Richard A Neher et al J. Stat. Mech. (2008) P01011 doi:10.1088/1742-5468/2008/01/P01011
Richard A Neher1,3, Klaus Mecke2 and Herbert Wagner1
Show affiliationsGlobal physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two-dimensional lattice graphs, we use the universal scaling form of the cluster size distributions to derive a relation between the mean Euler characteristic of the critical percolation patterns and the threshold density pc. From this relation, we deduce a simple rule to estimate pc, which is remarkably accurate. We present some evidence that similar relations might hold for continuum percolation and percolation in higher dimensions.
E-print Number: 0708.3250
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 01 (January 2008)
Received 9 October 2007, accepted for publication 9 November 2007
Published 11 January 2008
Richard A Neher et al J. Stat. Mech. (2008) P01011
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