Gardner transition coincides with the emergence of jamming scalings in hard spheres and disks (2410.23797v1)
Abstract: The Gardner transition in structural glasses is characterized by full-replica symmetry breaking of the free-energy landscape and the onset of anomalous aging dynamics due to marginal stability. Here we show that this transition also has a structural signature in finite-dimensional glasses consisting of hard spheres and disks. By analyzing the distribution of inter-particle gaps in the simulated static configurations at different pressures, we find that the Gardner transition coincides with the emergence of two well-known jamming scalings in the gap distribution, which enables the extraction of a structural order parameter. The jamming scalings reflect a compressible effective force network formed by contact and quasi-contact gaps, while non-contact gaps that do not participate in the effective force network are incompressible. Our results suggest that the Gardner transition in hard-particle glasses is a precursor of the jamming transition. The proposed structural signature and order parameter provide a convenient approach to detecting the Gardner transition in future granular experiments.
- D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Physical review letters 35, 1792 (1975).
- G. Parisi, Infinite number of order parameters for spin-glasses, Physical Review Letters 43, 1754 (1979).
- G. Parisi, A sequence of approximated solutions to the sk model for spin glasses, Journal of Physics A: Mathematical and General 13, L115 (1980).
- M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications, Vol. 9 (World Scientific Publishing Company, 1987).
- G. Parisi, Nobel lecture: Multiple equilibria, Reviews of Modern Physics 95, 030501 (2023).
- F. Guerra, Sum rules for the free energy in the mean field spin glass model, Fields Institute Communications 30 (2001).
- F. Guerra, Broken replica symmetry bounds in the mean field spin glass model, Communications in mathematical physics 233, 1 (2003).
- M. Talagrand, The parisi formula, Annals of mathematics , 221 (2006).
- D. Panchenko, The parisi ultrametricity conjecture, Annals of Mathematics , 383 (2013).
- E. Gardner, Spin glasses with p-spin interactions, Nuclear Physics B 257, 747 (1985).
- P. Urbani, Y. Jin, and H. Yoshino, The gardner glass, in Spin Glass Theory and Far Beyond: Replica Symmetry Breaking After 40 Years (World Scientific, 2023) pp. 219–238.
- G. Parisi, P. Urbani, and F. Zamponi, Theory of simple glasses: exact solutions in infinite dimensions (Cambridge University Press, 2020).
- Y. Jin and H. Yoshino, Exploring the complex free-energy landscape of the simplest glass by rheology, Nature communications 8, 14935 (2017).
- Q. Liao and L. Berthier, Hierarchical landscape of hard disk glasses, Physical Review X 9, 011049 (2019).
- A. Seguin and O. Dauchot, Experimental evidence of the gardner phase in a granular glass, Physical review letters 117, 228001 (2016).
- L. Kool, P. Charbonneau, and K. E. Daniels, Gardner-like crossover from variable to persistent force contacts in granular crystals, Physical Review E 106, 054901 (2022).
- H. Xiao, A. J. Liu, and D. J. Durian, Probing gardner physics in an active quasithermal pressure-controlled granular system of noncircular particles, Physical Review Letters 128, 248001 (2022).
- C. Scalliet, L. Berthier, and F. Zamponi, Absence of marginal stability in a structural glass, Physical review letters 119, 205501 (2017).
- C. Scalliet, L. Berthier, and F. Zamponi, Marginally stable phases in mean-field structural glasses, Physical Review E 99, 012107 (2019).
- W. G. Hoover, N. E. Hoover, and K. Hanson, Exact hard-disk free volumes, The Journal of Chemical Physics 70, 1837 (1979).
- B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk packings, Journal of statistical Physics 60, 561 (1990).
- Z. Salsburg and W. Wood, Equation of state of classical hard spheres at high density, The Journal of Chemical Physics 37, 798 (1962).
- E. Lerner, G. Düring, and M. Wyart, Low-energy non-linear excitations in sphere packings, Soft Matter 9, 8252 (2013).
- Y. Jin and H. Yoshino, A jamming plane of sphere packings, Proceedings of the National Academy of Sciences 118, e2021794118 (2021).
- C. Brito and M. Wyart, On the rigidity of a hard-sphere glass near random close packing, Europhysics Letters 76, 149 (2006).
- Y.-W. Li and M. P. Ciamarra, Attraction tames two-dimensional melting: From continuous to discontinuous transitions, Phys. Rev. Lett. 124, 218002 (2020).
- C. H. Rycroft, VORO++: A three-dimensional Voronoi cell library in C++, Chaos: An Interdisciplinary Journal of Nonlinear Science 19, 041111 (2009).
- N. Grønbech-Jensen and O. Farago, Constant pressure and temperature discrete-time langevin molecular dynamics., The Journal of chemical physics 141 19, 194108 (2014).