1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 8, 2017
  5. Article

Annual Review of Condensed Matter Physics

Volume 8, 2017

Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

Abstract

Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.

Keyword(s): dimension dependence, dynamical transition, Gardner transition, hard sphere, marginal stability, mean-field theory
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031016-025334
2017-03-31
2024-10-16
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/8/1/annurev-conmatphys-031016-025334.html?itemId=/content/journals/10.1146/annurev-conmatphys-031016-025334&mimeType=html&fmt=ahah

Literature Cited

  1. Witten E. 1.  1980. Phys. Today 33:38–43 [Google Scholar]
  2. Wyler D, Rivier N, Frisch HL. 2.  1987. Phys. Rev. A 36:2422–31 [Google Scholar]
  3. Frisch HL, Percus JK. 3.  1999. Phys. Rev. E 60:2942–48 [Google Scholar]
  4. Georges A, Kotliar G, Krauth W, Rozenberg MJ. 4.  1996. Rev. Mod. Phys. 68:13–125 [Google Scholar]
  5. Svidzinsky A, Scully M, Herschbach D. 5.  2014. Phys. Today 67:33 [Google Scholar]
  6. Drouffe JM, Parisi G, Sourlas N. 6.  1979. Nucl. Phys. B 161:397–416 [Google Scholar]
  7. Kirkpatrick TR, Wolynes PG. 7.  1987. Phys. Rev. A 35:3072–80 [Google Scholar]
  8. Kirkpatrick TR, Wolynes PG. 8.  1987. Phys. Rev. B 36:8552–64 [Google Scholar]
  9. Kirkpatrick TR, Thirumalai D. 9.  1987. Phys. Rev. Lett. 58:2091–94 [Google Scholar]
  10. Kirkpatrick TR, Thirumalai D. 10.  1987. Phys. Rev. B 36:5388–97 [Google Scholar]
  11. Kirkpatrick TR, Thirumalai D. 11.  1988. Phys. Rev. A 37:4439–48 [Google Scholar]
  12. Kirkpatrick TR, Thirumalai D. 12.  1989. J. Phys. A 22:L149–55 [Google Scholar]
  13. Kirkpatrick TR, Thirumalai D, Wolynes PG. 13.  1989. Phys. Rev. A 40:1045–54 [Google Scholar]
  14. Parisi G, Zamponi F. 14.  2006. J. Stat. Mech. 2006:P03017 [Google Scholar]
  15. Parisi G, Zamponi F. 15.  2010. Rev. Mod. Phys. 82:789–845 [Google Scholar]
  16. Kauzmann W. 16.  1948. Chem. Rev. 43:219–56 [Google Scholar]
  17. Bouchaud JP, Biroli G. 17.  2004. J. Chem. Phys. 121:7347 [Google Scholar]
  18. Conway JH, Sloane. 18.  1999. A Series of Comprehensive Mathematics 290 SS Chern, B Eckmann, P de la Harpe, H Hironaka, F Hirzebruch et al. New York: Springer-Verlag, 3rd ed.. [Google Scholar]
  19. Skoge M, Donev A, Stillinger FH, Torquato S. 19.  2006. Phys. Rev. E 74:041127 [Google Scholar]
  20. Eaves JD, Reichman DR. 20.  2009. PNAS 106:15171 [Google Scholar]
  21. van Meel JA, Frenkel D, Charbonneau P. 21.  2009. Phys. Rev. E 79:030201(R) [Google Scholar]
  22. van Meel JA, Charbonneau B, Fortini A, Charbonneau P. 22.  2009. Phys. Rev. E 80:061110 [Google Scholar]
  23. Charbonneau P, Ikeda A, van Meel JA, Miyazaki K. 23.  2010. Phys. Rev. E 81:040501 [Google Scholar]
  24. Charbonneau P, Ikeda A, Parisi G, Zamponi F. 24.  2011. Phys. Rev. Lett. 107:185702 [Google Scholar]
  25. Charbonneau B, Charbonneau P, Tarjus G. 25.  2012. Phys. Rev. Lett. 108:035701 [Google Scholar]
  26. Charbonneau B, Charbonneau P, Tarjus G. 26.  2013. J. Chem. Phys. 138:12A515 [Google Scholar]
  27. Sengupta S, Karmakar S, Dasgupta C, Sastry S. 27.  2013. J. Chem. Phys. 138:12A548 [Google Scholar]
  28. Zhang K, Smith WW, Wang M, Liu Y, Schroers J. 28.  et al. 2014. Phys. Rev. E 90:032311 [Google Scholar]
  29. Maimbourg T, Kurchan J, Zamponi F. 29.  2016. Phys. Rev. Lett. 116:015902 [Google Scholar]
  30. Cugliandolo LF, Kurchan J. 30.  1993. Phys. Rev. Lett. 71:173–76 [Google Scholar]
  31. Cugliandolo LF. 31.  2003. Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter J-L Barrat, MV Feigelman, J Kurchan, J Dalibard 367–521 Berlin: Springer [Google Scholar]
  32. Bouchaud JP, Cugliandolo LF, Kurchan J, Mézard M. 32.  1997. Spin Glasses and Random Fields AP Young 161–223 Singapore: World Sci. [Google Scholar]
  33. Götze W. 33.  2008. Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory 143 Oxford, UK: Oxford Univ. Press [Google Scholar]
  34. Charbonneau P, Ikeda A, Parisi G, Zamponi F. 34.  2012. PNAS 109:13939–43 [Google Scholar]
  35. Charbonneau P, Jin Y, Parisi G, Zamponi F. 35.  2014. PNAS 111:15025–30 [Google Scholar]
  36. Charbonneau B, Charbonneau P, Jin Y, Parisi G, Zamponi F. 36.  2013. J. Chem. Phys. 139:164502 [Google Scholar]
  37. Kurchan J, Parisi G, Zamponi F. 37.  2012. J. Stat. Mech. 2012:P10012 [Google Scholar]
  38. Kurchan J, Parisi G, Urbani P, Zamponi F. 38.  2013. J. Phys. Chem. B 117:12979–94 [Google Scholar]
  39. Franz S, Parisi G. 39.  2000. J. Phys. Condens. Matter 12:6335 [Google Scholar]
  40. Donati C, Franz S, Glotzer S, Parisi G. 40.  2002. J. Non-Cryst. Solids 307:215–24 [Google Scholar]
  41. Biroli G, Bouchaud JP, Miyazaki K, Reichman DR. 41.  2006. Phys. Rev. Lett. 97:195701 [Google Scholar]
  42. Berthier L, Biroli G, Bouchaud JP, Kob W, Miyazaki K, Reichman DR. 42.  2007. J. Chem. Phys. 126:184503 [Google Scholar]
  43. Berthier L, Biroli G, Bouchaud JP, Kob W, Miyazaki K, Reichman DR. 43.  2007. J. Chem. Phys. 126:184504 [Google Scholar]
  44. Berthier L, Biroli G, Bouchaud JP, Cipelletti L. Masri D. 44. , El et al. 2005. Science 310:1797–800 [Google Scholar]
  45. Berthier L, Biroli G, Bouchaud JP, Cipelletti L, van Saarloos W. 45.  2011. Dynamical Heterogeneities and Glasses Oxford, UK: Oxford Univ. Press [Google Scholar]
  46. Franz S, Parisi G, Ricci-Tersenghi F, Rizzo T. 46.  2011. Eur. Phys. J. E 34:1–17 [Google Scholar]
  47. Franz S, Jacquin H, Parisi G, Urbani P, Zamponi F. 47.  2012. PNAS 109:18725–30 [Google Scholar]
  48. Franz S, Jacquin H, Parisi G, Urbani P, Zamponi F. 48.  2013. J. Chem. Phys. 138:12A540 [Google Scholar]
  49. Nandi SK, Biroli G, Tarjus G. 49.  2016. Phys. Rev. Lett. 116:145701 [Google Scholar]
  50. Ikeda A, Miyazaki K. 50.  2010. Phys. Rev. Lett. 104:255704 [Google Scholar]
  51. Schmid B, Schilling R. 51.  2010. Phys. Rev. E 81:041502 [Google Scholar]
  52. Mangeat M, Zamponi F. 52.  2016. Phys. Rev. E 93:012609 [Google Scholar]
  53. Coslovich D, Ikeda A, Miyazaki K. 53.  2016. Phys. Rev. E 93:042602 [Google Scholar]
  54. Mézard M, Parisi G, Virasoro MA. 54.  1987. Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications Singapore: World Sci. [Google Scholar]
  55. Bray A, Moore M. 55.  1980. J. Phys. C 13:L469 [Google Scholar]
  56. Biroli G, Kurchan J. 56.  2001. Phys. Rev. E 64:016101 [Google Scholar]
  57. Barrat A, Burioni R, Mézard M. 57.  1996. J. Phys. A 29:L81 [Google Scholar]
  58. Franz S, Parisi G. 58.  1995. J. Phys. I 5:1401–15 [Google Scholar]
  59. Franz S, Parisi G. 59.  2013. J. Stat. Mech. 2013:P02003 [Google Scholar]
  60. Franz S, Parisi G, Urbani P. 60.  2015. J. Phys. A 48:19FT01 [Google Scholar]
  61. Edwards S, Oakeshott R. 61.  1989. Physica A 1571080–90 [Google Scholar]
  62. Kurchan J. 62.  2001. Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales AJ Liu, SR Nagel 72–79 London: Taylor & Francis [Google Scholar]
  63. Crisanti A, Ritort F. 63.  2000. Europhys. Lett. 51:147 [Google Scholar]
  64. Franz S, Virasoro MA. 64.  2000. J. Phys. A 33:891 [Google Scholar]
  65. Caltagirone F, Ferrari U, Leuzzi L, Parisi G, Ricci-Tersenghi F, Rizzo T. 65.  2012. Phys. Rev. Lett. 108:085702 [Google Scholar]
  66. Parisi G, Rizzo T. 66.  2013. Phys. Rev. E 87:012101 [Google Scholar]
  67. Barrat A, Franz S, Parisi G. 67.  1997. J. Phys. A 30:5593–612 [Google Scholar]
  68. Rainone C, Urbani P, Yoshino H, Zamponi F. 68.  2015. Phys. Rev. Lett. 114:015701 [Google Scholar]
  69. Rainone C, Urbani P. 69.  2016. J. Stat. Mech. 2016:053302 [Google Scholar]
  70. Berthier L, Charbonneau P, Jin Y, Parisi G, Seoane B, Zamponi F. 70.  2016. PNAS 113:8397–401 [Google Scholar]
  71. Biroli G, Urbani P. 71.  2016. Nat. Phys. 121130–33 [Google Scholar]
  72. Franz S, Parisi G, Urbani P, Zamponi F. 72.  2015. PNAS 112:14539–44 [Google Scholar]
  73. Charbonneau P, Corwin EI, Parisi G, Poncet A, Zamponi F. 73.  2015. Phys. Rev. Lett. 117:045503 [Google Scholar]
  74. Charbonneau P, Kurchan J, Parisi G, Urbani P, Zamponi F. 74.  2014. Nat. Commun. 5:3725 [Google Scholar]
  75. Charbonneau P, Kurchan J, Parisi G, Urbani P, Zamponi F. 75.  2014. J. Stat. Mech. 2014:P10009 [Google Scholar]
  76. Gardner E. 76.  1985. Nucl. Phys. B 257:747–65 [Google Scholar]
  77. Gross D, Kanter I, Sompolinsky H. 77.  1985. Phys. Rev. Lett. 55:304 [Google Scholar]
  78. Charbonneau P, Jin Y, Parisi G, Rainone C, Seoane B, Zamponi F. 78.  2015. Phys. Rev. E 92:012316 [Google Scholar]
  79. Berthier L, Coslovich D, Ninarello A, Ozawa M. 79.  2016. Phys. Rev. Lett. 116:238002 [Google Scholar]
  80. Singh S, Ediger M, de Pablo JJ. 80.  2013. Nat. Mater. 12:139–44 [Google Scholar]
  81. Dyre JC. 81.  2006. Rev. Mod. Phys. 78:953 [Google Scholar]
  82. Seguin A, Dauchot O. 82.  2016. Phys. Rev. Lett. 117:228001 [Google Scholar]
  83. Urbani P, Biroli G. 83.  2015. Phys. Rev. B 91:100202 [Google Scholar]
  84. Liu AJ, Nagel SR. 84.  1998. Nature 396:21–22 [Google Scholar]
  85. O'Hern CS, Langer SA, Liu AJ, Nagel SR. 85.  2002. Phys. Rev. Lett. 88:075507 [Google Scholar]
  86. O'Hern CS, Silbert LE, Liu AJ, Nagel SR. 86.  2003. Phys. Rev. E 68:011306 [Google Scholar]
  87. Torquato S, Stillinger FH. 87.  2010. Rev. Mod. Phys. 82:2633–72 [Google Scholar]
  88. Müller M, Wyart M. 88.  2015. Annu. Rev. Condens. Matter Phys. 6:177–200 [Google Scholar]
  89. Bo L, Mari R, Song C, Makse HA. 89.  2014. Soft Matter 10:7379–92 [Google Scholar]
  90. Silbert L, Liu A, Nagel S. 90.  2005. Phys. Rev. Lett. 95:098301 [Google Scholar]
  91. Wyart M, Nagel S, Witten T. 91.  2005. Europhys. Lett. 72:486–92 [Google Scholar]
  92. Wyart M, Silbert L, Nagel S, Witten T. 92.  2005. Phys. Rev. E 72:051306 [Google Scholar]
  93. DeGiuli E, Laversanne-Finot A, Düring G, Lerner E, Wyart M. 93.  2014. Soft Matter 10:5628–44 [Google Scholar]
  94. Xu N, Vitelli V, Liu AJ, Nagel SR. 94.  2010. Europhys. Lett. 90:56001 [Google Scholar]
  95. Wyart M. 95.  2012. Phys. Rev. Lett. 109:125502 [Google Scholar]
  96. DeGiuli E, Lerner E, Brito C, Wyart M. 96.  2014. PNAS 111:17054 [Google Scholar]
  97. Charbonneau P, Corwin EI, Parisi G, Zamponi F. 97.  2015. Phys. Rev. Lett. 114:125504 [Google Scholar]
  98. Lerner E, Düring G, Wyart M. 98.  2013. Soft Matter 9:8252–63 [Google Scholar]
  99. Charbonneau P, Corwin EI, Parisi G, Zamponi F. 99.  2012. Phys. Rev. Lett. 109:205501 [Google Scholar]
  100. Chaudhuri P, Berthier L, Sastry S. 100.  2010. Phys. Rev. Lett. 104:165701 [Google Scholar]
  101. Ozawa M, Kuroiwa T, Ikeda A, Miyazaki K. 101.  2012. Phys. Rev. Lett. 109:205701 [Google Scholar]
  102. Goodrich CP, Liu AJ, Nagel SR. 102.  2012. Phys. Rev. Lett. 109:095704 [Google Scholar]
  103. Brito C, Wyart M. 103.  2009. J. Chem. Phys. 131:024504 [Google Scholar]
  104. Stillinger FH, Weber TA. 104.  1982. Phys. Rev. A 25:978–89 [Google Scholar]
  105. Sciortino F, Kob W, Tartaglia P. 105.  1999. Phys. Rev. Lett. 83:3214–17 [Google Scholar]
  106. Biroli G, Monasson R. 106.  2000. Europhys. Lett. 50:155–61 [Google Scholar]
  107. Berthier L, Jacquin H, Zamponi F. 107.  2011. Phys. Rev. E 84:051103 [Google Scholar]
  108. Monasson R. 108.  1995. Phys. Rev. Lett. 75:2847–50 [Google Scholar]
  109. Rizzo T. 109.  2013. Phys. Rev. E 88:032135 [Google Scholar]
  110. Cugliandolo L, Kurchan J. 110.  1994. J. Phys. A 27:5749–72 [Google Scholar]
  111. Van Hecke M. 111.  2010. J. Phys.: Condens. Matter 22:033101 [Google Scholar]
  112. Baule A, Morone F, O'Hern CS, Makse HA. 112.  2016. Rev. Mod. Phys. In review arXiv:1602.04369 [Google Scholar]
  113. Lubachevsky BD, Stillinger FH. 113.  1990. J. Stat. Phys. 60:561–83 [Google Scholar]
  114. Lerner E, Düring G, Wyart M. 114.  2013. Comput. Phys. Commun. 184:628–37 [Google Scholar]
  115. Torquato S, Jiao Y. 115.  2010. Phys. Rev. E 82:061302 [Google Scholar]
  116. Hopkins AB, Stillinger FH, Torquato S. 116.  2013. Phys. Rev. E 88:022205 [Google Scholar]
  117. Xu N, Frenkel D, Liu A. 117.  2011. Phys. Rev. Lett. 106:245502 [Google Scholar]
  118. Asenjo D, Paillusson F, Frenkel D. 118.  2014. Phys. Rev. Lett. 112:098002 [Google Scholar]
  119. Paillusson F, Frenkel D. 119.  2012. Phys. Rev. Lett. 109:208001 [Google Scholar]
  120. Paillusson F. 120.  2015. Phys. Rev. E 91:012204 [Google Scholar]
  121. Franz S, Parisi G. 121.  2016. J. Phys. A 49:145001 [Google Scholar]
  122. Sellitto M, Zamponi F. 122.  2013. J. Phys. Conf. Ser. 473:012020 [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031016-025334
Loading
Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
Annual Review of Condensed Matter Physics 8, 265 (2017); https://doi.org/10.1146/annurev-conmatphys-031016-025334
/content/journals/10.1146/annurev-conmatphys-031016-025334
/content/journals/10.1146/annurev-conmatphys-031016-025334
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error