Dependence of percolation thresholds on lattice connectivity

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Abstract
We investigate site percolation on lattices with directed bonds. Numerical simulations in which the lattice coordination number of the percolation lattices is systematically varied show that the inverse of the percolation threshold depends approximately linearly on the lattice coordination number. We show that this linear relationship is due to a similarity of percolation clusters in lattices for different coordination numbers. We compare this relationship to results obtained by Flory [Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953), Chap. IX] in the study of gelation processes and discuss its general applicability for related percolation models.

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