Abstract
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.
