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Hyperuniformity near jamming transition over a wide range of bidispersity

Duc T. Dam1,*, Takeshi Kawasaki1,2,3, Atsushi Ikeda4,5, and Kunimasa Miyazaki1,†

  • *Contact author: dam@r.phys.nagoya-u.ac.jp
  • †Contact author: miyazaki@r.phys.nagoya-u.ac.jp
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Phys. Rev. E 114, 015407 – Published 8 July, 2026

DOI: https://doi.org/10.1103/vclw-6h8s

Abstract

We numerically investigate hyperuniformity in two-dimensional jammed packings of frictionless bidisperse particles. Hyperuniformity is characterized by the suppression of density fluctuations at large length scales, and the structure factor vanishes at small wave numbers as S(q)∝qα, where α>0. Jammed packings are known to exhibit hyperuniformity over a wide-wave-number window, down to q*σ≈0.2, where σ is the particle diameter. In two dimensions, we find that the exponent α is approximately 0.6–0.7, in contrast to the reported value α=1 in three-dimensional systems. We then extend the analysis to a wide range of particle size ratios, from the monodisperse limit to highly disparate mixtures. To reduce unwanted spatial heterogeneities associated with polycrystalline domains at very large or very small size disparities, we employ a recently proposed method by Rissone et al. [Phys. Rev. Lett. 127, 038001 (2021)]. This method enables a more precise determination of α. We find that α remains nearly constant over the entire range of size ratios, except in the monodisperse case, where crystallization occurs.

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References (50)

  1. S. Torquato and F. H. Stillinger, Local density fluctuations, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003).
  2. S. Torquato, Hyperuniform states of matter, Phys. Rep. 745, 1 (2018).
  3. A. Gabrielli, M. Joyce, and F. S. Labini, Glass-like universe: Real-space correlation properties of standard cosmological models, Phys. Rev. D 65, 083523 (2002).
  4. Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem, Phys. Rev. E 89, 022721 (2014).
  5. A. Mayer, V. Balasubramanian, T. Mora, and A. M. Walczak, How a well-adapted immune system is organized, Proc. Natl. Acad. Sci. USA 112, 5950 (2015).
  6. G. Zhang, F. H. Stillinger, and S. Torquato, The perfect glass paradigm: Disordered hyperuniform glasses down to absolute zero, Sci. Rep. 6, 36963 (2016).
  7. A. Donev, S. Torquato, and F. H. Stillinger, Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings, Phys. Rev. E 71, 011105 (2005).
  8. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings, Phys. Rev. Lett. 106, 178001 (2011).
  9. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres, Phys. Rev. E 83, 051308 (2011).
  10. S. Atkinson, G. Zhang, A. B. Hopkins, and S. Torquato, Critical slowing down and hyperuniformity on approach to jamming, Phys. Rev. E 94, 012902 (2016).
  11. A. J. Liu and S. R. Nagel, Jamming is not just cool any more, Nature (London) 396, 21 (1998).
  12. C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E 68, 011306 (2003).
  13. M. van Hecke, Jamming of soft particles: Geometry, mechanics, scaling and isostaticity, J. Phys.: Condens. Matter 22, 033101 (2010).
  14. M. Wyart, On the rigidity of amorphous solids, Ann. Phys. Fr. 30, 1 (2005).
  15. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Fractal free energy landscapes in structural glasses, Nat. Commun. 5, 3725 (2014).
  16. S. Torquato, T. M. Truskett, and P. G. Debenedetti, Is random close packing of spheres well defined? Phys. Rev. Lett. 84, 2064 (2000).
  17. A. Donev, F. H. Stillinger, and S. Torquato, Unexpected density fluctuations in jammed disordered sphere packings, Phys. Rev. Lett. 95, 090604 (2005).
  18. L. Berthier, P. Chaudhuri, C. Coulais, O. Dauchot, and P. Sollich, Suppressed compressibility at large scale in jammed packings of size-disperse spheres, Phys. Rev. Lett. 106, 120601 (2011).
  19. Y. Wu, P. Olsson, and S. Teitel, Search for hyperuniformity in mechanically stable packings of frictionless disks above jamming, Phys. Rev. E 92, 052206 (2015).
  20. R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres, Phys. Rev. E 91, 012302 (2015).
  21. M. Ozawa, L. Berthier, and D. Coslovich, Exploring the jamming transition over a wide range of critical densities, SciPost Phys. 3, 027 (2017).
  22. A. T. Chieco, M. Zu, A. J. Liu, N. Xu, and D. J. Durian, Spectrum of structure for jammed and unjammed soft disks, Phys. Rev. E 98, 042606 (2018).
  23. A. Ikeda, L. Berthier, and G. Parisi, Large-scale structure of randomly jammed spheres, Phys. Rev. E 95, 052125 (2017).
  24. A. Ikeda and L. Berthier, Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids, Phys. Rev. E 92, 012309 (2015).
  25. N. Xu and E. S. C. Ching, Effects of particle-size ratio on jamming of binary mixtures at zero temperature, Soft Matter 6, 2944 (2010).
  26. M. Henkel, H. Hinrichsen, and S. Lübeck, Non-equilibrium Phase Transitions Volume 1: Absorbing Phase Transitions (Springer, Dordrecht, 2008).
  27. S. Wilken, R. E. Guerra, D. Levine, and P. M. Chaikin, Random close packing as a dynamical phase transition, Phys. Rev. Lett. 127, 038002 (2021).
  28. S. Wilken, A. Z. Guo, D. Levine, and P. M. Chaikin, Dynamical approach to the jamming problem, Phys. Rev. Lett. 131, 238202 (2023).
  29. H. Matsuyama, M. Toyoda, T. Kurahashi, A. Ikeda, T. Kawasaki, and K. Miyazaki, Geometrical properties of mechanically annealed systems near the jamming transition, Eur. Phys. J. E 44, 133 (2021).
  30. D. J. Koeze, D. Vågberg, B. B. T. Tjoa, and B. P. Tighe, Mapping the jamming transition of bidisperse mixtures, Europhys. Lett. 113, 54001 (2016).
  31. K. Saitoh and B. P. Tighe, Jamming transition and normal modes of polydispersed soft particle packing, Soft Matter 21, 1263 (2025).
  32. J. Ricouvier, R. Pierrat, R. Carminati, P. Tabeling, and P. Yazhgur, Optimizing hyperuniformity in self-assembled bidisperse emulsions, Phys. Rev. Lett. 119, 208001 (2017).
  33. C. P. Goodrich, A. J. Liu, and S. R. Nagel, Solids between the mechanical extremes of order and disorder, Nat. Phys. 10, 578 (2014).
  34. T. Kawasaki and K. Miyazaki, Unified understanding of nonlinear rheology near the jamming transition point, Phys. Rev. Lett. 132, 268201 (2024).
  35. D. Pan, Y. Wang, H. Yoshino, J. Zhang, and Y. Jin, A review on shear jamming, Phys. Rep. 1038, 1 (2023).
  36. H. Tong, P. Tan, and N. Xu, From crystals to disordered crystals: A hidden order-disorder transition, Sci. Rep. 5, 15378 (2015).
  37. H. Ikeda, Jamming and replica symmetry breaking of weakly disordered crystals, Phys. Rev. Res. 2, 033220 (2020).
  38. C. E. Maher, Y. Jiao, and S. Torquato, Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions, Phys. Rev. E 108, 064602 (2023).
  39. P. Rissone, E. I. Corwin, and G. Parisi, Long-range anomalous decay of the correlation in jammed packings, Phys. Rev. Lett. 127, 038001 (2021).
  40. E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett. 97, 170201 (2006).
  41. T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Jamming transition in granular systems, Phys. Rev. Lett. 98, 058001 (2007).
  42. H. Tong and H. Tanaka, Structural order as a genuine control parameter of dynamics in simple glass formers, Nat. Commun. 10, 5596 (2019).
  43. C. P. Goodrich, A. J. Liu, and S. R. Nagel, Finite-size scaling at the jamming transition, Phys. Rev. Lett. 109, 095704 (2012).
  44. K. Binder, M. Nauenberg, V. Privman, and A. P. Young, Finite-size tests of hyperscaling, Phys. Rev. B 31, 1498 (1985).
  45. M. Wittmann and A. P. Young, Finite-size scaling above the upper critical dimension, Phys. Rev. E 90, 062137 (2014).
  46. C. E. Maher and S. Torquato, Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks, Phys. Rev. E 110, 064605 (2024).
  47. H.-D. Wang, B. Wang, Q.-L. Lei, and Y.-Q. Ma, Anomalous criticality of absorbing state transition toward jamming, arXiv:2510.06641v5.
  48. Y. Wang, Z. Qian, H. Tong, and H. Tanaka, Hyperuniform disordered solids with crystallike stability, Nat. Commun. 16, 1398 (2025).
  49. D. Hexner, A. J. Liu, and S. R. Nagel, Two diverging length scales in the structure of jammed packings, Phys. Rev. Lett. 121, 115501 (2018).
  50. D. Hexner, P. Urbani, and F. Zamponi, Can a large packing be assembled from smaller ones? Phys. Rev. Lett. 123, 068003 (2019).

Outline

Information

Phys. Rev. E 114, 015407– Published 8 July, 2026
  • Received 30 July 2025
  • Revised 9 April 2026
  • Accepted 26 May 2026
Article part of CHORUS
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