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Encyclopedia of Complexity and Systems Science pp 4209–4240Cite as

Glasses and Aging, A Statistical Mechanics Perspective on

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Definition of the Subject

Glasses belong to a well-known state of matter: we easily design glasses with desired mechanical or optical properties on an industrial scale,they are widely present in our daily life. Yet, a deep microscopic understanding of the glassy state of matter remains a challenge for condensedmatter physicists [6,67]. Glasses share similaritieswith crystalline solids (they are both mechanically rigid), but also with liquids (they both have similar disordered structures at the molecularlevel). It is mainly this mixed character that makes them fascinating even to non-scientists.

A glass can be obtained by cooling the temperature of a liquid below its glass temperature, T g. The quench must be fast enough that the more standard first order phase transition towards thecrystalline phase is avoided. The glass ‘transition’ is not a thermodynamic transition at all, since T gis only empirically defined as the temperature below which the material has become too viscous to...

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Notes

  1. 1.

    The terminology ‘strong’ and ‘fragile’ is not related to the mechanical properties of the glass but to the evolution of the short-range order close to T g. Strong liquids, such as SiO2, have a locally tetrahedric structure which persists both below and above the glass transition contrary to fragile liquids whose short-range amorphous structure disappears rapidly upon heating above T g.

  2. 2.

    The decrease at long times constitutes a major difference with spin glasses. In a spin glass, \( { \chi_4 } \) would be a monotonically increasing function of time whose long-time limit coincides with the static spin glass susceptibility. Physically, the difference is that spin glasses develop long-range static amorphous order while structual glasses do not or, at least, in a different and more subtle way.

  3. 3.

    In order to have a well-defined thermodynamics, Bethe lattices are generated as random graphs with fixed connectivity, also called random regular graphs.

  4. 4.

    There is of course no crystal state in disordered systems such as in Eq. (8). In the case of lattice glass models, there is a crystal phase but it can disappear depending whether the Bethe lattice is a Cayley tree or a random regular graph.

  5. 5.

    A critical (different) behaviour is expected and predicted for models having a transition [158].

  6. 6.

    This type of plaquette models, and other spin models, were introduced originally [123,149] to show how ultra-slow glassy dynamics can emerge because of growing free energy barriers.

  7. 7.

    Most KCMs do not have a finite temperature dynamical transition and the ones displaying a transition have critical properties different from MCT.

Abbreviations

Glossary:

In this preliminary section, a few concise definitions of the most important concepts discussed in this article are given.

Glass transition:

For molecular liquids, the glass transition denotes a crossover from a viscous liquid to an amorphous solid. Experimentally, the crossover takes place at the glass temperature, T g, conventionally defined as the temperature where the liquid's viscosity reaches the arbitrary value of 1012 Pas. The glass transition more generally applies to many different condensed matter systems where a crossover or, less frequently, a true phase transition, takes place between an ergodic phase and a frozen, amorphous glassy phase.

Aging:

In the glass phase, disordered materials are characterized by relaxation times that exceed common observation timescales, so that a material quenched in its glass phase never reaches equilibrium (neither a metastable equilibrium). It exhibits instead an aging behaviour during which its physical properties keep evolving with time.

Dynamic heterogeneity:

Relaxation spectra of dynamical observables, e. g. the dynamical structure factor, are very broad in supercooled liquids. This is associated to a spatial distribution of timescales: at any given time, different regions in the liquid relax at different rates. Since the supercooled liquid is ergodic, slow regions eventually become fast, and vice versa. Dynamic heterogeneity refers to the existence of these non-trivial spatio-temporal fluctuations in the local dynamical behaviour, a phenomenon observed in virtually all disordered systems with slow dynamics.

Effective temperature:

An aging material relaxes very slowly, trying (in vain) to reach its equilibrium state. During this process, the system probes states that do not correspond to thermodynamic equilibrium, so that its thermodynamic properties can not be rigorously defined. Any practical measurement of its temperature becomes a frequency-dependent operation. A ‘slow’ thermometer tuned to the relaxation timescale of the aging system measures an effective temperature corresponding to the ratio between spontaneous fluctuations (correlation) and linear response (susceptibility). This corresponds to a generalized form of the fluctuation‐dissipation theorem for off-equilibrium materials.

Frustration:

Impossibility of simultaneously minimizing all the interaction terms in the energy function of the system. Frustration might arise from quenched disorder (as in spin glass models), from competing interactions (as in geometrically frustrated magnets), or from competition between a ‘locally preferred order’, and global, e. g. geometric, constraints (as in hard spheres packing problems).

Bibliography

  1. Abou B, Gallet F (2004) Phys Rev Lett 93:160603

    ADS  Google Scholar 

  2. Adam G, Gibbs JH (1958) J Chem Phys 43:139

    ADS  Google Scholar 

  3. Adhikari AN, Capurso NA, Bingemann D (2007) J Chem Phys 127:114508

    ADS  Google Scholar 

  4. Allen M, Tildesley D (1987) Computer Simulation of Liquids. Oxford University Press, Oxford

    MATH  Google Scholar 

  5. Angell CA (1997) J Res NIST 102:171

    Google Scholar 

  6. Angell CA (1995) Science 267:1924

    ADS  Google Scholar 

  7. Appignanesi GA, Rodriguez JA Fris, Montani RA, Kob W (2006) Phys Rev Lett 96:057801

    ADS  Google Scholar 

  8. Barrat A (1998) Phys Rev E 57:3629

    ADS  Google Scholar 

  9. Barrat J-L, Dalibard J, Feigelman M, Kurchan J (eds) (2003) Slow relaxations and nonequilibrium dynamics in condensed matter. Springer, Berlin

    Google Scholar 

  10. Bassler H (1987) Phys Rev Lett 58:767

    ADS  Google Scholar 

  11. Bellon L, Ciliberto S, Laroche C (2001) Europhys Lett 53:511

    ADS  Google Scholar 

  12. Bellon L, Ciliberto S (2002) Physica D 168:325

    ADS  Google Scholar 

  13. Bengtzelius U, Götze W, Sjölander A (1984) J Phys C 17:5915

    Google Scholar 

  14. Bennemann C, Donati C, Baschnagel J, Glotzer SC (1999) Nature 399:246; Lacevic N, Starr FW, Schroder TB, Glotzer SC (2003) J Chem Phys 119:7372

    Google Scholar 

  15. Bert F, Dupuis V, Vincent E, Hammann J, Bouchaud J-P (2004) Phys Rev Lett 92:167203

    ADS  Google Scholar 

  16. Berthier L, Barrat J-L (2002) J Chem Phys 116:6228

    ADS  Google Scholar 

  17. Berthier L, Barrat J-L, Kurchan J (1999) Eur Phys J B 11:635

    ADS  Google Scholar 

  18. Berthier L, Barrat J-L, Kurchan J (2000) Phys Rev E 61:5464

    ADS  Google Scholar 

  19. Berthier L, Barrat J-L (2002) Phys Rev Lett 89:095702

    ADS  Google Scholar 

  20. Berthier L, Biroli G, Bouchaud J-P, Cipelletti L, D El Masri, L'Hôte D, Ladieu F, Pierno M (2005) Science 310:1797

    Google Scholar 

  21. Berthier L, Biroli G, Bouchaud J-P, Kob W, Miyazaki K, Reichman DR (2007) J Chem Phys 126:184503

    ADS  Google Scholar 

  22. Berthier L, Biroli G, Bouchaud J-P, Kob W, Miyazaki K, Reichman DR (2007) J Chem Phys 126:184504

    ADS  Google Scholar 

  23. Berthier L, Bouchaud J-P (2002) Phys Rev B 66:054404

    ADS  Google Scholar 

  24. Berthier L, Chandler D, Garrahan JP (2005) Europhys Lett 69:320

    ADS  Google Scholar 

  25. Berthier L, Garrahan JP (2003) J Chem Phys 119:4367

    ADS  Google Scholar 

  26. Berthier L, Garrahan JP (2005) J Phys Chem B 109:3578

    Google Scholar 

  27. Berthier L, Kob W (2007) J Phys: Condens Matter 19:205130

    ADS  Google Scholar 

  28. Berthier L (2004) Phys Rev E 69:020201(R)

    ADS  Google Scholar 

  29. Berthier L (2007) Phys Rev E 76:011507

    ADS  Google Scholar 

  30. Berthier L (2007) Phys Rev Lett 98:220601

    ADS  Google Scholar 

  31. Berthier L, Viasnoff V, White O, Orlyanchik V, Krzakala F, in Reference [9]

    Google Scholar 

  32. Berthier L, Young AP (2005) Phys Rev B 71:214429

    ADS  Google Scholar 

  33. Binder K, Kob W (2005) Glassy materials and disordered solids. World Scientific, Singapore

    MATH  Google Scholar 

  34. Biroli G, Bouchaud J-P, Miyazaki K, Reichman DR (2006) Phys Rev Lett 97:195701

    ADS  Google Scholar 

  35. Biroli G, Bouchaud J-P, Tarjus G (2005) J Chem Phys 123:044510

    ADS  Google Scholar 

  36. Biroli G, Bouchaud JP (2004) Europhys Lett 67:21

    ADS  Google Scholar 

  37. Biroli G, Mézard M (2001) Phys Rev Lett 88:025501

    Google Scholar 

  38. Bouchaud J-P, Biroli G (2004) J Chem Phys 121:7347

    ADS  Google Scholar 

  39. Bouchaud J-P, Dupuis V, Hammann J, Vincent E (2001) Phys Rev B 65:024439

    ADS  Google Scholar 

  40. Bouchaud JP (1992) J Phys I France 2:1705

    Google Scholar 

  41. Bray AJ (1994) Adv Phys 43:357

    MathSciNet  ADS  Google Scholar 

  42. Bray AJ, Moore MA (1984) J Phys C 17:L463; and in (1987) Heidelberg Colloquim on Glassy Dynamics In: van Hemmen JL, Morgenstern I (eds), Lectures Notes in Physics, vol 275. Springer, Berlin

    Google Scholar 

  43. Bray AJ, Moore MA (1987) Phys Rev Lett 58:57

    ADS  Google Scholar 

  44. Buisson L, Bellon L, Ciliberto S (2003) J Phys Condens Matter 15:S1163

    ADS  Google Scholar 

  45. Buisson L, Ciliberto S, Garcimartin A (2003) Europhys Lett 63:603

    ADS  Google Scholar 

  46. Butler S, Harrowell P (1991) J Chem Phys 95:4454 ((1991) J Chem Phys 95:4466)

    ADS  Google Scholar 

  47. Calabrese P, Gambassi A (2005) J Phys A 38:R133

    MathSciNet  ADS  MATH  Google Scholar 

  48. Castellani T, Cavagna A (2005) J Stat Mech P05012

    Google Scholar 

  49. Cavagna A, Grigera TS, Verrocchio P (2007) Phys Rev Lett 98:187801

    ADS  Google Scholar 

  50. Chandler D, Garrahan JP, Jack RL, Maibaum L, Pan AC (2006) Phys Rev E 74:051501

    ADS  Google Scholar 

  51. Chaudhuri P, Berthier L, Kob W (2007) Phys Rev Lett 99:060604

    ADS  Google Scholar 

  52. Cheng Z, J, Chaikin PM, Phan S, Russel WB (2002) Phys Rev E 65:041405

    Google Scholar 

  53. Cohen MH, Grest GS (1982) Phys Rev B 26:6313

    ADS  Google Scholar 

  54. Coluzzi B, Verrocchio P (2002) J Chem Phys 116:3789

    ADS  Google Scholar 

  55. Mézard M, Bouchaud J-P, Dalibard J (eds) (2007) Complex systems. Springer, Berlin

    Google Scholar 

  56. Coslovich D, Pastore G (2007) J Chem Phys 127:124504

    ADS  Google Scholar 

  57. Crisanti A, Ritort F (2003) J Phys A 36:R181

    MathSciNet  ADS  MATH  Google Scholar 

  58. Cugliandolo LF in Reference [9]

    Google Scholar 

  59. Cugliandolo LF, Kurchan J, Peliti L (1997) Phys Rev E 55:3898

    ADS  Google Scholar 

  60. Cugliandolo LF, Kurchan J (1993) Phys Rev Lett 71:173

    ADS  Google Scholar 

  61. Cugliandolo LF, Kurchan J (1994) J Phys A 27:5749

    MathSciNet  ADS  MATH  Google Scholar 

  62. D'Anna G, Gremaud G (2001) Nature 413:407

    ADS  Google Scholar 

  63. Dalle-Ferrier C, Thibierge C, Alba-Simionesco C, Berthier L, Biroli G, Bouchaud J-P, Ladieu F, L'Hôte D, Tarjus G (2007) Phys Rev E 76:041510

    Google Scholar 

  64. Das SP, Mazenko GF (1986) Phys Rev A 34:2265

    ADS  Google Scholar 

  65. Dauchot O, Marty G, Biroli G (2005) Phys Rev Lett 95:265701

    ADS  Google Scholar 

  66. Debenedetti PG (1996) Metastable liquids. Princeton University Press, Princeton

    Google Scholar 

  67. Debenedetti PG, Stillinger FH (2001) Nature 410:259

    ADS  Google Scholar 

  68. Depken M, Stinchcombe R (2005) Phys Rev E 71:065102

    ADS  Google Scholar 

  69. Donati C, Douglas J, Kob W, Plimpton SJ, Poole PH, Glotzer SC (1998) Phys Rev Lett 80:2338

    ADS  Google Scholar 

  70. Downton MT, Kennett MP (2007) Phys Rev E 76:031502

    ADS  Google Scholar 

  71. Dzero M, Schmalian J, Wolynes PG (2005) Phys Rev B 72:100201

    ADS  Google Scholar 

  72. Ediger MD (2000) Annu Rev Phys Chem 51:99

    ADS  Google Scholar 

  73. Fielding S, Sollich P (2002) Phys Rev Lett 88:050603

    ADS  Google Scholar 

  74. Fisher DS, Huse DA (1986) Phys Rev Lett 56:1601

    ADS  Google Scholar 

  75. Franck FC (1952) Proc R Soc London 215:43

    Google Scholar 

  76. Franz S, Donati C, Parisi G, Glotzer SC (1999) Philos Mag B 79:1827

    ADS  Google Scholar 

  77. Franz S, Mulet R, Parisi G (2002) Phys Rev E 65:021506

    ADS  Google Scholar 

  78. Franz S, Mézard M, Parisi G, Peliti L (1998) Phys Rev Lett 81:1758

    Google Scholar 

  79. Franz S, Parisi G (2000) J Phys Condens Matter 12:6335

    ADS  Google Scholar 

  80. Franz S, Stat J (2005) Mech P04001; (2006) Europhys Lett 73:492

    Google Scholar 

  81. Fredrickson GH, Andersen HC (1984) Phys Rev Lett 53:1244

    ADS  Google Scholar 

  82. Fredrickson GH, Brawer SA (1986) J Chem Phys 84:3351

    ADS  Google Scholar 

  83. Fuchs M, Cates ME (2002) Phys Rev Lett 89:248304

    ADS  Google Scholar 

  84. Garrahan JP, Chandler D (2002) Phys Rev Lett 89:035704

    ADS  Google Scholar 

  85. Garrahan JP, Chandler D (2003) Proc Natl Acad Sc USA 100:9710

    ADS  Google Scholar 

  86. Garrahan JP (2002) J Phys Condens Matter 14:1571

    ADS  Google Scholar 

  87. Glarum SH (1960) J Chem Phys 33:639

    MathSciNet  ADS  Google Scholar 

  88. Gleim T, Kob W, Binder K (1998) Phys Rev Lett 81:4404

    ADS  Google Scholar 

  89. Godrèche C, Luck J-M (2000) J Phys A 33:1151; Lippiello E, Zannetti M (2000) Phys Rev E 61:3369

    Google Scholar 

  90. Godrèche C, Luck J-M (2000) J Phys A 33:9141

    Google Scholar 

  91. Goldstein M (1969) J Chem Phys 51:3728

    ADS  Google Scholar 

  92. Grigera TS, Israeloff NE (1999) Phys Rev Lett 83:5038

    ADS  Google Scholar 

  93. Gross J, Mézard M (1984) Nucl Phys B 240:431

    Google Scholar 

  94. Götze W (1999) J Phys Condens Matter 11:A1

    Google Scholar 

  95. Hansen JP, McDonald IR (1986) Theory of Simple Liquids. Academic, London

    Google Scholar 

  96. Hodge I (1997) J Res NIST 102:195

    ADS  Google Scholar 

  97. Holyst R (2001) Physica A 292:255

    MathSciNet  ADS  MATH  Google Scholar 

  98. Horbach J, Kob W (2001) Phys Rev E 64:041503

    ADS  Google Scholar 

  99. Hurley MM, Harrowell P (1995) Phys Rev E 52:1694

    ADS  Google Scholar 

  100. Jack RL, Berthier L, Garrahan JP (2006) J Stat Mech P12005

    Google Scholar 

  101. Jack RL, Berthier L, Garrahan JP (2005) Phys Rev E 72:016103

    ADS  Google Scholar 

  102. Jack RL, Garrahan JP (2005) J Chem Phys 123:164508

    ADS  Google Scholar 

  103. Jack RL, Mayer P, Sollich P (2006) J Stat Mech Theory Exp P03006

    Google Scholar 

  104. Jaeger HM, Nagel SR, Behringer RP (1996) Rev Mod Phys 68:1259

    ADS  Google Scholar 

  105. Johari GP (2000) J Chem Phys 112:8958

    ADS  Google Scholar 

  106. Jung Y, Garrahan JP, Chandler D (2004) Phys Rev E 69:061205

    ADS  Google Scholar 

  107. Jönsson PE, Mathieu R, Nordblad P, Yoshino H, H Aruga Katori, Ito A (2004) Phys Rev B 70:174402

    Google Scholar 

  108. Kauzmann AW (1948) Chem Rev 43:219

    Google Scholar 

  109. Kegel WK, van Blaaderen A (2000) Science 287:290

    ADS  Google Scholar 

  110. Keys AS, Abate AR, Glotzer SC, Durian DJ (2007) Nat Phys 3:260

    Google Scholar 

  111. Kirkpatrick TR, Thirumalai D (1987) Phys Rev Lett 58:2091; Kirkpatrick TR, Wolynes PG (1987) Phys Rev A 35:3072

    Google Scholar 

  112. Kirkpatrick TR, Thirumalai D, Wolynes PG (1989) Phys Rev A 40:1045

    ADS  Google Scholar 

  113. Kisker J, Santen L, Schreckenberg M, Rieger H (1996) Phys Rev B 53:6418

    ADS  Google Scholar 

  114. Kivelson D, Kivelson SA, Zhao X-L, Nussinov Z, Tarjus G (1995) Physica A 219:27

    ADS  Google Scholar 

  115. Kob W, Andersen HC (1993) Phys Rev E 48:4364

    ADS  Google Scholar 

  116. Kob W, Donati C, Plimpton SJ, Poole PH, Glotzer SC (1997) Phys Rev Lett 79:2827

    ADS  Google Scholar 

  117. Krzakala F, Montanari A, F Ricci-Tersenghi, Semerjian G, Zdeborová L (2007) Proc Natl Acad Sci 104:10318

    Google Scholar 

  118. Krzakala F (2005) Phys Rev Lett 94:077204

    ADS  Google Scholar 

  119. Kurchan J, Laloux L (1996) J Phys A 29:1929

    MathSciNet  ADS  MATH  Google Scholar 

  120. Kurchan J (2005) Nature 433:222

    ADS  Google Scholar 

  121. Larson RG (1999) The Structure and Rheology of Complex Fluids. Oxford University Press, New York

    Google Scholar 

  122. Leutheusser E (1984) Phys Rev A 29:2765

    ADS  Google Scholar 

  123. Lipowski A, Johnston D, Espriu D (2000) Phys Rev E 62:3404

    ADS  Google Scholar 

  124. Liu AJ, Nagel SR (1998) Nature 396:21

    ADS  Google Scholar 

  125. Léonard S, Mayer P, Sollich P, Berthier L, Garrahan JP (2007) J Stat Mech P07017

    Google Scholar 

  126. Mapes MK, Swallen SF, Ediger MD (2006) J Chem Phys 124:054710

    ADS  Google Scholar 

  127. Marty G, Dauchot O (2005) Phys Rev Lett 94:015701

    ADS  Google Scholar 

  128. Mayer P, Berthier L, Garrahan JP, Sollich P (2003) Phys Rev E 68:016116

    ADS  Google Scholar 

  129. Mayer P, Léonard S, Berthier L, Garrahan JP, Sollich P (2006) Phys Rev Lett 96:030602

    Google Scholar 

  130. Mayer P, Sollich P (2007) J Phys A 40:5823

    MathSciNet  ADS  MATH  Google Scholar 

  131. McCullagh GD, Cellai D, Lawlor A, Dawson KA, Phys. Rev. E 71:030102 (2005)

    Google Scholar 

  132. McKenna GB, Kovacs AJ (1984) Polym Eng Sci 24:1131

    Google Scholar 

  133. Menon N, Nagel SR, Phys. Rev. Lett 74:1230 (1995); Fernandez LA, Martin V-Mayor, Verrocchio P (2006) Phys Rev E 73:020501; and [49]

    Google Scholar 

  134. Miyazaki K, Reichman DR (2002) Phys Rev E 66:050501(R)

    ADS  Google Scholar 

  135. Monasson R (1995) Phys Rev Lett 75:2847

    ADS  Google Scholar 

  136. Mézard M, Parisi G (1999) Phys Rev Lett 82:747

    Google Scholar 

  137. Mézard M, Parisi G, Virasoro M (1988) Spin Glass Theory and Beyond. World Scientific, Singapore

    Google Scholar 

  138. Nauroth M, Kob W (1997) Phys Rev E 55:657

    ADS  Google Scholar 

  139. Nelson DR (2002) Defects and Geometry in Condensed Matter Physics. Cambridge University Press, Cambridge

    Google Scholar 

  140. Nicodemi M (1999) Phys Rev Lett 82:3734

    ADS  Google Scholar 

  141. Pan AC, Garrahan JP, Chandler D (2005) Phys Rev E 72:041106

    ADS  Google Scholar 

  142. Pardo LC, Lunkenheimer P, Loidl A (2007) Phys Rev E 76:030502(R)

    ADS  Google Scholar 

  143. Parisi G, Zamponi F (2005) J Chem Phys 123:144501

    ADS  Google Scholar 

  144. Pusey PN and van Megen W (1986) Nature 320:340

    ADS  Google Scholar 

  145. Richert R, Angell CA (1998) J Chem Phys 108:9016

    ADS  Google Scholar 

  146. Ritort F, Sollich P (2003) Adv Phys 52:219

    ADS  Google Scholar 

  147. Rivoire O, Biroli G, Martin OC, Mézard M (2004) Eur Phys J B 37:55

    Google Scholar 

  148. Réfrégier P, Vincent E, Hammann J, Ocio M (1987) J Phys France 48:1533

    Google Scholar 

  149. Sethna JP, Shore JD, Huang M (1991) Phys Rev B 44:4943

    ADS  Google Scholar 

  150. Sollich P, Lequeux F, Hebraud P, Cates ME (1997) Phys Rev Lett 78:2020

    ADS  Google Scholar 

  151. Sollich P (1998) Phys Rev E 58:738

    ADS  Google Scholar 

  152. Struik LCE (1978) Physical aging in amorphous polymers and other materials. Elsevier, Amsterdam

    Google Scholar 

  153. Szamel G, Flenner E (2004) Europhys Lett 67:779

    ADS  Google Scholar 

  154. Tarjus G, Kivelson D (1995) J Chem Phys 103:3071

    ADS  Google Scholar 

  155. Tarjus G, Kivelson SA, Nussinov Z, Viot P (2005) J Phys Condens Matter 17:R1143

    ADS  Google Scholar 

  156. Thalmann F (2002) J Chem Phys 116:3378

    ADS  Google Scholar 

  157. Toninelli C, Biroli G, Fisher DS (2004) Phys Rev Lett 92:185504

    ADS  Google Scholar 

  158. Toninelli C, Biroli G, Fisher DS (2006) Phys Rev Lett 96:035702

    ADS  Google Scholar 

  159. Toninelli C, Wyart M, Berthier L, Biroli G, Bouchaud J-P (2005) Phys Rev E 71:041505

    ADS  Google Scholar 

  160. Tracht U, Wilhelm M, Heuer A, Feng H, K Schmidt-Rohr, Spiess HW (1998) Phys Rev Lett 81:2727; Reinsberg SA, Qiu XH, Wilhelm M, Spiess HW, Ediger MD (2001) J Chem Phys 114:7299

    Google Scholar 

  161. Vidal Russell E,Israeloff NE (2000) Nature 408:695

    ADS  Google Scholar 

  162. Viot P, Talbot J, Tarjus G (2003) Fractals 11:185

    MATH  Google Scholar 

  163. Vogel M, Glotzer SC (2004) Phys Rev E 70:061504

    ADS  Google Scholar 

  164. Wang P, Song CM, Makse HA (2006) Nat Phys 2:526

    Google Scholar 

  165. Weeks E, Crocker JC, Levitt AC, Schofield A, Weitz DA (2000) Science 287:627

    ADS  Google Scholar 

  166. Weeks ER, Crocker JC, Weitz DA (2007) J Phys Condens Matter 19:205131

    ADS  Google Scholar 

  167. Whitelam S, Berthier L, Garrahan JP (2005) Phys Rev E 71:026128

    ADS  Google Scholar 

  168. Whitelam S, Berthier L, Garrahan JP (2004) Phys Rev Lett 92:185705

    ADS  Google Scholar 

  169. Whitelam S, Garrahan JP (2004) J Phys Chem B 108:6611

    Google Scholar 

  170. Wuttke J, Petry W, Pouget S (1996) J Chem Phys 105:5177

    ADS  Google Scholar 

  171. Xia XY, Wolynes PG (2000) Proc Natl Acad Sci USA 97:2990

    ADS  Google Scholar 

  172. Yamamoto R, Onuki A (1998) Phys Rev E 58:3515

    ADS  Google Scholar 

  173. Young AP (ed) (1998) Spin glasses and random fields. World Scientific, Singapore

    Google Scholar 

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Acknowledgments

We thank C. Marchetti for inviting us to write this review and the collaborators who worked with us onglass physics. We thank J.-P. Bouchaud, A. Lefèvre, T. Sarlat for a careful reading of our manuscript and suggestions. Our work is supported by ANRGrants CHEF, TSANET and DYNHET.

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Authors and Affiliations

  1. Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II and CNRS, Montpellier, France

    Ludovic Berthier

  2. CEA, DSM, Institut de Physique Théorique, IPhT, CNRS, MPPU, URA2306, Saclay, Gif-sur-Yvette, France

    Giulio Biroli

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Berthier, L., Biroli, G. (2009). Glasses and Aging, A Statistical Mechanics Perspective on. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_248

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