Percolation and Cluster Size Distribution

  • Dietrich Stauffer
Chapter
Part of the NATO ASI Series book series (NSSE, volume 100)

Abstract

What am I doing here, except to look at the sea and the bathers? Apparently the organizers did not know that this summer school is on growth and forms and that percolation usually is not a growth process. Thus I will try to make the best of their error: I will use percolation theory to explain some of the concepts that are also used by the “growth people.” Percolation is simpler than many growth processes, and thus much more is known about some percolation properties than about the corresponding properties in various growth processes.

Keywords

Fractal Dimension Large Cluster Critical Exponent Percolation Threshold Triangular Lattice 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Deutscher, R. Zallen and J. Adler, eds, Percolation Structures and Processes, Ann. Israel Phys. Soc. 5 ( Adam Hilger, Bristol, 1983 ).Google Scholar
  2. 2.
    D. Stauffer, Introduction to Percolation Theory ( Taylor and Francis, London, 1985 ).CrossRefGoogle Scholar
  3. 3.
    R. B. Pandey, D. Stauffer, A. Margolina and J. G. Zabolitzky, J. Statist. Phys. 34, 427 (1984).CrossRefGoogle Scholar
  4. 4.
    C. Kalle and S. Wansleben, Comput. Phys. Comm. 33, 343 (1984).CrossRefGoogle Scholar
  5. 5.
    S. Kirkpatrick and E. Stoll, J. Comput. Phys. 40, 517 (1981).CrossRefGoogle Scholar
  6. 6.
    G. Marsaglia, “Random Number Generation,” in Encyclopedia of Computer Science.Google Scholar
  7. 7.
    D. C. Rapaport, J. Phys. A 18, L175 (1985) and to be published.Google Scholar
  8. 8.
    P. L. Leath, Phys. Rev. B 14, 5064 (1976).Google Scholar
  9. 9.
    Z. Alexandrowitz, Phys. Letters A 80, 284 (1980).Google Scholar
  10. 10.
    P. Grassberger, J. Phys. A 18, L215 (1985) and to be published.Google Scholar
  11. 11.
    S. Havlin, B. Trus, G. H. Weiss and D. Ben-Avraham, J. Phys. A 18, L247 (1985).Google Scholar
  12. 12.
    D. Wilkinson and M. Barsony, J. Phys. A 17, L129 (1984).Google Scholar
  13. 13.
    D. Stauffer, Phys. Rev. Lett. 41, 1333 (1978).CrossRefGoogle Scholar
  14. 14.
    J. Hoshen and R. Kopelman, Phys. Rev. B 14, 3428 (1976).CrossRefGoogle Scholar
  15. 15.
    G. MacKay and N. Jan, J. Phys. A 17, L757 (1984); E. Guyon, Percolation et matiere en grains, sect. 4.5, Academie des Sciences, Institut de France, séance du 22 juin 1981.Google Scholar
  16. 16.
    H. J. Herrmann, D. C. Hong and H. E. Stanley, J. Phys. A 17, L261 (1984).Google Scholar
  17. 17.
    P. G. de Gennes, La Recherche 7, 919 (1976).Google Scholar
  18. 18.
    C. Mitescu and R. Roussenq, Chapt. 4 in Ref. 1.Google Scholar
  19. 19.
    S. Alexander and R. Orbach, J. Physique (Paris) 43, L625 (1982).Google Scholar
  20. 20.
    Y. Gefen, A. Aharony and S. Alexander, Phys. Rev. Lett. 50, 77 (1983).CrossRefGoogle Scholar
  21. 21.
    R. Rammal, J. C. Angles c. TAuriac and A. Benoit, Phys. Rev. B 50, 4087 (1984).Google Scholar
  22. 22.
    H. E. Stanley, I. Majid, A. Margolina and A. Bunde, Phys. Rev. Lett. 53, 1706 (1984).CrossRefGoogle Scholar
  23. 23.
    D. Stauffer, Eur. J. Phys. 5, 6 (1984).CrossRefGoogle Scholar
  24. 24.
    M. E. Fisher, Physics 5, 255 (1967). Leo KadanoffGoogle Scholar
  25. 25.
    P. Grassberger, Ref. 10, and three preprints to be published in J. Phys. A by J. Kertesz, by M. Sahimi, and by N. Jan, D. C. Hong and H. E. Stanley.Google Scholar
  26. 26.
    H. Kunz and B. Souillard, J. Stat. Phys. 19, 77 (1978).CrossRefGoogle Scholar
  27. 27.
    T. Vicsek and F. Family, Phys. Rev. Lett. 52, 1669 (1984).CrossRefGoogle Scholar
  28. 28.
    A. Aharony, Phys. Rev. B 22, 400 (1980).Google Scholar

Copyright information

© Martinus Nijhoff Publishers, Dordrecht 1986

Authors and Affiliations

  • Dietrich Stauffer
    • 1
  1. 1.Institute of Theoretical PhysicsCologne UniversityKöln 41West Germany

Personalised recommendations