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Pair connectedness and shortest-path scaling in critical percolation

Peter Grassberger

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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 1998 Phys. Rev. E 58 R5205. Our data also provide upper bounds on the probability that two near-by points are on different infinite clusters.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

MSC

82B43 Percolation (See also 60K35)

82B27 Critical phenomena

Subjects

Statistical physics and nonlinear systems

Dates

Issue 35 (3 September 1999)

Received 24 June 1999



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