Bridge Percolation

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, for p > pc, even far away from the critical point of classical percolation, the set of bridge bonds is fractal with a fractal dimension dBB = 1.215±0.002. 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 discontinuous-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/ν, 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 dimension six 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.