Highly efficient algorithm for percolative transport studies in two dimensions

Abstract

We present a fast algorithm using the Y-∇ transformation for calculating the conductance of large two-dimensional random resistor lattices. The procedure can also be used to calculate other quantities for which Y-∇ transformations can be defined. As an example of the method’s usefulness, we present extensive data on square random resistor lattices as large as 1000 bonds on a side. Using this data, we estimate that the conductivity exponent t${=1.303\mathrm{}}_{\mathrm{-}0.014}^{+0.004\mathrm{}}$ in two dimensions.