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Scaling Phenomena in Disordered Systems pp 301–306Cite as

Magnetic Properties Near Percolation

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Abstract

At the percolation threshold, clusters of connected sites exhibit self-similar fractal geometry, in which many geometrical properties scale as powers of the relevant length scales. This motivated both the construction of fractal models, on which physical problems may be solved exactly,1,2 and the detailed study of various geometrical characteristics of percolation clusters.3,4 In this lecture we shall review the effects of this fractal geometry on the magnetic correlations of spins at and near the percolation threshold. The results reflect on neutron scattering experiments from percolation clusters and similar fractals.

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References

  1. Y. Gefen, A. Aharony, B.B. Mandelbrot and S. Kirkpatrick, Phys. Rev. Lett. 47: 1771 (1981).

    Article  MathSciNet  Google Scholar 

  2. B.B. Mandelbrot and J. Given, Phys. Rev. Lett. 52: 1853 (1984).

    Article  Google Scholar 

  3. R. Pike and H.E. Stanley, J. Phys. A14: L169 (1981).

    Google Scholar 

  4. A. Coniglio, Phys. Rev. Lett. 46: 250 (1981);

    Article  Google Scholar 

  5. A. Coniglio, J. Phys. A15: 3829 (1982).

    MathSciNet  Google Scholar 

  6. Y. Gefen, B.B. Mandelbrot and A. Aharony, Phys. Rev. Lett. 45: 855 (1980).

    Article  MathSciNet  Google Scholar 

  7. Y. Gefen, A. Aharony and B.B. Mandelbrot, J. Phys. A16: 1267 (1983).

    MathSciNet  Google Scholar 

  8. Y. Gefen, A. Aharony, Y. Shapir and B.B. Mandelbrot, J. Phys. A17: 435 (1984).

    MathSciNet  Google Scholar 

  9. Y. Gefen, A. Aharony and B.B. Mandelbrot, J. Phys. A17: 1277 (1984).

    MathSciNet  Google Scholar 

  10. Y. Gefen, Y. Meir, B.B. Mandelbrot and A. Aharony, Phys. Rev. Lett. 50: 145 (1983).

    Article  MathSciNet  Google Scholar 

  11. A. Aharony, Y. Gefen and Y. Kantor, J. Stat. Phys. 36: 767 (1984).

    Article  MathSciNet  Google Scholar 

  12. R.J. Birgeneau, R.A. Cowley, G. Shirane and H. Yoshizawa, J. Stat. Phys. 34: 817 (1984).

    Article  Google Scholar 

  13. J. Adler, Z. Phys. 55: 227 (1984).

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Amnon Aharony

  2. Institute of Theoretical Physics, University of California, Santa Barbara, California, 93106, USA

    Yuval Gefen

  3. Exxon Corporate Research Laboratory, Clinton, New Jersey, 08801, USA

    Yacov Kantor

Authors
  1. Amnon Aharony
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  2. Yuval Gefen
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  3. Yacov Kantor
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Editor information

Editors and Affiliations

  1. Laue-Langevin Institute, 38042, Grenoble, France

    Roger Pynn

  2. Institute for Energy Technology, 2007, Kjeller, Norway

    Arne Skjeltorp

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© 1991 Springer Science+Business Media New York

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Aharony, A., Gefen, Y., Kantor, Y. (1991). Magnetic Properties Near Percolation. In: Pynn, R., Skjeltorp, A. (eds) Scaling Phenomena in Disordered Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1402-9_25

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  • DOI: https://doi.org/10.1007/978-1-4757-1402-9_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1404-3

  • Online ISBN: 978-1-4757-1402-9

  • eBook Packages: Springer Book Archive

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