Pair Connectedness and Shortest Path Scaling in Critical Percolation
Statistical Mechanics
2009-10-31 v1
Abstract
We present high statistics data on the distribution of shortest path lengths between two near-by points on the same cluster at the percolation threshold. Our data are based on a new and very efficient algorithm. For they clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58}, R5205 (1998). Our data also provide upper bounds on the probability that two near-by points are on different infinite clusters.
Cite
@article{arxiv.cond-mat/9906309,
title = {Pair Connectedness and Shortest Path Scaling in Critical Percolation},
author = {P. Grassberger},
journal= {arXiv preprint arXiv:cond-mat/9906309},
year = {2009}
}
Comments
7 pages, including 4 postscript figures