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Partially Connected Systems

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Percolation, Localization, and Superconductivity

Part of the book series: NATO Science Series ((SPEPO,volume 109))

Abstract

Many physical structures are made of random “islands”,/ and in certain conditions, among these islands, one macroscopic continent emerges. This idea was displayed first in a historical article of Broadbent and Hammersley.1 It was rediscovered soon after (in connection with substitutional alloys) by Lafore, Millot, and the present writer.2 From this point on, most numerical studies on this “percolation phenomenon” were performed on periodic lattices where a fraction p of the sites (or of the bonds) was active, and a fraction 1-p was inactive — different sites (or bonds) being uncorrelated. But the results are more general: the statistics of islands near threshold is very universal.

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References

  1. S.R. Broadbent and J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 629 (1957).

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  2. P.G. de Gennes, P. Lafore, and J.P. Millot, J. Physique (Paris) 20, 624 (1959).

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  3. J.P. Clerc, G. Giraud, J. Rossenq, R. Blanc, J.P. Carton, E. Guyon, H. Ottavi, and D. Stauffer, Annales de Physique 8, 1 (1983). See also S. Kirkpatrick, Rev. Mod. Phys. 45, 574 (1973).

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  4. Y. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett. 50, 77 (1983); R. Rammal and G. Toulouse, J. Physique Lett. 44L, 13 (1983).

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  5. P.G. deGennes, Comptes Rend. Acad. Sci. Paris 292, 9 (1981).

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  6. P.G. deGennes, Comptes Rend. Acad. Sci. Paris 292, 279 (1981).

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  7. See for instances, P.G. de Gennes, “Superconductivity of metals and alloys”, Benjamin, NY (1964).

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  8. S. Alexander, to be published.

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  9. R. Rammal, T. Lubensky, and G. Toulouse, J. de Physique Lett. 44L, 65 (1983).

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Author information

Authors and Affiliations

  1. Ecole de Physique et Chemie, Paris, France

    P. G. de Gennes

Authors
  1. P. G. de Gennes
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Editor information

Editors and Affiliations

  1. School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota, USA

    Allen M. Goldman

  2. Metal Physics Branch, Naval Research Laboratory, Washington, D.C., USA

    Stuart A. Wolf

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© 1984 Plenum Press, New York

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de Gennes, P.G. (1984). Partially Connected Systems. In: Goldman, A.M., Wolf, S.A. (eds) Percolation, Localization, and Superconductivity. NATO Science Series, vol 109. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9394-2_4

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  • DOI: https://doi.org/10.1007/978-1-4615-9394-2_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9396-6

  • Online ISBN: 978-1-4615-9394-2

  • eBook Packages: Springer Book Archive

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