Abstract
A striking size dependence of the mean-square displacement of diffusing particles in the two-dimensional lattice gas of hard squares has been observed by Monte Carlo simulation. It is shown that the size effect is due to the formation of a stable cage structure in small lattices when the particle concentration is high. The formation of cages is governed by a new type of percolation problem related to bootstrap percolation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Ertel, K. Froböse, and J. Jäckle,J. Chem. Phys. 88:5027 (1988).
J. Jäckle,Rep. Progr. Phys. 49:171 (1986).
G. Adam and J. H. Gibbs,J. Chem. Phys. 43:139 (1965).
R. G. Palmer, D. L. Stein, E. Abrahams, and P. W. Anderson,Phys. Rev. Lett. 53:958 (1984).
A. K. Doolittle,J. Appl. Phys. 22:1471 (1951).
M. H. Cohen and D. Turnbull,J. Chem. Phys. 31:1164 (1959).
G. H. Fredrickson and H. C. Andersen,Phys. Rev. Lett. 53:1244 (1984);J. Chem. Phys. 83:5822 (1985).
G. H. Fredrickson and S. A. Brawer,J. Chem. Phys. 84:3351 (1986).
G. H. Fredrickson,Ann. N. Y. Acad. Sci. 484:185 (1986).
H. Nakanishi and H. Takano,Phys. Lett. A 115:117 (1986).
J. Chalupa, P. L. Leath, and G. R. Reich,J. Phys. C 12:L31 (1981).
P. M. Kogut and P. L. Leath,J. Phys. C 14:3187 (1981).
J. Adler,Physica A, submitted.
K. Froböse,J. Stat. Phys. 55:1285 (1989).
J. Adler, D. Stauffer, and A. Aharony,J. Phys. A: Math. Gen. 22:L297 (1989).
A. C. D. van Enter, J. Adler, and J. A. M. S. Duarte,J. Stat. Phys. 60:323 (1990).
A. C. D. van Enter,J. Stat. Phys. 48:943 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jäckie, J., Froböse, K. & Knödler, D. Size dependence of self-diffusion in the hard-square lattice gas. J Stat Phys 63, 249–260 (1991). https://doi.org/10.1007/BF01026602
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01026602