Monochromatic path crossing exponents and graph connectivity in 2D percolation
Statistical Mechanics
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0207063,
title = {Monochromatic path crossing exponents and graph connectivity in 2D percolation},
author = {Jesper Lykke Jacobsen and Paul Zinn-Justin},
journal= {arXiv preprint arXiv:cond-mat/0207063},
year = {2007}
}
Comments
3 pages, 2 eps-figures