Both the infinite cluster and its backbone are self-similar at the percolation threshold, pc. This self-similarity also holds at concentrations p near pc, 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 LD, 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.
- Percolation theory
- anomalous diffusion at percolation
- fractal dimensionality
- fractal model for percolation
- magnetic correlations at percolation
- percolation above six dimensions