Conductivity of a random directed-diode network near the percolation threshold

Abstract

We have investigated the conductivity in a random directed network of "ohmic" diodes, elements which exhibit ohmic response under a forward-bias voltage. A numerical method is developed to identify first the correct "state" of the network, the distribution of forward- and back-biased diodes within the directed backbone, and then calculate the conductivity near the percolation threshold. Extrapolation of Monte Carlo data on the square lattice by anisotropic finite-size scaling yields a directed conductivity exponent of $t_{+}\cong 0.60$.