Exact critical exponent for the shortest-path scaling function in percolation
Abstract
It is shown that the critical exponent g1 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 g1 = 25/24. This prediction is consistent with existing simulation results.
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