Abstract
We examined the diffusion of lattice gases, where double occupancy of sites is excluded, on three-dimensional percolation lattices at the percolation thresholdp c . The critical exponent for the root-mean-square displacement was determined to bek=0.183±0.010, which is similiar to the result of Roman for the problem of the “ant in the labyrinth.” Furthermore, we found a plateau value fork at intermediate times for systems with higher concentrations of lattice gas particles.
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References
D. Stauffer,Introduction into Percolation Theory (Taylor and Francis, 1985).
P. D. de Gennes,La Recherche 7:919 (1976).
S. Alexander and R. Orbach,J. Phys. Lett. (Paris)43:L625 (1982).
C. Mitescu and J. Roussenq,Ann. Israel Phys. Soc. 5:81 (1983).
B. B. Mandelbrot,Ann. Israel Phys. Soc. 5:59 (1983).
Y. Gefen, A. Aharony, and S. Alexander,Phys. Rev. Lett. 50:77 (1983).
K. W. Kehr,J. Stat. Phys. 30:509 (1983).
D. Ben-Avraham and S. Havlin,J. Phys. A: Math. Gen. 15:L691 (1982).
R. Kutner and K. W. Kehr,Phil. Mag. A 48:199 (1983).
P. C. Hohenberg and B. I. Halperin,Rev. Mod. Phys. 49:435 (1977).
C. Mitescu and M. J. Musolf,J. Phys. Lett. (Paris)44:L679 (1983).
B. Derrida, D. Stauffer, H. J. Herrmann and J. Vannimenus,J. Phys. Lett. 44:L701 (1983).
R. B. Pandey, D. Stauffer, A. Margolina, and J. G. Zabolitzky,J. Stat. Phys. 34:427 (1984).
O. Paetzold,J. Phys. Lett. (Paris)45:L193 (1984).
R. B. Pandey, D. Stauffer, and J. G. Zabolitzky,J. Stat. Phys. 49:849 (1987).
R. Rammel, J. C. Angles d'Auriac, and A. Benoit,Phys. Rev. B 30:4087 (1984).
H. E. Roman,J. Stat. Phys. 58:375 (1990).
K. W. Kehr and K. Binder, inApplications of the Monte-Carlo Method in Statistical Physics (Springer, Berlin, 1987), p. 181.
L. Heupel,J. Stat. Phys. 42:541 (1986).
M. Braun and K. W. Kehr,Phil. Mag. A, in press.
M. Przyborowski and M. von Woerkum,Eur. J. Phys. 6:242 (1985).
H. Harder, A. Bunde, and W. Dieterich,J. Chem. Phys. 85:4123 (1986).
C. Amitrano, A. Bunde, and H. E. Stanley,J. Phys. A: Math. Gen. 18:L923 (1985).
R. Blumberg Selinger and H. E. Stanley, Preprint (1989).
K. W. Kehr, R. Kutner, and K. Binder,Phys. Rev. B 23:4931 (1981).
O. Paetzold,Comp. Phys. Comm., submitted.
D. Stauffer, Private communication.
S. Havlin and D. Ben Avraham,Adv. Phys. 36:695 (1987).
J. Haus and K. W. Kehr,Phys. Rep. 150:263 (1987).
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Paetzold, O. Diffusion of lattice gases without double occupancy on three-dimensional percolation lattices. J Stat Phys 61, 495–500 (1990). https://doi.org/10.1007/BF01013977
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DOI: https://doi.org/10.1007/BF01013977