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Partial dimensional sequences and percolation

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Abstract

We discuss a new mathematical approach of describing fractal lattices by means of transfer matrices of fractals (TMFs). These matrices have interesting mathematical properties. Possible physical applications of the TMFs are briefly indicated.

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References

  1. B. B. Mandelbrot, Y. Gefen, A. Aharony, and J. Peyriére, to be published: Y. Gefen, thesis, Tel-Aviv University, unpublished.

  2. B. B. Mandelbrot,The Fractal Nature of the Universe (Freeman, San Francisco, 1982).

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  3. Y. Gefen, B. B. Mandelbrot, and A. Aharony,Phys. Rev. Lett. 45:855 (1980); Y. Gefen, A. Aharony, B. B. Mandelbrot, and Y. Meir,Phys. Rev. Lett. 50:145 (1983); Y. Gefen, A. Aharony, and B. B. Mandelbrot,J. Phys. A. 17:1277 (1984).

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of California, 93106, Santa Barbara, California

    Yuval Gefen

  2. I.B.M. Thomas J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, New York

    B. B. Mandelbrot

  3. Department of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel

    A. Aharony

  4. Institute for Polymers and Organic Solids, University of California, 93106, Santa Barbara, California

    A. Kapitulnik

Authors
  1. Yuval Gefen
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  2. B. B. Mandelbrot
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  3. A. Aharony
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  4. A. Kapitulnik
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Gefen, Y., Mandelbrot, B.B., Aharony, A. et al. Partial dimensional sequences and percolation. J Stat Phys 36, 827–830 (1984). https://doi.org/10.1007/BF01012942

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  • DOI: https://doi.org/10.1007/BF01012942

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