Multifractality of conductance jumps in percolation

We show that the distributions of conductance and resistance jumps in a random resistor network at the percolation threshold are multifractal. These two spectra are related to each other by a simple translation. We discuss the relations between these spectra and that of the current distribution at the percolation threshold. These novel multifractal behaviors at the critical point give rise to power laws appearing in the distributions of the conductance and resistance jumps when recorded throughout a random dilution process from the intact state to the percolation threshold. We demonstrate these ideas through numerical simulations and through analytical calculations on simple models. We discuss the relation between this problem and that of local versus global damage criteria in connection with the rupture of brittle disordered materials.