Critical Behavior of Random Resistor Networks

We present numerical data and scaling theories for the critical behavior of random resistor networks near the percolation threshold. We determine the critical exponents of a suitably defined resistance correlation function by a Padé analysis of low-concentration expansions as a function of dimensionality. We verify that $d=6\mathrm{}$ is the critical dimensionality for the onset of mean-field behavior. We use the coherent-potential approximation to construct a mean-field scaling function for the critical region.