## Abstract

Both the infinite cluster and its backbone are self-similar at the percolation threshold, p_{c}. This self-similarity also holds at concentrations p near p_{c}, for length scales L which are smaller than the percolation connectedness length, ξ. For L<ξ, the number of bonds on the infinite cluster scales as L^{D}, where the fractal dimensionality D 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.

Original language | English |
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Pages (from-to) | 931-939 |

Number of pages | 9 |

Journal | Journal of Statistical Physics |

Volume | 34 |

Issue number | 5-6 |

DOIs | |

State | Published - Mar 1984 |

## Keywords

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