Advertisement

Classical and quantum behavior in mean-field glassy systems

  • Felix Ritort
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)

Abstract

In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the dynamical instability found in mean-field spin glasses with a discontinuous transition. In mean-field models with pairwise interactions in a transverse field it is shown, in the framework of the static approximation, that such instability is suppressed at zero temperature.

Keywords

Spin Glass Quantum Fluctuation Transverse Field Configurational Entropy Saddle Point Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Binder and A. P. Young, Spin Glasses: Experimental Facts, Theoretical Concepts and Open Questions Rev. Mod. Phys. 58, 801 (1986)CrossRefADSGoogle Scholar
  2. 1a.
    M. Mézard, G. Parisi and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore 1987)zbMATHGoogle Scholar
  3. 1b.
    K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press 1991)Google Scholar
  4. 1c.
    G. Parisi, Field Theory, Disorder and Simulations (World Scientific, Singapore 1992)zbMATHCrossRefGoogle Scholar
  5. 2.
    W. Gotze, Liquid, freezing and the Glass transition, Les Houches (1989), J. P. Hansen, D. Levesque, J. Zinn-Justin editors, North Holland; C. A. Angell, Science, 267, 1924 (1995)Google Scholar
  6. 3.
    S. Sachdev in Statphys 19 Ed. Hao Bailin, World Scientific 1996; S. L. Sondhi, S. M. Girvin, J. P. Carini and D. Shahar, Continuous quantum phase transitions. Preprint cond-mat/9609279.Google Scholar
  7. 4.
    T. R. Kirkpatrick and D. Thirumalai, J. Phys. A (Math. Gen.) (1989) L149Google Scholar
  8. 5.
    J. P. Bouchaud and M. Mezard, J. Physique I (Paris) 4 (1994) 1109.ADSCrossRefGoogle Scholar
  9. 6.
    J. Bernasconi, J. Physique 48 559Google Scholar
  10. 7.
    E. Marinari, G. Parisi and F. Ritort, J. Phys. A (Math. Gen.) 27 (1994) 7615zbMATHCrossRefADSMathSciNetGoogle Scholar
  11. 8.
    E. Marinari, G. Parisi and F. Ritort, J. Phys. A 27 (1994) 7647zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. 9.
    E. Marinari, G. Parisi and F. Ritort, J. Phys. A (Math. Gen.) 28 (1995) 327CrossRefADSMathSciNetGoogle Scholar
  13. 10.
    L. F. Cugliandolo, J. Kurchan, G. Parisi and F. Ritort, Phys. Rev. Lett. 74 (1995) 1012CrossRefADSGoogle Scholar
  14. 11.
    S. Franz and J. Hertz, Phys. Rev. Lett 74 2114 (1995)CrossRefADSGoogle Scholar
  15. 12.
    G. Parisi, J. Phys. A (Math. Gen.) 27 (1994) 7555zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 12a.
    E. Marinari, G. Parisi and F. Ritort, J. Phys. A (Math. Gen.) 28 (1995) 4481zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 13.
    P. Chandra, L. B. Ioffe and D. Sherrington, Phys. Rev. Lett. 75 (1995) 713CrossRefADSGoogle Scholar
  18. 14.
    S. F. Edwards and P. W. Anderson, J. Phys. F (Metal. Phys.) 5 (1975) 965CrossRefADSGoogle Scholar
  19. 15.
    D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).CrossRefADSGoogle Scholar
  20. 16.
    D. J. Gross, I. Kanter and H. Sompolinsky, Phys. Rev. Lett. 55 (1985) 304.CrossRefADSGoogle Scholar
  21. 17.
    E. Gardner, Nucl. Phys. B257 (1985) 747.CrossRefADSGoogle Scholar
  22. 18.
    B. Derrida, Phys. Rev. B24 (1981) 2613.ADSMathSciNetGoogle Scholar
  23. 19.
    D. J. Gross and M. Mezard, Nucl. Phys. B240 (1984) 431.CrossRefADSMathSciNetGoogle Scholar
  24. 20.
    J. H. Gibbs and E. A. Di Marzio, J. Chem. Phys. 28 373 (1958)CrossRefADSGoogle Scholar
  25. 20 a.
    G. Adams and J. H. Gibbs, J. Chem. Phys. 43 139 (1965).CrossRefADSGoogle Scholar
  26. 21.
    W. Kauzmann, Chem. Rev. 43 (1948) 219.CrossRefGoogle Scholar
  27. 22.
    T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36, (1987) 5342Google Scholar
  28. 22a.
    Phys. Rev. B 36, (1987) 5388; Phys. Rev. B38 (1988) 4881Google Scholar
  29. 22b.
    T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. B 36, (1987) 8552.ADSGoogle Scholar
  30. 23.
    A. Crisanti, H. Horner and H.-J. Sommers, Z. Phys. B92 (1993) 257CrossRefADSGoogle Scholar
  31. 23a.
    L. F. Cugliandolo and J. Kurchan, Phys. Rev. Lett. 71 (1993) 173CrossRefADSGoogle Scholar
  32. 24.
    G. Cwilich and T. R. Kirkpatrick, J. Phys A 22, (1989) 4971CrossRefADSMathSciNetGoogle Scholar
  33. 24a.
    E. De Santis, G. Parisi and F. Ritort, J. Phys A 28, (1995) 3025.CrossRefADSMathSciNetGoogle Scholar
  34. 25.
    Th. M. Nieuwenhuizen, Complexity as the driving force for dynamical glassy transitions. Preprint cond-mat/9504059Google Scholar
  35. 26.
    R. Monasson, Phys. Rev. Lett 75 (1995) 2847CrossRefADSGoogle Scholar
  36. 26a.
    S. Franz and G. Parisi, J. Physique I 5 (1995) 1401CrossRefADSMathSciNetGoogle Scholar
  37. 27.
    M. Mezard in Statphys 19 Ed. Hao Bailin, World Scientific 1996; J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan and M. Mezard; Physica A226 (1996) 243.Google Scholar
  38. 28.
    A. J. Bray and M. A. Moore, J. Phys C. 13, L655 (1980).Google Scholar
  39. 29.
    K. D. Usadel, Solid State Commun. 58, 629 (1986).CrossRefADSGoogle Scholar
  40. 30.
    H. Ishii and Y. Yamamoto, J. Phys. C 18, 6225 (1985); J. Phys. C 20, 6053 (1987)CrossRefADSGoogle Scholar
  41. 31.
    G. Büttner and K. D. Usadel, Phys. Rev. B 41, 428 (1990)CrossRefADSGoogle Scholar
  42. 31a.
    Y. Y. Goldschmidt and P. Y. Lai, Phys. Rev. Lett. 64, 2467 (1990).zbMATHCrossRefADSMathSciNetGoogle Scholar
  43. 32.
    D. Thirumalai, Q. Li, T. R. Kirkpatrick, J. Phys. A. 22, 3339 (1989).CrossRefADSMathSciNetGoogle Scholar
  44. 33.
    J. Miller and D. Huse, Phys. Rev. Lett. 70, 3147 (1993)CrossRefADSGoogle Scholar
  45. 34.
    J. Ye, S. Sachdev and N. Read, Phys. Rev. Lett. 70, 4011 (1993)CrossRefADSGoogle Scholar
  46. 34a.
    N. Read, S. Sachdev and J. Ye, Phys. Rev. B 52, 384 (1995)CrossRefADSGoogle Scholar
  47. 35.
    D. Lancaster and F. Ritort, Solving the Schröedinger equation for the Sherrington-Kirkpatrick model in a transverse field. Preprint cond-mat 9611022.Google Scholar
  48. 36.
    F. Ritort, Q uantum critical effects in mean-field glassy systems. Preprint condmat 9607044 Google Scholar
  49. 37.
    C. Itzykson and J-B Zuber, J. Math. Phys. 21, 411 (1980).CrossRefADSMathSciNetzbMATHGoogle Scholar
  50. 38.
    A. Georges. G. Kotliar, W. Krauth and M. J. Rozenberg, Rev. Mod. Phys. 68 (1996) 13CrossRefADSMathSciNetGoogle Scholar
  51. 39.
    Y. Y. Goldschmidt, Phys. Rev. B 41, 4858 (1990); V. Dobrosavljevic and D. Thirumalai, J. Phys. A 22 L767 (1990)CrossRefADSMathSciNetGoogle Scholar
  52. 40.
    T. Senhil and S. N. Majumdar, Phys. Rev. Lett. 76, 3001 (1996).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Felix Ritort
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations