Monochromatic path crossing exponents and graph connectivity in 2D percolation

Details Monochromatic path crossing exponents and graph connectivity in 2D percolation Monochromatic path crossing exponents and graph connectivity in 2D percolation

2002-07-02

arxiv.org/abs/cond-mat/0207063v1

Physics

Condensed Matter

Statistical Mechanics

3 pages, 2 eps-figures

Scientific paper

We consider the fractal dimensions d_k of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions X_k = 2-d_k describe the asymptotic decay of the probabilities P(r,R) ~ (r/R)^{X_k} that an annulus of radii r<<1 and R>>1 is traversed by k disjoint paths, all living on the percolation clusters. Using a transfer matrix approach, we obtain numerical results for X_k, k<=6. They are well fitted by the Ansatz X_k = 1/12 k^2 + 1/48 k + (1-k)C, with C = 0.0181+-0.0006.

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