Abstract
Computer simulation is used to study the diffusion at the percolation threshold on large simple cubic lattices. The exponentk for the rms displacementr witht inr ∼ tk is found to be smaller than 0.2, while the Alexander-Orbach 4/3 rule for the spectral dimension predictsk=0.201 ± 0.002.
This is a preview of subscription content, log in via an institution to check access.
References
D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, 1985).
S. Alexander and R. Orbach,J. Phys. (Paris) Lett. 43:L625 (1982).
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. W. Essam and F. M. Bhatti,J. Phys. A 18:3577 (1985).
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).
R. Rammal, J. C. Angles d'Auriac, and A. Benoit,Phys. Rev. B 30:4087 (1984).
R. B. Pandey, D. Stauffer, J. G. Zabolitzky, and A. Margolina,J. Stat. Phys. 34:427 (1984).
J. Adler,Z. Phys. B 55:227 (1984).
D. Stauffer and J. G. Zabolitzky,J. Phys. A 19:3705 (1986).
S. Havlin and D. Ben Avraham,Adv. Phys., submitted.
Y. Gefen, A. Aharony, and S. Alexander,Phys. Rev. Lett. 50:77 (1983); D. Ben Avraham and S. Havlin,J. Phys. A 15:L691 (1982).
Author information
Authors and Affiliations
Additional information
on leave from Minnesota Supercomputer Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455.
Rights and permissions
About this article
Cite this article
Pandey, R.B., Stauffer, D. & Zabolitzky, J.G. Monte Carlo evidence for the deviation from the Alexander-Orbach rule in three-dimensional percolation. J Stat Phys 49, 849–854 (1987). https://doi.org/10.1007/BF01009361
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01009361