Journal of Statistical Physics

, Volume 58, Issue 1–2, pp 375–382 | Cite as

Diffusion in three-dimensional random systems at their percolation thresholds

  • H. Eduardo Roman
Short Communications


Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd w is found to be 1/d w =0.250±0.003.

Key words

Percolation anomalous diffusion Alexander-Orbach rule vector computer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. G. de Gennes,Recherche 7:919 (1976).Google Scholar
  2. 2.
    D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, 1985).Google Scholar
  3. 3.
    S. Alexander and R. Orbach,J. Phys. Lett. (Paris) 43:L625 (1982).Google Scholar
  4. 4.
    J. G. Zabolitzky,Phys. Rev. B 30:4077 (1984); H. J. Herrmann, B. Derrida, and J. Vannimenus,Phys. Rev. B 30:4080 (1984); D. C. Hong, S. Havlin, H. J. Herrmann, and H. E. Stanley,Phys. Rev. B 30:4083 (1984); C. J. Lobb and D. J. Frank,Phys. Rev. B 30:4090 (1984); J. M. Normand, H. J. Herrmann, and M. Hajjar,J. Stat. Phys. 52:441 (1988).Google Scholar
  5. 5.
    J. W. Essam and F. M. Bhatti,J. Phys. A 18:3577 (1985).Google Scholar
  6. 6.
    A. B. Harris, S. Kim, and T. C. Lubensky,Phys. Rev. Lett. 53:743 (1984); T. C. Lubensky and J. Wang,Phys. Rev. B 33:4998 (1986).Google Scholar
  7. 7.
    R. B. Pandey, D. Stauffer, J. G. Zabolitzky, and A. Margolina,J. Stat. Phys. 34:427 (1984).Google Scholar
  8. 8.
    R. Rammal, J. C. Angles d'Auriac, and A. Benoit,Phys. Rev. B 30:4087 (1984).Google Scholar
  9. 9.
    R. B. Pandey, D. Stauffer, and J. G. Zabolitzky,J. Stat. Phys. 49:849 (1987).Google Scholar
  10. 10.
    S. Havlin and D. Ben-Avraham,Adv. Phys. 36:695 (1987).Google Scholar
  11. 11.
    P. L. Leath,Phys. Rev. B 14:5046 (1976).Google Scholar
  12. 12.
    R. M. Ziff and G. Stell, preprint.Google Scholar
  13. 13.
    J. Adler, Y. Meir, A. Aharony, A. B. Harris, and L. Klein,J. Stat. Phys., in press.Google Scholar
  14. 14.
    A. Bunde, S. Havlin, and H. E. Roman, preprint.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • H. Eduardo Roman
    • 1
  1. 1.HLRZc/o KFA JülichJülich 1Federal Republic of Germany

Personalised recommendations