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.
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Aharony, A. Percolation, fractals, and anomalous diffusion. J Stat Phys 34, 931–939 (1984). https://doi.org/10.1007/BF01009449
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DOI: https://doi.org/10.1007/BF01009449