Exact critical exponent for the shortest-path scaling function in percolation

Details Exact critical exponent for the shortest-path scaling function in percolation Exact critical exponent for the shortest-path scaling function in percolation

1999-07-20

arxiv.org/abs/cond-mat/9907305v3

J. Phys. A. 32, L457-L459 (27 October 1999)

Physics

Condensed Matter

Statistical Mechanics

References updated, small corrections 4 pages. Published version

Scientific paper

10.1088/0305-4470/32/43/101

It is shown that the critical exponent $g_1$ related to pair-connectiveness
and shortest-path (or chemical distance) scaling, recently studied by Porto et
al., Dokholyan et al., and Grassberger, can be found exactly in 2d by using a
crossing-probability result of Cardy, with the outcome $g_1 = 25/24$. This
prediction is consistent with existing simulation results.

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