Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold

Abstract

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth moments of the current distribution, finding {\it e.g.\/} that $t/\nu=2.282(5)$ where $t$ is the conductivity exponent and $\nu$ is the correlation length exponent.