Conductivity of a square-lattice bond-mixed resistor network

Abstract

Within a real-space renormalization-group framework based on self-dual clusters, we calculate the conductivity of a square-lattice quenched bond--random resistor network, the conductance on each bond being ${g}_{1}$ or ${g}_{2}$ with probabilities 1-p and p, respectively. The group recovers several already known exact results (including slopes), and is consequently believed to be numerically quite reliable for almost all values of p, and all ratios ${g}_{1}$/${g}_{2}$ (in particular, ${g}_{1}$=0 and ${g}_{1}$=\ensuremath{\infty} with finite ${g}_{2}$, respectively, correspond to the insulator-resistor and superconductor-resistor mixtures).