Journal of Statistical Physics

, Volume 34, Issue 5–6, pp 931–939 | Cite as

Percolation, fractals, and anomalous diffusion

  • Amnon Aharony
Articles
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Abstract

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p c . This self-similarity also holds at concentrationsp nearp c , for length scalesL which are smaller than the percolation connectedness length,ξ. ForL<ξ, the number of bonds on the infinite cluster scales asL D , where the fractal dimensionalityD is equal to(d-β/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.

Key words

Percolation theory fractal dimensionality self-similarity fractal model for percolation percolation above six dimensions magnetic correlations at percolation anomalous diffusion at percolation 
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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Amnon Aharony
    • 1
  1. 1.Department of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

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