Complexity as the driving force for glassy transitions

  • Th. M. Nieuwenhuizen
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)


The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential.

In the spin glass model there occurs a dynamical transition, where the the system condenses in a state of lower entropy. The extensive entropy loss, called complexity or information entropy, is calculated by analysis of the metastable (TAP) states. This yields a well behaved thermodynamics of the dynamical transition. The multitude of glassy states also implies an extensive difference between the internal energy fluctuations and the specific heat.

In the directed polymer problem there occurs a thermodynamic phase transition in non-extensive terms of the free energy. At low temperature the polymer condenses in a set of highly degenerate metastable states.


Free Energy Dynamical Transition Spin Glass Directed Polymer Spin Glass Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Jäckle, Phil. Magazine B 44 (1981) 533CrossRefGoogle Scholar
  2. [2]
    R.G. Palmer, Adv. in Physics 31 (1982) 669CrossRefADSGoogle Scholar
  3. [3]
    This sudden loss of entropy is reminiscent of the collaps of the wave function in the quantum measurement.Google Scholar
  4. [4]
    T.R. Kirkpatrick and D. Thirumalai, Phys. Rev. Lett. 58 (1987) 2091CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    A. Crisanti and H.J. Sommers, Z. Physik B 87 (1992) 341CrossRefADSGoogle Scholar
  6. [6]
    A. Crisanti, H. Horner, and H.J. Sommers, Z. Phys. B 92 (1993) 257CrossRefADSGoogle Scholar
  7. [7]
    L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71 (1993) 173CrossRefADSGoogle Scholar
  8. [8]
    E. Leutheusser, Phys. Rev. A 29 (1984) 2765CrossRefADSGoogle Scholar
  9. [8a]
    U. Bengtzelius, W. Götze, and A. Sjölander, J. Phys. C 17 (1984) 5915CrossRefADSGoogle Scholar
  10. [9]
    R. Schmitz, J.W. Dufty, and P. De, Phys. Rev. Lett. 71 (1993) 2066CrossRefADSGoogle Scholar
  11. [10]
    J. Kurchan, G. Parisi, and M.A. Virasoro, J. Phys. I (France) 3 (1993) 1819CrossRefGoogle Scholar
  12. [11]
    A. Crisanti and H.J. Sommers, J. de Phys. I France 5 (1995) 805CrossRefGoogle Scholar
  13. [12]
    Th.M. Nieuwenhuizen, Phys. Rev. Lett. 74 (1995) 3463CrossRefADSGoogle Scholar
  14. [13]
    Th.M. Nieuwenhuizen, Phys. Rev. Lett. 74 (1995) 4289CrossRefADSGoogle Scholar
  15. [13a]
  16. [14]
    H. Rieger, Phys. Rev. B 46 (1992) 14665CrossRefADSGoogle Scholar
  17. [15]
    T.R. Kirkpatrick and P.G. Wolynes, Phys. Rev. B 36 (1987) 8552CrossRefADSGoogle Scholar
  18. [15a]
    D. Thirumalai and T.R. Kirkpatrick, Phys. Rev. B 38 (1988) 4881CrossRefADSGoogle Scholar
  19. [15b]
    T.R. Kirkpatrick and D. Thirumalai, J. Phys. I France 5 (1995) 777CrossRefGoogle Scholar
  20. [16]
    A.J. Bray and M.A. Moore, J. Phys. C 13 (1980) L469Google Scholar
  21. [16a]
    F. Tanaka and S.F. Edwards, J. Phys. F 10 (1980) 2769CrossRefADSGoogle Scholar
  22. [16b]
    C. De Dominicis, M. Gabay, T. Garel, and H. Orland, J. Phys. (Paris) 41 (1980) 923Google Scholar
  23. [17]
    Th.M. Nieuwenhuizen, unpublished (1996)Google Scholar
  24. [18]
    V. Dobrosavljevic and D. Thirumalai, J. Phys. A 23 (1990) L767RGoogle Scholar
  25. [19]
    Th.M. Nieuwenhuizen and M.C.W. van Rossum, Phys. Lett. A 160 (1991) 461CrossRefADSGoogle Scholar
  26. [20]
    This happens since at H=0 its (free) energy fluctuations are not O(\(\sqrt N\)) but O(1), as can be seen by expanding the result for ln [Z n]av to order n 2. For H=0 there appear no terms of order n 2 N; for H ≠ 0 they do appear.Google Scholar
  27. [21]
    G. Parisi and G. Toulouse, J. de Phys. Lett. 41 (1980) L361Google Scholar
  28. [22]
    Such behavior has been observed for T>T g in a numerical cooling experiment in the 3d Edwards-Anderson model. (H. Rieger, private communication, April 1995)Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Th. M. Nieuwenhuizen
    • 1
  1. 1.Van der Waals-Zeeman LaboratoriumUniversiteit van AmsterdamAmsterdamThe Netherlands

Personalised recommendations