Pair Connectedness and Shortest Path Scaling in Critical Percolation

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 $d=2$ 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.

7 pages, including 4 postscript figures

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