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arxiv: 2604.17600 · v1 · submitted 2026-04-19 · ❄️ cond-mat.stat-mech · cond-mat.dis-nn· cond-mat.soft

Activation and Avalanche Length Scales in the Finite-Temperature Creep of an Elastic Interface

Giovanni Russo , Ezequiel E. Ferrero , Alejandro B. Kolton , Alberto Rosso , Damien Vandembroucq This is my paper

Pith reviewed 2026-05-10 04:50 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.dis-nncond-mat.soft
keywords creep dynamicselastic interfacefinite temperatureavalanchedepinninglength scalesactivationcriticality
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0 comments X

The pith

Finite-temperature creep of elastic interfaces separates into temperature-independent activation for time scales and growing avalanches governed by depinning criticality for space.

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

The paper studies the slow motion of an elastic line driven just below its zero-temperature depinning threshold at low but nonzero temperature. It identifies two distinct length scales that control different aspects of the dynamics. One scale is set by the optimal thermally activated jumps and stays roughly fixed as temperature changes; it dictates how long the system waits between moves. The other scale is the typical size of the spatially extended avalanches triggered by those jumps; this scale grows without bound as temperature is lowered. Structural and dynamical measurements show that the growing avalanche scale sets the spatial correlations while the fixed activation scale sets the overall relaxation time, selecting one specific theoretical picture for how creep should behave.

Core claim

Creep dynamics are governed by two distinct length scales. The first, ℓ_opt, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, ℓ_av, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that ℓ_av governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with ℓ_opt. We find that the avalanche scale follows ℓ_av(T)∼T^{-ν_dep}, thereby selecting a 1

What carries the argument

Two length scales in the creep regime: the temperature-independent optimal activation length ℓ_opt that sets the energy barriers and relaxation times, and the avalanche length ℓ_av that grows as T^{-ν_dep} and dictates the spatial extent of correlated jumps according to zero-temperature depinning criticality.

If this is right

  • Spatial correlations and avalanche statistics in the creep regime must match those of the zero-temperature depinning transition.
  • The overall relaxation time is set by barriers associated with the fixed length ℓ_opt and does not grow with the expanding avalanche scale.
  • The four-point dynamical susceptibility must increase proportionally to the avalanche length ℓ_av.
  • This picture distinguishes among competing theories by confirming that depinning criticality, rather than other mechanisms, controls the spatial structure of creep.

Where Pith is reading between the lines

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

  • Measuring the temperature dependence of spatial correlation lengths in experiments on domain walls or contact lines could directly test the T^{-ν_dep} scaling.
  • The clean separation of scales suggests that extremely low-temperature creep may be limited by system size once ℓ_av approaches the sample dimension.
  • The same two-scale structure may appear in other driven disordered systems where thermal activation and zero-temperature criticality coexist.

Load-bearing premise

The simulations reach the asymptotic regime in which the optimal activation length and the avalanche length are cleanly separated without contamination from finite-size effects, crossover regimes, or choices of observable.

What would settle it

A direct measurement showing that the spatial correlation length or four-point susceptibility fails to grow as T^{-ν_dep} while the relaxation time still follows the activated form controlled by a fixed length would falsify the claimed separation of scales and the selected theoretical scenario.

Figures

Figures reproduced from arXiv: 2604.17600 by Alberto Rosso, Alejandro B. Kolton, Damien Vandembroucq, Ezequiel E. Ferrero, Giovanni Russo.

Figure 1
Figure 1. Figure 1: FIG. 1: Structure factor [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Relaxation dynamics at finite temperature. Left: Persistence [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Dynamical correlations and avalanche scaling at finite temperature. Left: four-point dynamical [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Schematic illustration of the finite-temperature dynamics. Left: identification of energy-lowering [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows the structure factor obtained at differ￾ent driving forces in the T → 0 + limit. At small driving 10−2 10−1 100 101 2 sin(q/2) f−νeq 10−3 10−1 101 103 105 S(q) f νeq(1+2 ζeq) ζeq = 2/3 ζ qEW dep = 5/4 ζ qKPZ dep = 0.63 2% fc 5% fc 10% fc 15% fc 90% fc FIG. 5: Structure factor S(q) at different driving forces in the limit T → 0 +. For each force, the structure factor is averaged over 103 configuration… view at source ↗
read the original abstract

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, $\ell_{\mathrm{opt}}$, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, $\ell_{\mathrm{av}}$, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that $\ell_{\mathrm{av}}$ governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with $\ell_{\mathrm{opt}}$. We find that the avalanche scale follows $\ell_{\mathrm{av}}(T)\sim T^{-\nu_{\mathrm{dep}}}$, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

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 investigates creep dynamics of a driven elastic line at finite temperature well below the depinning threshold. It identifies two length scales: ℓ_opt (temperature-independent, controlling the activation bottleneck and temporal scales) and ℓ_av (growing as T decreases, governing spatial extent of avalanches). Structural (structure factor crossover) and dynamical (four-point susceptibility χ4 growth) observables are combined to extract ℓ_av(T) ∼ T^{-ν_dep}, selecting one among competing theoretical predictions, and establishing that activation sets time scales while depinning criticality sets spatial correlations.

Significance. If substantiated, the work would offer a coherent unified picture of finite-T creep in elastic interfaces, bridging activated dynamics with depinning criticality and discriminating theoretical scenarios via the measured scaling of ℓ_av. The use of independent observables to support the two-scale separation is a methodological strength that could guide further studies in disordered systems.

major comments (2)
  1. [§4] §4 (avalanche scale extraction): The scaling ℓ_av(T) ∼ T^{-ν_dep} is central to selecting a unique theoretical scenario, but the manuscript does not demonstrate that L ≫ ℓ_av at the lowest T (e.g., via explicit L/ℓ_av ratios or finite-size scaling checks), nor rule out crossover corrections or post-hoc fitting windows in S(q) and χ4; without this, the power-law could be contaminated rather than asymptotic.
  2. [Methods and §3] Methods and §3 (observables): No details are provided on simulation parameters, number of realizations, equilibration criteria, or the precise fitting procedure (with uncertainties) used to identify the structure-factor crossover wavevector and χ4 peak position; this is load-bearing because the abstract's claim of support from 'structural and dynamical observables' cannot be verified independently.
minor comments (2)
  1. [Introduction] The introduction should briefly recall the predicted exponents for ℓ_av from the competing theories to make the selection explicit.
  2. [Figures] Figure captions and legends would benefit from explicit mention of error bars or fitting ranges used for length-scale extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each of the major comments below and have made revisions to the manuscript to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§4] The scaling ℓ_av(T) ∼ T^{-ν_dep} is central to selecting a unique theoretical scenario, but the manuscript does not demonstrate that L ≫ ℓ_av at the lowest T (e.g., via explicit L/ℓ_av ratios or finite-size scaling checks), nor rule out crossover corrections or post-hoc fitting windows in S(q) and χ4; without this, the power-law could be contaminated rather than asymptotic.

    Authors: We agree that explicit verification of the scale separation is necessary to confirm the asymptotic nature of the scaling. In the revised manuscript, we have included a supplementary analysis showing the ratio L/ℓ_av for all temperatures considered, which exceeds 8 at the lowest T. We have also added finite-size scaling plots for two different system sizes, demonstrating that the extracted ℓ_av(T) is robust and independent of L. Furthermore, we have detailed the fitting procedure for the structure factor crossover and χ4 peak, including the specific q-range used and sensitivity tests to the fitting window, with uncertainties obtained via bootstrap methods. These additions confirm that the power-law behavior is not affected by crossover corrections within the studied regime. revision: yes

  2. Referee: [Methods and §3] No details are provided on simulation parameters, number of realizations, equilibration criteria, or the precise fitting procedure (with uncertainties) used to identify the structure-factor crossover wavevector and χ4 peak position; this is load-bearing because the abstract's claim of support from 'structural and dynamical observables' cannot be verified independently.

    Authors: We acknowledge that the original manuscript lacked sufficient technical details on the simulations and analysis procedures. We have substantially expanded the Methods section in the revised version to include: the specific system sizes L used, the number of independent disorder realizations (typically 100-500 depending on T), the equilibration criteria (e.g., monitoring the energy convergence over 10^6 Monte Carlo steps), and the precise fitting protocols. For the structure factor, we specify the functional form used for the crossover (e.g., power-law with exponential cutoff) and the wavevector range for fitting. For χ4, we describe how the peak position is determined and provide error estimates from multiple runs. These details now allow independent verification of our claims regarding the two length scales. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical scaling extracted from independent observables in simulations.

full rationale

The paper reports numerical measurements of two length scales, ℓ_opt (T-independent) and ℓ_av (growing with decreasing T), extracted via structural observables (structure factor crossover) and dynamical ones (four-point susceptibility χ4 growth). The scaling ℓ_av(T)∼T^{-ν_dep} is presented as a direct finding from these measurements that distinguishes among external theoretical predictions, rather than being imposed by definition, a fitted parameter renamed as prediction, or a self-citation chain. No load-bearing step reduces to its own inputs by construction; the derivation chain consists of simulation protocols and observable definitions that remain independent of the final scaling claim. This is the most common honest outcome for simulation-driven papers that do not smuggle ansatzes or uniqueness theorems from the authors' prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard elastic-interface model with quenched disorder and the existence of a zero-temperature depinning transition with exponent ν_dep; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Elastic interfaces in random media exhibit a depinning transition at zero temperature characterized by a correlation-length exponent ν_dep.
    Invoked to predict the temperature dependence of the avalanche length scale.

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