Abstract
The basic physical phenomena of percolation are reviewed within the context of the modern theory of critical phenomena. The connection between percolation and the Potts model, a statistical mechanical model of ferromagnetism, is discussed. Recent advances in calculating critical exponents by position-space renormalization group methods are also described. Several open questions are also raised, including the nature of cluster structure and transport near the percolation threshold, and the anomalous geometrical properties of self-similar structures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexander, S. and Orbach, R. 1982, J. de Physique 43, L625.
Bernasconi, J., 1978, Phys. Rev. B. 18, 2185.
Broadbent, S.R. and Hammersley, J.M., 1957, Proc. Camb. Philos. Soc. 53, 624.
Coniglio, A., 1981a, Phys. Rev. Lett. 46, 250.
Coniglio, A., 1981b, in Lecture Notes in Physics, Disordered Systems and Localization, Proc. Rome Conf., 1981, ed. C. Castllani, C. Di Castro and L. Peliti (Springer: Berlin).
Coniglio, A., 1982, J. Phys. A. 15, 3824.
Derrida, B. and Vannimenus, J., 1982, J. Phys. A. 15, L557.
Essam, J.W., 1980, Rep. Prog. Phys. 43, 833.
Family, F., 1980, J. Phys. A. 13, L325.
Fogelholm, R., 1980, J. Phys. C. 13, L571.
Fortuin, C.M. and Kasteleyn, P.W., 1972, Physica 57, 536.
Frank, D.J. and Lobb, C.J., 1983, unpublished.
Gefen, Y., Aharony, A., and Alexander, S., 1983, Phys. Rev. Lett 50, 77.
Gefen, Y., Aharony, A., Mandelbrot, B.B. and Kirkpatrick, 1981. Phys. Rev. Lett. 47, 1771.
de Gennes, P.G., 1976, La Recherche 7, 919.
Kasteleyn, P.W. and Fortuin, C.M. 1969, J. Phys. Soc. Japan (suppl) 26, 11.
Lobb, C.J. and Frank, D.J., 1979, J. Phys. C. 9, L827.
Ma, S.-K., 1976, Modern Theory of Critical Phenomena (Benjamin: Reading MA).
den Nijs, M.P.M., 1979, J. Phys. A. 12, 1857.
Pearson, R.B., 1980, Phys. Rev. B. 22, 2579.
Pfeuty, P. and Toulouse, G., 1977, Introduction to the Renormalization Group and to Critical Phenomena (Wiley: London).
Pike, R. and Stanley, H.E., 1981, J. Phys. A 14, L169.
Rammal, R. and Toulouse, G., 1983, J. de Physique 44, L13.
Render, S., 1982, Phys. Rev. B 24, 3242.
Redner, S., 1983, in Percolation Structure and Processes, ed. G. Deutscher, R. Zallen, and J. Adler. Annals of the Israel Physical Society, vol. 5 (Hilger: Bristol).
Redner, S. and Reynolds, P.J., 1981, J. Phys. A 14, 2679.
Reynolds, P.J., Klein, W. and Stanley, H.E., 1977, J. Phys. C 10, L167.
Reynolds, P.J., Stanley, H.E., and Klein, W., 1980, Phys. Rev. B 21, 1223.
Skal, A.S. and Shklovskii, B.I., 1975, Sov. Phys. Semicond. 8, 1029.
Stanley, H.E., 1981, in Lecture Notes in Physics, Disordered Systems and Localization, Proc. Rome Conf. 1981, ed C. Castellani, C. Di Castro and L. Peliti (Springer: Berlin).
Stanley, H.E., and Coniglio, A., in Percolation Structure and Processes, ed. G. Deutscher, R. Zallen, and J. Adler. Annals of the Israel Physical Society, vol 5 (Hilger: Bristol).
Stanley, H.E., Reynolds, P.J., Redner, S., and Family, F., 1982 in "Real-Space Renormalization" Topics in Current Physics 30, chap 7 (Springer: Berlin).
Stauffer, D., 1979, Phys. Rept. 54, 1
Stephen, M.J., 1976, Phys. Lett. 56A, 149.
Wu, F.Y., 1982. Rev. Mod. Phys. 54, 235.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Redner, S. (1983). Recent progress and current puzzles in percolation. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073260
Download citation
DOI: https://doi.org/10.1007/BFb0073260
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12707-9
Online ISBN: 978-3-540-38693-3
eBook Packages: Springer Book Archive