Spin Dynamics in Dilute Systems

  • R. Rammal
Part of the NATO ASI Series book series (volume 167)


At the percolation threshold, both the infinite cluster and its backbone are self-similar (fractals). This self-similarity also holds at concentrations p near pc for length scales which are smaller than the percolation length ξp. For e < ξp, the number of bonds (or sites) on the infinite cluster scales as e dp, where dp = d − βp/v p denotes the fractal dimensionality and β p, v p are the percolation transition critical exponents. The influence of the scale invariance on the physics of fractals is now very well known. For instance, anomalous behavior of physical properties described by linear problems (classical diffusion, spectrum of the discrete [Laplacian operator, localization, etc.) has been shown to occur on fractals.1,2


Energy Barrier Correlation Length Spin Glass Percolation Cluster Crossover Temperature 
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  1. 1.
    R. Rammal, J. Stat. Phys. 36: 547 (1984).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    S. Alexander, Ann. Isr. Phys. Soc. 5: 149 (1983).Google Scholar
  3. 3.
    For a review on dilute magnetism, see R. B. Stinchcombe in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983 ) Vol. 7.Google Scholar
  4. 4.
    G. Aeppli, H. Guggenheim, and Y. J. Uemura, Phys. Rev. Lett. 52: 942 (1980); G. Aeppli et al., to be published (1987).Google Scholar
  5. 5.
    E. F. Shender, Sov. Phys. JETP 43: 1124 (1976); D. Kumar, Phys. Rev. B30: 2961 (1984).Google Scholar
  6. 6.
    R. Rammal and A. Benoit, Phys. Rev. Lett. 55, 649; R. Rammal, J. Phys. (Paris) 46: 1837 (1985); R. Rammal and A. Benoit, J. Phys. (Paris) Lett. 46: 667 (1985).ADSGoogle Scholar
  7. 7.
    C. L. Henley, Phys. Rev. Let. 54: 2030 (1985).MathSciNetCrossRefGoogle Scholar
  8. 8.
    R. J. Glauber, J. Math Phys. (N.Y) 4: 294 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    For a recent review, see M. Suzuki, in Dynamical Critical Phenomena and Related Topics, edited by C. P. Enz, Lecture Notes in Physics, Vol. 104 (Springer, New York, 1979) p. 75. See also G. F. Mazenko, ibid p. 92.Google Scholar
  10. 10.
    S. Jain, J. Phys. A 19: L 57 and L 667 (1986).Google Scholar
  11. 11.
    S. Jain, R. B. Stinchcombe and E. J. S. Lage, preprint (1987).Google Scholar
  12. 12.
    D. Chowdhury and D. Stauffer, J. Phys. A 19: L 19 (1986).Google Scholar
  13. 13.
    D. Dhar in Stochastic Processes: Formalism and Applications, Lecture Notes in Physics (Springer, Berlin) 1983, Vol. 184, p. 130.Google Scholar
  14. 14.
    U. Larsen, Phys. Lett. 105A: 307 (1984).CrossRefGoogle Scholar
  15. 15.
    H. Sompolinsky, unpublished.Google Scholar
  16. 16.
    J. C. Angles d’Auriac and R. Rammal, preprint 1987.Google Scholar
  17. 17.
    J. Villain, J. Phys. (Paris) 46: 1843 (1985).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • R. Rammal
    • 1
    • 2
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.CRTBT-CNRSGrenobleFrance

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