Il Nuovo Cimento D

, Volume 15, Issue 12, pp 1467–1481 | Cite as

Spectrum of relaxation times for ising spin clusters in random fields

  • G. Ismail
  • A. -A. Salem


Exact results on the single-spin-flip Glauber dynamics of six-coupled random field Ising spins with the coordination number of four are presented. Two distributions of random fields (RF), binary (BD) and Gaussian (GD) ones, are investigated. The effects of the static magnetic field are discussed. In the zero-magnetic-field case, the number of diverging relaxation times is equal to the number of energy minima minus one. This rule breaks in the presence of a magnetic field. The longest relaxation times in the absence of the field verify the Arrhenius law with the energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperature, according to the Arrhenius law, the spectrum of relaxation times shows a two-peaked distribution on a logarithmic scale. In the GD case of RF, the energy barrier distribution is continuous, while it is quasi-discrete in the BD case.

PACS 75.10

General theory and models of magnetic ordering 


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  1. [1]
    G. Aeppli andR. Bruinsma:Phys. Lett. A,97, 117 (1983).MathSciNetCrossRefADSGoogle Scholar
  2. [2]
    H. Yoshizawa, R. A. Cowly, G. Shirane, R. J. Birgeneau, H. J. Guggenheim andH. Ikeda:Phys. Rev. Lett.,48, 438 (1982).CrossRefADSGoogle Scholar
  3. [3]
    D. P. Belanger, A. R. King andV. Jaccarino:Phys. Rev. Lett.,48, 1050 (1982).CrossRefADSGoogle Scholar
  4. [4]
    D. Andelman:Phys. Rev. B,34, 6214 (1986).CrossRefADSGoogle Scholar
  5. [5]
    I. Vilfan andJ. Stefan:Solid State Commun.,54, 795 (1985).CrossRefGoogle Scholar
  6. [6]
    E. T. Gawlinski, K. Kaski, M. Grant andJ. D. Guntor:Phys. Rev. Lett.,53, 2266 (1984).CrossRefADSGoogle Scholar
  7. [7]
    M. Grant andJ. D. Guntor:Phys. Rev. B,29, 6266 (1984).CrossRefADSGoogle Scholar
  8. [8]
    G. Forgacs, D. Mukamel andR. A. Pelcovits:Phys. Rev. B,30, 205 (1984).MathSciNetCrossRefADSGoogle Scholar
  9. [9]
    E. Pytte andJ. F. Fernandez:Phys. Rev. B,31, 616 (1985).CrossRefADSGoogle Scholar
  10. [10]
    T. Uezu andK. Kawasaki:J. Phys. Soc. Jpn.,56, 918 (1987).CrossRefGoogle Scholar
  11. [11]
    K. Kawasaki andT. Uezu:J. Phys. Soc. Jpn.,57, 3532 (1988).Google Scholar
  12. [12]
    J. R. Banavar, M. Cieplak andM. Muthukumar:J. Phys. C,18, L157 (1985).CrossRefADSGoogle Scholar
  13. [13]
    G. Ismail andA. A. Salem: inThe XVII International Congress for Statistics, Computer Science, Scientific and Social Applications, Vol. 6 (Scientific Computer Center, Ain Shans University, Cairo, Egypt, 1992), p. 141.Google Scholar
  14. [14]
    R. J. Glauber:J. Math. Phys.,4, 294 (1963).MATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    M. Cieplak andG. Ismail:Acta Phys. Pol. A,76, 513 (1989).Google Scholar
  16. [16]
    W. L. McMillan:Phys. Rev. B,28, 5216 (1983).CrossRefADSGoogle Scholar
  17. [17]
    M. Cieplak andJ. Łusakowski:J. Phys. C,19, 5253 (1986).CrossRefADSGoogle Scholar
  18. [18]
    M. Cieplak, M. Z. Cieplak andJ. Łusakowski:Phys. Rev. B,36, 620 (1987).CrossRefADSGoogle Scholar
  19. [19]
    G. Ismail: Ph. D. Thesis, Warsaw University, Warsaw, Poland (1989).Google Scholar

Copyright information

© Società Italiana di Fisica 1993

Authors and Affiliations

  • G. Ismail
    • 1
  • A. -A. Salem
    • 1
  1. 1.Mathematical Department, Faculty of ScienceZagazig UniversityZagazigEgypt

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