Journal of Statistical Physics

, Volume 54, Issue 1–2, pp 515–529 | Cite as

Fluctuations in Derrida's random energy and generalized random energy models

  • Antonio Galves
  • Servet Martinez
  • Pierre Picco
Article

Abstract

The fluctuations of the finite-size corrections to the free energy per site of the random energy model (REM) and the generalized random energy model (GREM) are investigated. Almost sure behavior for the corrections of order (logN)/N is given. We also prove convergence in distribution for the corrections of order 1/N.

Key words

Random energy random variables finite-size corrections Poisson point process 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Derrida,Phys. Rev. Lett. 45:79–82 (1980);Phys. Rev. B 24:2613–2626 (1981);J. Phys. Lett. 46:L401, L407 (1985); B. Derrida and E. Gardner,J. Phys. C, in press.Google Scholar
  2. 2.
    D. Sherrington and S. Kirkpatrick,Phys. Rev. Lett. 35:1792–1796 (1975).Google Scholar
  3. 3.
    M. Mezard, G. Parisi, and M. Virasoro,Spin Glass Theory and Beyond (Word Scientific, 1987).Google Scholar
  4. 4.
    M. Mezard, G. Parisi, and M. Virasoro,J. Phys. Lett. (Paris)46:L217-L222 (1985).Google Scholar
  5. 5.
    M. Mezard, G. Parisi, and M. Virasoro,Europhys. Lett. 1:77–82 (1986).Google Scholar
  6. 6.
    M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro,J. Phys. (Paris)45:843–854 (1984).Google Scholar
  7. 7.
    B. Derrida and G. Toulouse,J. Phys. Lett. (Paris)46:L223-L228 (1985).Google Scholar
  8. 8.
    C. De Dominicis and M. Hilhorst,J. Phys. Lett. (Paris)46:L909-L914 (1985).Google Scholar
  9. 9.
    D. Ruelle,Commun. Math. Phys. 198:225–239 (1987).Google Scholar
  10. 10.
    E. Olivieri and P. Picco,Commun. Math. Phys. 96:125–144 (1984).Google Scholar
  11. 11.
    D. Capocaccia, M. Cassandro, and P. Picco,J. Stat. Phys. 46:493–505 (1987).Google Scholar
  12. 12.
    M. R. Leadbetter, G. Lindgren, and H. Rootzen,Extremes and Related Properties of Random Sequences and Processes (Springer-Verlag, New York, 1980).Google Scholar
  13. 13.
    J. Neveu, inLecture Notes in Mathematics, No. 598 (Springer-Verlag, Berlin, 1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Antonio Galves
    • 1
    • 2
  • Servet Martinez
    • 1
    • 3
  • Pierre Picco
    • 1
  1. 1.Centre de Physique Théorique (Laboratoire Propre, LP7061)MarseilleFrance
  2. 2.Universidade de São PauloSão PauloBrazil
  3. 3.Universidad de ChileSantiagoChile

Personalised recommendations