- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Thermal Avalanches Drive Logarithmic Creep in Disordered Media

Daniel J. Korchinski1,*, Dor Shohat2,3,*, Yoav Lahini2,3, and Matthieu Wyart4

  • *These authors contributed equally to this work.
PDF

Phys. Rev. X 15, 031024 – Published 23 July, 2025

DOI: https://doi.org/10.1103/x7rr-vxnr

Abstract

Disordered materials under an imposed forcing can display creep and aging effects, accompanied by intermittent, spatially heterogeneous dynamics. We propose a testable microscopic description of these phenomena, based on the notion that as the system ages, the density of local barriers that enable relaxation displays a slowly evolving gap. As a result, the relaxation dynamics is dominated by the activation of the lowest, extremal tail of the distribution. This framework predicts logarithmic creep, as well as correlated bursts of slow activated rearrangements, or “thermal avalanches,” whose size grows logarithmically with their duration. The time interval between events within avalanches obeys a universal power-law distribution, with a cutoff that is simply proportional to the age of the system. We show that these predictions hold both in numerical models of amorphous solids, as well as in experiments with thin crumpled sheets. This analysis suggests that the heterogeneous dynamics occurring during logarithmic creep is related to other phenomena, including dynamical heterogeneities characterizing the glass transition.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Many disordered materials—like glass, polymers, crumpled sheets, and even geological systems—gradually deform over time under constant stress, in a process known as creep. Although this slow deformation is often accompanied by sudden internal rearrangements, there has not been a theory linking microscopic activity to the overall material behavior. In this study, we propose a simple theory connecting creep to the evolution of the material’s energy landscape: As the material deforms, it progressively uses up easy-to-reach rearrangements, forcing it to undergo harder, slower ones over time. This results in a slowdown of the deformation process and leads to rare, collective events called thermal avalanches.

To support our theory, we study two very different systems: computer simulations of an amorphous solid and experiments with crumpled Mylar sheets. Surprisingly, both systems show similar behavior: Deformation occurs through rare, slow, and correlated rearrangements. These thermal avalanches grow larger the longer they last, and the time between them follows universal patterns based only on how much time has passed since the material was loaded. This suggests that a shared microscopic mechanism governs the slow dynamics of many different disordered systems.

Our findings help explain how materials age and fail over time, by connecting small-scale internal activity to long-term deformation. This theory can apply broadly—from understanding how sand or polymers behave under stress, to modeling the slow buildup of stress in earthquake faults. It also offers insights into other complex processes like the glass transition, where systems show similar signs of aging and slow, bursty internal changes.

Article Text

References (90)

  1. K. Matan, R. B. Williams, T. A. Witten, and S. R. Nagel, Crumpling a thin sheet, Phys. Rev. Lett. 88, 076101 (2002).
  2. Y. Lahini, O. Gottesman, A. Amir, and S. M. Rubinstein, Nonmonotonic aging and memory retention in disordered mechanical systems, Phys. Rev. Lett. 118, 085501 (2017).
  3. Y. Lahini, S. M. Rubinstein, and A. Amir, Crackling noise during slow relaxations in crumpled sheets, Phys. Rev. Lett. 130, 258201 (2023).
  4. D. Shohat, Y. Friedman, and Y. Lahini, Logarithmic aging via instability cascades in disordered systems, Nat. Phys. 19, 1890 (2023).
  5. D. Shohat, D. Hexner, and Y. Lahini, Memory from coupled instabilities in unfolded crumpled sheets, Proc. Natl. Acad. Sci. U.S.A. 119, e2200028119 (2022).
  6. D. Shohat and Y. Lahini, Dissipation indicates memory formation in driven disordered systems, Phys. Rev. Lett. 130, 048202 (2023).
  7. R. Woltjer, A. Hamada, and E. Takeda, Time dependence of p-MOSFET hot-carrier degradation measured and interpreted consistently over ten orders of magnitude, IEEE Trans. Electron Devices 40, 392 (1993).
  8. A. Vaknin, Z. Ovadyahu, and M. Pollak, Aging effects in an Anderson insulator, Phys. Rev. Lett. 84, 3402 (2000).
  9. T. Grenet, J. Delahaye, M. Sabra, and F. Gay, Anomalous electric-field effect and glassy behaviour in granular aluminium thin films: Electron glass?, Eur. Phys. J. B 56, 183 (2007).
  10. J. H. Dieterich and B. D. Kilgore, Direct observation of frictional contacts: New insights for state-dependent properties, Pure Appl. Geophys. 143, 283 (1994).
  11. O. Ben-David, S. M. Rubinstein, and J. Fineberg, Slip-stick and the evolution of frictional strength, Nature (London) 463, 76 (2010).
  12. S. M. Rubinstein, G. Cohen, and J. Fineberg, Contact area measurements reveal loading-history dependence of static friction, Phys. Rev. Lett. 96, 256103 (2006).
  13. P. Duval, Anelastic behaviour of polycrystalline ice, J. Glaciol. 21, 621 (1978).
  14. M. Nicolas, P. Duru, and O. Pouliquen, Compaction of a granular material under cyclic shear, Eur. Phys. J. E 3, 309 (2000).
  15. K. A. Murphy, J. W. Kruppe, and H. M. Jaeger, Memory in nonmonotonic stress relaxation of a granular system, Phys. Rev. Lett. 124, 168002 (2020).
  16. E. Ben-Naim, J. B. Knight, E. R. Nowak, H. M. Jaeger, and S. R. Nagel, Slow relaxation in granular compaction, Physica (Amsterdam) 123D, 380 (1998).
  17. J. B. Knight, C. G. Fandrich, C. N. Lau, H. M. Jaeger, and S. R. Nagel, Density relaxation in a vibrated granular material, Phys. Rev. E 51, 3957 (1995).
  18. T. Boutreux and P. G. de Gennes, Compaction of granular mixtures: A free volume model, Physica (Amsterdam) 244A, 59 (1997).
  19. V. H. Purrello, J. L. Iguain, A. B. Kolton, and E. A. Jagla, Creep and thermal rounding close to the elastic depinning threshold, Phys. Rev. E 96, 022112 (2017).
  20. A. B. Kolton, A. Rosso, and T. Giamarchi, Creep motion of an elastic string in a random potential, Phys. Rev. Lett. 94, 047002 (2005).
  21. A. Cottrell, The time laws of creep, J. Mech. Phys. Solids 1, 53 (1952).
  22. D. Bouttes and D. Vandembroucq, Creep of amorphous materials: A mesoscopic model, AIP Conf. Proc. 1518, 481 (2013).
  23. M. Popović, T. W. J. de Geus, W. Ji, A. Rosso, and M. Wyart, Scaling description of creep flow in amorphous solids, Phys. Rev. Lett. 129, 208001 (2022).
  24. V. V. Vasisht, P. Chaudhuri, and K. Martens, Residual stress in athermal soft disordered solids: Insights from microscopic and mesoscale models, Soft Matter 18, 6426 (2022).
  25. C. Liu, S. Dutta, P. Chaudhuri, and K. Martens, Elastoplastic approach based on microscopic insights for the steady state and transient dynamics of sheared disordered solids, Phys. Rev. Lett. 126, 138005 (2021).
  26. R. Cabriolu, J. Horbach, P. Chaudhuri, and K. Martens, Precursors of fluidisation in the creep response of a soft glass, Soft Matter 15, 415 (2019).
  27. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Crackling noise, Nature (London) 410, 242 (2001).
  28. E. K. Salje and K. A. Dahmen, Crackling noise in disordered materials, Annu. Rev. Condens. Matter Phys. 5, 233 (2014).
  29. A. Rosso, J. P. Sethna, and M. Wyart, Avalanches and deformation in glasses and disordered systems, arXiv:2208.04090.
  30. M. Kardar, Nonequilibrium dynamics of interfaces and lines, Phys. Rep. 301, 85 (1998).
  31. D. S. Fisher, Collective transport in random media: From superconductors to earthquakes, Phys. Rep. 301, 113 (1998).
  32. P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59, 381 (1987).
  33. P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality, Phys. Rev. A 38, 364 (1988).
  34. D. L. Turcotte and B. D. Malamud, Landslides, forest fires, and earthquakes: Examples of self-organized critical behavior, Physica (Amsterdam) 340A, 580 (2004).
  35. P. Chauve, T. Giamarchi, and P. Le Doussal, Creep and depinning in disordered media, Phys. Rev. B 62, 6241 (2000).
  36. T. W. De Geus, A. Rosso, and M. Wyart, Dynamical heterogeneities of thermal creep in pinned interfaces, Phys. Rev. E 111, L013503 (2025).
  37. A. Tahaei, G. Biroli, M. Ozawa, M. Popović, and M. Wyart, Scaling description of dynamical heterogeneity and avalanches of relaxation in glass-forming liquids, Phys. Rev. X 13, 031034 (2023).
  38. G. Durin, V. M. Schimmenti, M. Baiesi, A. Casiraghi, A. Magni, L. Herrera-Diez, D. Ravelosona, L. Foini, and A. Rosso, Earthquakelike dynamics in ultrathin magnetic films, Phys. Rev. B 110, L020405 (2024).
  39. E. Ferrero, L. Foini, T. Giamarchi, A. Kolton, and A. Rosso, Creep motion of elastic interfaces driven in a disordered landscape, Annu. Rev. Condens. Matter Phys. 12, 111 (2021).
  40. Y. Takaha, H. Mizuno, and A. Ikeda, Avalanche criticality emerges by thermal fluctuation in a quiescent glass, arXiv:2409.15775.
  41. W. Kob, C. Donati, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Dynamical heterogeneities in a supercooled Lennard-Jones liquid, Phys. Rev. Lett. 79, 2827 (1997).
  42. R. Yamamoto and A. Onuki, Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion, Phys. Rev. E 58, 3515 (1998).
  43. C. Dalle-Ferrier, C. Thibierge, C. Alba-Simionesco, L. Berthier, G. Biroli, J.-P. Bouchaud, F. Ladieu, D. L’Hôte, and G. Tarjus, Spatial correlations in the dynamics of glassforming liquids: Experimental determination of their temperature dependence, Phys. Rev. E 76, 041510 (2007).
  44. S. Karmakar, C. Dasgupta, and S. Sastry, Growing length scales and their relation to timescales in glass-forming liquids, Annu. Rev. Condens. Matter Phys. 5, 255 (2014).
  45. M. Ozawa and G. Biroli, Elasticity, facilitation, and dynamic heterogeneity in glass-forming liquids, Phys. Rev. Lett. 130, 138201 (2023).
  46. B. Guiselin, C. Scalliet, and L. Berthier, Microscopic origin of excess wings in relaxation spectra of deeply supercooled liquids, Nat. Phys. 18, 468 (2022).
  47. E. E. Ferrero, L. Foini, T. Giamarchi, A. B. Kolton, and A. Rosso, Spatiotemporal patterns in ultraslow domain wall creep dynamics, Phys. Rev. Lett. 118, 147208 (2017).
  48. C. Gavazzoni, C. Brito, and M. Wyart, Testing theories of the glass transition with the same liquid but many kinetic rules, Phys. Rev. Lett. 132, 248201 (2024).
  49. D. Korchinski and J. Rottler, Dynamic phase diagram of plastically deformed amorphous solids at finite temperature, Phys. Rev. E 106, 034103 (2022).
  50. D. J. Korchinski and J. Rottler, Thermally activated intermittent flow in amorphous solids, Soft Matter 20, 7891 (2024).
  51. J. Chattoraj, C. Caroli, and A. Lemaître, Universal additive effect of temperature on the rheology of amorphous solids, Phys. Rev. Lett. 105, 266001 (2010).
  52. N. Xu, A. J. Liu, and S. R. Nagel, Instabilities of jammed packings of frictionless spheres under load, Phys. Rev. Lett. 119, 215502 (2017).
  53. A. A. Middleton, Thermal rounding of the charge-density-wave depinning transition, Phys. Rev. B 45, 9465 (1992).
  54. D. Xu, S. Zhang, A. J. Liu, S. R. Nagel, and N. Xu, Discontinuous instabilities in disordered solids, Proc. Natl. Acad. Sci. U.S.A. 120, e2304974120 (2023).
  55. G. Picard, A. Ajdari, F. Lequeux, and L. Bocquet, Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids, Eur. Phys. J. E 15, 371 (2004).
  56. A. S. Argon, V. V. Bulatov, P. H. Mott, and U. W. Suter, Plastic deformation in glassy polymers by atomistic and mesoscopic simulations, J. Rheol. 39, 377 (1995).
  57. A. Heuer, Exploring the potential energy landscape of glass-forming systems: From inherent structures via metabasins to macroscopic transport, J. Phys. Condens. Matter 20, 373101 (2008).
  58. E. E. Ferrero, K. Martens, and J.-L. Barrat, Relaxation in yield stress systems through elastically interacting activated events, Phys. Rev. Lett. 113, 248301 (2014).
  59. M. Popović, T. W. J. de Geus, W. Ji, and M. Wyart, Thermally activated flow in models of amorphous solids, Phys. Rev. E 104, 025010 (2021).
  60. A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat, Deformation and flow of amorphous solids: Insights from elastoplastic models, Rev. Mod. Phys. 90, 045006 (2018).
  61. D. Shohat, Y. Lahini, and D. Hexner, Emergent marginality in frustrated multistable networks, J. Chem. Phys. 162, 114505 (2025).
  62. M. Paczuski, S. Maslov, and P. Bak, Avalanche dynamics in evolution, growth, and depinning models, Phys. Rev. E 53, 414 (1996).
  63. H. M. Jaeger, C. H. Liu, and S. R. Nagel, Relaxation at the angle of repose, Phys. Rev. Lett. 62, 40 (1989).
  64. O. Wyatt, Transient creep in pure metals, Proc. Phys. Soc. London Sect. B 66, 459 (1953).
  65. J. Andrejevic, L. M. Lee, S. M. Rubinstein, and C. H. Rycroft, A model for the fragmentation kinetics of crumpled thin sheets, Nat. Commun. 12, 1470 (2021).
  66. E. M. Kramer and A. E. Lobkovsky, Universal power law in the noise from a crumpled elastic sheet, Phys. Rev. E 53, 1465 (1996).
  67. T. Jules, F. Lechenault, and M. Adda-Bedia, Plasticity and aging of folded elastic sheets, Phys. Rev. E 102, 033005 (2020).
  68. C. E. Maloney and D. J. Lacks, Energy barrier scalings in driven systems, Phys. Rev. E 73, 061106 (2006).
  69. J. Lin, E. Lerner, A. Rosso, and M. Wyart, Scaling description of the yielding transition in soft amorphous solids at zero temperature, Proc. Natl. Acad. Sci. U.S.A. 111, 14382 (2014).
  70. D. J. Korchinski, J. G. Orlandi, S.-W. Son, and J. Davidsen, Criticality in spreading processes without timescale separation and the critical brain hypothesis, Phys. Rev. X 11, 021059 (2021).
  71. T. Jocteur, S. Figueiredo, K. Martens, E. Bertin, and R. Mari, Yielding is an absorbing phase transition with vanishing critical fluctuations, Phys. Rev. Lett. 132, 268203 (2024).

  72. A skeptical experimentalist might be reassured to note that T=10−2 is sufficient to reduce these timescales to experimentally accessible ones of order Δt≈106.

  73. J. Lin and M. Wyart, Mean-field description of plastic flow in amorphous solids, Phys. Rev. X 6, 011005 (2016).
  74. M. Müller and M. Wyart, Marginal stability in structural, spin, and electron glasses, Annu. Rev. Condens. Matter Phys. 6, 177 (2015).
  75. H. Bauke, Parameter estimation for power-law distributions by maximum likelihood methods, Eur. Phys. J. B 58, 167 (2007).
  76. A. S. Balankin, Rolando Cortes Montes de Oca, and D. S. Ochoa, Intrinsically anomalous self-similarity of randomly folded matter, Phys. Rev. E 76, 032101 (2007).

  77. For simulations, we use k=1 to reduce error, but for experiments, we use the higher moment k=2 because the p(s) distribution has an exponent τ>2 for small t0/tg.

  78. V. B. Nguyen, T. Darnige, A. Bruand, and E. Clement, Creep and fluidity of a real granular packing near jamming, Phys. Rev. Lett. 107, 138303 (2011).
  79. K. Farain and D. Bonn, Thermal properties of athermal granular materials, Phys. Rev. Lett. 133, 028203 (2024).
  80. J. P. Bouchaud, Weak ergodicity breaking and aging in disordered systems, J. Phys. I (France) 2, 1705 (1992).
  81. A. Amir, Y. Oreg, and Y. Imry, On relaxations and aging of various glasses, Proc. Natl. Acad. Sci. U.S.A. 109, 1850 (2012).
  82. S. Boettcher and P. A. Gago, Instability cascades in disordered systems indicate record dynamics, arXiv:2312.12254.
  83. A. Kovacs, Glass transition in amorphous polymers: A phenomenological study, Adv. Polym. Sci. 3, 394 (1963).
  84. B. Riechers, L. A. Roed, S. Mehri, T. S. Ingebrigtsen, T. Hecksher, J. C. Dyre, and K. Niss, Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time, Sci. Adv. 8, eabl9809 (2022).
  85. C. Josserand, A. V. Tkachenko, D. M. Mueth, and H. M. Jaeger, Memory effects in granular materials, Phys. Rev. Lett. 85, 3632 (2000).
  86. S. Dillavou and S. M. Rubinstein, Nonmonotonic aging and memory in a frictional interface, Phys. Rev. Lett. 120, 224101 (2018).
  87. C. Scalliet and L. Berthier, Rejuvenation and memory effects in a structural glass, Phys. Rev. Lett. 122, 255502 (2019).
  88. M. Ozawa, L. Berthier, G. Biroli, A. Rosso, and G. Tarjus, Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl. Acad. Sci. U.S.A. 115, 6656 (2018).
  89. M. Popović, T. W. J. de Geus, and M. Wyart, Elastoplastic description of sudden failure in athermal amorphous materials during quasistatic loading, Phys. Rev. E 98, 040901(R) (2018).
  90. V. Rubino, N. Lapusta, and A. Rosakis, Intermittent lab earthquakes in dynamically weakening fault gouge, Nature (London) 606, 922 (2022).

Outline

Information

Phys. Rev. X 15, 031024– Published 23 July, 2025
  • Received 27 September 2024
  • Accepted 9 June 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation