12310,"duration_ms":111737,"temperature":0.7,"pith_summary":"This paper asks what happens to the avalanche statistics of driven disordered elastic interfaces when the overdamped assumption is dropped and the material keeps relaxing after each burst of instability. With a controlled-displacement model and a slow-dissipation relaxation phase (strength $\\Theta=0.5$), it claims the critical behavior leaves the standard depinning class. In two dimensions with long-range elastic interactions, a finite drive stiffness $k_c\\approx0.11$ marks the onset of a stick-slip regime in which pinned and flowing states coexist and some avalanches span the whole system. In one-dimensional long-range systems and in short-range systems in both dimensions, no coexistence appears, but the avalanche size distribution develops a pronounced bump at large sizes instead of a pure power law, caused by rare avalanches that expand ballistically. If right, experimental crack fronts and frictional interfaces should show these signatures, and the usual depinning exponents would not describe them.","feed_headline":"Slow relaxation turns avalanche power laws into a bump","feed_subtitle":"In 2D long-range systems, pinned and flowing states coexist; elsewhere, large avalanches expand ballistically.","key_machinery":"The mechanism is a three-step protocol—drive, avalanche, relaxation—on a lattice of $L^D$ blocks. In the relaxation phase, after a block slips, the stress it emitted is partly restored over time: $\\sigma_j \\to \\sigma_j + \\Theta(1-\\Phi(\\tau)) G_{ij}$ for neighbors, while the slipped site's stress increases back. Slow dissipation holds $\\Phi(\\tau)=1$ for the whole avalanche and lets it decay only after the avalanche stops, generating aftershocks. The paper's critical object is this slow-dissipation relaxation, with strength $\\Theta$; it converts the dynamics from gradient descent into one that can reactivate sites and promote coherent fronts. The other load-bearing ingredient is the long-range","core_discovery":"At the paper's center is a numerically established claim: turning on post-avalanche relaxation takes the system out of the overdamped depinning universality class, and the way it leaves depends on dimensionality and interaction range. The model is a $D$-dimensional interface of $L^D$ blocks, each block slipping when its local force exceeds a random threshold; after a slip, stress is redistributed by an elastic kernel $G_{ij}\\sim1/r^{D+\\alpha}$, and in the slow-dissipation relaxation phase a fraction $\\Theta$ of the redistributed stress is gradually restored only after the avalanche stops. For $\\alpha=1$ in $D=2$, the paper finds a critical stiffness $k_c\\simeq0.11$: for $k_0>k_c$ avalanches","pith_inferences":["Editorial extension: if the slow-dissipation rule captures rate-and-state friction, quasi-2D laboratory faults loaded by a spring of tunable stiffness should show the bimodal avalanche histogram and quasi-periodic force drops only below a critical stiffness; acoustic-emission catalogs are a ready place to look for the predicted bump.","The failed-synchronization picture suggests a concrete analogy with integrate-and-fire oscillator systems: the ballistic fronts are supercritical nuclei that would synchronize if the interaction range or dimensionality were sufficient, and one testable consequence is that front velocity and bump position scale with $\\Theta$ and $k_0$ in a way shared by both classes.","The authors expect fast relaxation to suppress synchronization in short-range and 1D long-range systems and to require a finite $\\Theta_c$ in 2D long-range; this predicts a control axis—relaxation time relative to avalanche duration—that should separate bump-free from bump-dominated statistics in the same material.","Transferred to the yielding of amorphous solids, the paper's argument for anisotropic long-range stress redistribution implies synchronization should localize into shear bands of dimension $D-1$ rather than the whole system, predicting anomalous ballistic fronts inside shear bands before global failure."],"forward_implications":["Force-controlled driving of a 2D long-range frictional interface should show hysteresis and a finite coexistence region between pinned and flowing states, because displacement control already yields system-spanning stick-slip events.","The avalanche cutoff scales with spring stiffness as $S_{\\max}\\sim k_0^{-\\sigma}$ with $\\sigma$ roughly 2 at $\\Theta=0.5$ in the long-range cases, so fitting overdamped depinning exponents to relaxation-affected data would misread the stiffness dependence and the transition location.","Large avalanches in the anomalous regime are identifiable by their ballistic expansion: the average distance from the hypocenter grows linearly in generation time, unlike the $t^{1/z}$ superdiffusive growth of depinning avalanches.","Since $\\tau$ and $\\sigma$ shift with relaxation strength $\\Theta$ and violate the usual scaling relations, the critical exponents of non-overdamped disordered systems are protocol-dependent rather than universal."],"supporting_citations":[{"why":"Supplies the overdamped depinning framework, critical exponents, and superdiffusive avalanche growth used as the baseline throughout the paper.","marker":"[8-10]"},{"why":"Provides the prediction that relaxation increases interface roughness, which the paper tests through structure-factor measurements.","marker":"[15]"},{"why":"Defines the fast-dissipation inertial limit of non-overdamped dynamics, contrasted with slow dissipation.","marker":"[16,18]"},{"why":"Establishes the slow-dissipation and aftershock relaxation protocol and its geophysical motivation via rate-and-state friction and viscoelasticity.","marker":"[22,23,30,31]"},{"why":"Shows that fully connected non-overdamped systems exhibit hysteresis under force control, the mean-field analogue of the 2D coexistence regime.","marker":"[18,20,21,25]"},{"why":"Demonstrates stick-slip dynamics with system-spanning instabilities under displacement control in mean-field models, the reference scenario for the finite-dimensional 2D result.","marker":"[22,27,28]"},{"why":"Supplies the synchronization theory used to interpret anomalous ballistic avalanches as failed synchronization attempts.","marker":"[29]"},{"why":"Reports related anomalous events near the cutoff in standard depinning, giving prior context for the ballistic bump.","marker":"[40]"}],"fun_headline_variants":["Relaxation turns power-law avalanches into a bump in driven systems","Slow relaxation reshapes avalanche statistics in elastic interfaces","Post-avalanche relaxation turns power laws into bumps","Anomalous avalanche bump from slow relaxation in disordered systems"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that the slow-dissipation relaxation phase—$\\Phi(\\tau)$ held at 1 for the whole avalanche and decaying only afterward, at strength $\\Theta=0.5$—faithfully represents real non-overdamped mechanisms such as inertia, viscoelasticity, or rate-and-state friction, and that the $k_c=0.11$ divergence in 2D is a thermodynamic transition rather than a finite-size effect at $L\\le800$.","fun_headline_variants_meta":{"raw":{"variants":["Relaxation turns power-law avalanches into a bump in driven systems","Slow relaxation reshapes avalanche statistics in elastic interfaces","Post-avalanche relaxation turns power laws into bumps","Anomalous avalanche bump from slow relaxation in disordered systems"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000926,"raw_usage":{"total_tokens":3771,"prompt_tokens":678,"completion_tokens":3093,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":422,"completion_tokens_details":{"reasoning_tokens":3025}},"tokens_in":422,"tokens_out":3093,"duration_ms":23146,"temperature":1.0,"reasoning_tokens":3025,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T20:56:34.231916+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure avalanche size distributions and the global force $F(w)$ in a displacement-controlled simulation of a 2D long-range interface with $L>800$ and $\\Theta$ tuned below 0.5: if $S_{\\max}$ stops diverging at $k_c=0.11$, or if a pronounced bump appears in the fast-dissipation 1D case (where the paper predicts none), the claimed coexistence transition and dimensional dichotomy would be ruled out. The experimental counterpart is a quasi-2D frictional interface loaded by a spring of controllable stiffness: the predicted bimodal histogram and quasi-periodic force drops should appear only below a","supporting_citations":[],"review_version":1}