Monochromatic path crossing exponents and graph connectivity in 2D percolation
| dc.creator | Jacobsen, Jesper Lykke | |
| dc.creator | Zinn-Justin, Paul | |
| dc.date | 2002-07-02 | |
| dc.date.accessioned | 2026-07-07T02:46:04Z | |
| dc.date.available | 2026-07-07T02:46:04Z | |
| dc.description | 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. | |
| dc.description | 3 pages, 2 eps-figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0207063 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0207063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/19529 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Monochromatic path crossing exponents and graph connectivity in 2D percolation | |
| dc.type | text |