Monochromatic path crossing exponents and graph connectivity in 2D percolation

dc.creatorJacobsen, Jesper Lykke
dc.creatorZinn-Justin, Paul
dc.date2002-07-02
dc.date.accessioned2026-07-07T02:46:04Z
dc.date.available2026-07-07T02:46:04Z
dc.descriptionWe 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.
dc.description3 pages, 2 eps-figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0207063
dc.identifierhttp://arxiv.org/abs/cond-mat/0207063
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/19529
dc.subjectStatistical Mechanics
dc.titleMonochromatic path crossing exponents and graph connectivity in 2D percolation
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