Negative moments of the current spectrum in the random-resistor network

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Abstract
We demonstrate numerically that the negative moments of the current distribution in the two-dimensional random-resistor network at the percolation threshold are governed by a singularity due to the smallest nonzero currents. The fractal dimension of this singularity is zero. This leads to constant-gap scaling for the negative moments. It is not ruled out that all the negative scaling exponents may be infinite, indicating that the moments do not scale with power laws. We also show that the fractal dimension of the perfectly balanced bonds is equal to that of the mass of the backbone itself.