Fractal free energy landscapes in structural glasses

Nature Communications

Volumn 5, Issue , 2014, Pages

  Charbonneau, Patrick ^a,b   Kurchan, Jorge ^c   Parisi, Giorgio ^d,e   Urbani, Pierfrancesco ^f   Zamponi, Francesco ^b  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS SUD   (France)

^c ECOLE NORMALE SUPÉRIEURE   (France)

^d SAPIENZA UNIVERSITY OF ROME   (Italy)

^e CNR   (Italy)

^f Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

GLASS; STRUCTURAL GLASS; UNCLASSIFIED DRUG;

GIBBS FREE ENERGY; GLASS; MECHANICS; NUMERICAL MODEL; PRESSURE EFFECT; TOPOLOGY;

ARTICLE; DYNAMICS; FORCE; FRACTAL ANALYSIS; FRACTAL FREE ENERGY LANDSCAPE; JAMMING TRANSITION; LANDSCAPE; PHASE TRANSITION; PHYSICAL PARAMETERS; PRESSURE; SIMULATION; TEMPERATURE;

EID: 84899478193     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms4725     Document Type: Article

References (70)

1. Goldstein, M. Viscous liquids and the glass transition: A potential energy barrier picture. J. Chem. Phys. 51, 3728-3739 (1969
2. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259-267 (2001
3. Cavagna, A. Supercooled liquids for pedestrians. Phys. Rep. 476, 51-124 (2009
4. Goldstein, M. Communications: Comparison of activation barriers for the Johari-Goldstein and alpha relaxations and its implications. J. Chem. Phys. 132, 041104 (2010
5. Hachenberg, J. et al. Merging of the a and b relaxations and aging via the Johari-Goldstein modes in rapidly quenched metallic glasses. Appl. Phys. Lett. 92, 131911 (2008
6. de Souza, V. K. & Wales, D. J. Energy landscapes for diffusion: Analysis of cagebreaking processes. J. Chem. Phys. 129, 164507 (2008
7. Heuer, A. Exploring the potential energy landscape of glass-forming systems: From inherent structures via metabasins to macroscopic transport. J. Phys. Condens. Matter 20, 373101 (2008
8. Yardimci, H. & Leheny, R. L. Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol. J. Chem. Phys. 124, 214503 (2006
9. Cugliandolo, L. F. & Kurchan, J. On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model. J. Phys. A 27, 5749-5772 (1994
10. Bernal, J. D., Mason, J. & Knight, K. R. Radial distribution of the random close packing of equal spheres. Nature 194, 957-958 (1962
11. Pusey, P. N. & van Megen, W. Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320, 340-342 (1986
12. van Megen, W., Underwood, S. M. & Pusey, P. N. Nonergodicity parameters of colloidal glasses. Phys. Rev. Lett. 67, 1586-1589 (1991
13. Brambilla, G. et al. Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition. Phys. Rev. Lett. 102, 085703 (2009
14. Lechenault, F., Dauchot, O., Biroli, G. & Bouchaud, J.-P. Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass. Europhys. Lett. 83, 46003 (2008
15. Krzakala, F. & Kurchan, J. Landscape analysis of constraint satisfaction problems. Phys. Rev. E 76, 021122 (2007
16. Me?zard, M. & Parisi, G. Glasses and replicas. in Structural Glasses and Supercooled Liquids: Theory, Experiment and Applications (eds Wolynes, P. G. & Lubchenko, V.) (Wiley & Sons, 2012
17. Go?tze, W. Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory Vol. 143 (Oxford University Press, 2009
18. Parisi, G. & Zamponi, F. Mean-field theory of hard sphere glasses and jamming. Rev. Mod. Phys. 82, 789-845 (2010
19. O?Hern, C. S., Langer, S. A., Liu, A. J. & Nagel, S. R. Random packings of frictionless particles. Phys. Rev. Lett. 88, 075507 (2002
20. van Hecke, M. Jamming of soft particles: Geometry, mechanics, scaling and isostaticity. J. Phys. Condens. Matter 22, 033101 (2010
21. Liu, A. J., Nagel, S. R., van Saarloos, W. &Wyart, M. The jamming scenario-an introduction and outlook. in Dynamical Heterogeneities and Glasses (eds Berthier, L., Biroli, G., Bouchaud, J.-P., Cipelletti, L. & van Saarloos, W.) (Oxford University Press, 2011
22. Ikeda, A., Berthier, L. & Sollich, P. Unified study of glass and jamming rheology in soft particle systems. Phys. Rev. Lett. 109, 018301 (2012
23. Wyart, M., Silbert, L. E., Nagel, S. R. & Witten, T. A. Effects of compression on the vibrational modes of marginally jammed solids. Phys. Rev. E 72, 051306 (2005
24. Brito, C. & Wyart, M. Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses. J. Stat. Mech. Theor. Exp. 2007, L08003 (2007
25. Brito, C. & Wyart, M. Geometric interpretation of previtrification in hard sphere liquids. J. Chem. Phys. 131, 024504 (2009
26. Kirkpatrick, T. R. & Wolynes, P. G. Stable and metastable states in mean-field Potts and structural glasses. Phys. Rev. B 36, 8552-8564 (1987
27. Kirkpatrick, T. R. & Thirumalai, D. Dynamics of the structural glass transition and the p-spin-interaction spin-glass model. Phys. Rev. Lett. 58, 2091-2094 (1987
28. Wolynes, P. & Lubchenko, V (eds). Structural Glasses and Supercooled Liquids: Theory, Experiment, and Applications (Wiley, 2012
29. Parisi, G. Order parameter for spin-glasses. Phys. Rev. Lett. 50, 1946-1948 (1983
30. Mezard, M., Parisi, G. & Virasoro, M. A. Spin Glass Theory and Beyond (World Scientific, Singapore, 1987
31. Cugliandolo, L. F. & Kurchan, J. Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model. Phys. Rev. Lett. 71, 173-176 (1993
32. Bouchaud, J.-P., Cugliandolo, L. F., Kurchan, J. & Me?zard, M. Out of equilibrium dynamics in spin-glasses and other glassy systems. in Spin Glasses and Random Fields (ed. Young, A. P.) (World Scientific, 1998
33. Gardner, E. Spin glasses with p-spin interactions. Nucl. Phys. B 257, 747-765 (1985
34. Kirkpatrick, T. R. & Wolynes, P. G. Connections between some kinetic and equilibrium theories of the glass transition. Phys. Rev. A 35, 3072-3080 (1987
35. Kurchan, J., Parisi, G. & Zamponi, F. Exact theory of dense amorphous hard spheres in high dimension. I. The free energy. J. Stat. Mech. Theor. Exp. 2012, P10012 (2012
36. Kurchan, J., Parisi, G., Urbani, P. & Zamponi, F. Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition. J. Phys. Chem. B 117, 12979-12994 (2013
37. Witten, E. Quarks, atoms, and the 1/n expansion. Phys. Today 33, 38-43 (1980
38. Georges, A. & Yedidia, J. S. How to expand around mean-field theory using high-temperature expansions. J. Phys. A 24, 2173-2192 (1991
39. Skoge, M., Donev, A., Stillinger, F. H. & Torquato, S. Packing hyperspheres in high-dimensional Euclidean spaces. Phys. Rev. E 74, 041127 (2006
40. Charbonneau, P., Corwin, E. I., Parisi, G. & Zamponi, F. Universal microstructure and mechanical stability of jammed packings. Phys. Rev. Lett. 109, 205501 (2012
41. Goodrich, C. P., Liu, A. J. & Nagel, S. R. Finite-size scaling at the jamming transition. Phys. Rev. Lett. 109, 095704 (2012
42. Tarjus, G. An overview of the theories of the glass transition. in Dynamical Heterogeneities and Glasses (eds Berthier, L., Biroli, G., Bouchaud, J.-P., Cipelletti, L. & van Saarloos, W.) (Oxford University Press, 2011
43. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587-645 (2011
44. Montanari, A. & Ricci-Tersenghi, F. On the nature of the low-temperature phase in discontinuous mean-field spin glasses. Eur. Phys. J. B 33, 339-346 (2003
45. Montanari, A. & Ricci-Tersenghi, F. Cooling-schedule dependence of the dynamics of mean-field glasses. Phys. Rev. B 70, 134406 (2004
46. Rizzo, T. Replica-symmetry-breaking transitions and off-equilibrium dynamics. Phys. Rev. E 88, 032135 (2013
47. Mu?ller, M. & Pankov, S. Mean-field theory for the three-dimensional Coulomb glass. Phys. Rev. B 75, 144201 (2007
48. Lerner, E., During, G. &Wyart, M. Low-energy non-linear excitations in sphere packings. Soft Matter 9, 8252-8263 (2013
49. Krzakala, F. & Zdeborova, L. Following Gibbs states adiabatically: The energy landscape of mean-field glassy systems. Europhys. Lett. 90, 66002 (2010
50. De Dominicis, C. & Kondor, I. Eigenvalues of the stability matrix for Parisi solution of the long-range spin-glass. Phys. Rev. B 27, 606-608 (1983
51. Charbonneau, P., Ikeda, A., Parisi, G. & Zamponi, F. Glass transition and random close packing above three dimensions. Phys. Rev. Lett. 107, 185702 (2011
52. Moukarzel, C. F. Isostatic phase transition and instability in stiff granular materials. Phys. Rev. Lett. 81, 1634-1637 (1998
53. Tkachenko, A. V. & Witten, T. A. Stress propagation through frictionless granular material. Phy. Rev. E 60, 687-696 (1999
54. Roux, J.-N. Geometric origin of mechanical properties of granular materials. Phys. Rev. E 61, 6802-6836 (2000
55. Pankov, S. Low-temperature solution of the Sherrington-Kirkpatrick model. Phys. Rev. Lett. 96, 197204 (2006
56. Ikeda, A., Berthier, L. & Biroli, G. Dynamic criticality at the jamming transition. J. Chem. Phys. 138, 12A507-17AA (2013
57. Donev, A., Torquato, S. & Stillinger, F. H. Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings. Phys. Rev. E 71, 011105 (2005
58. Wyart, M. Marginal stability constrains force and pair distributions at random close packing. Phys. Rev. Lett. 109, 125502 (2012
59. Sommers, H.-J. & Dupont, W. Distribution of frozen fields in the mean-field theory of spin glasses. J. Phys. C 17, 5785-5793 (1984
60. Atkinson, S., Stillinger, F. H. & Torquato, S. Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings. Phys. Rev. E 88, 062208 (2013
61. Yoshino, H. Replica theory of the rigidity of structural glasses. J. Chem. Phys. 136, 214108-214136 (2012
62. Le Doussal, P., Mu?ller, M. & Wiese, K. J. Avalanches in mean-field models and the Barkhausen noise in spin-glasses. Europhys. Lett. 91, 57004 (2010
63. Struik, L. C. E. Physical aging in plastics and other glassy materials. Polymer Eng. Sci. 17, 165-173 (1977
64. Vollmayr-Lee, K., Kob, W., Binder, J.-L. & Zippelius, A. Dynamical heterogeneities below the glass transition. J. Chem. Phys. 116, 5158-5166 (2002
65. Ballesta, P., Duri, A. & Cipelletti, L. Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition. Nat. Phys. 4, 550-554 (2008
66. Anderson, P. W., Halperin, B. I. & Varma, C. M. Anomalous low-temperature thermal properties of glasses and spin glasses. Philos. Mag. 25, 1-9 (1972
67. Kuhn, R. Universality in glassy low-temperature physics. Europhys. Lett. 62, 313 (2003
68. Capaccioli, S., Paluch, M., Prevosto, D., Wang, L.-M. & Ngai, K. L. Many-body nature of relaxation processes in glass-forming systems. J. Phys. Chem. Lett. 3, 735-743 (2012
69. Xu, N., Vitelli, V., Liu, A. J. & Nagel, S. R. Anharmonic and quasi-localized vibrations in jammed solids modes for mechanical failure. Europhys. Lett. 90, 56001 (2010
70. Stevenson, J. D. & Wolynes., P. G. A universal origin for secondary relaxations in supercooled liquids and structural glasses. Nat. Phys. 6, 62-68 (2010).