Bridge Percolation

Details Bridge Percolation Bridge Percolation

2011-03-16

arxiv.org/abs/1103.3256v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

In bridge percolation one gives a special weight to bridges, i.e., bonds that if occupied would create the first spanning cluster. We show that, above the classical-percolation threshold, the set of bridge bonds is fractal with a fractal dimension $d_{BB}=1.215\pm0.002$, for any $p>p_c$. This new percolation exponent is related to various different models like, e.g., the optimal path in strongly disordered media, the watershed line of a landscape, the shortest path of the optimal path crack, and the interface of the explosive-percolation clusters. Suppressing completely the growth of percolation clusters by blocking bridge bonds, a fracturing line is obtained splitting the system into two compact clusters. We propose a theta-point-like scaling between this fractal dimension and $1/\nu$, at the classical-percolation threshold, and disclose a hyperscaling relation with a crossover exponent. A similar scenario emerges for the cutting bonds. We study this new percolation model up-to six dimensions and find that, above the upper-critical dimension of classical percolation, the set of bridge bonds is dense and has the dimension of the system.

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