Real-space renormalization and effective-medium approximation to the percolation conduction problem

We present a new approach, the renormalized effective-medium approximation (REMA), for the percolation conductivity problem in disordered conductance networks. This approach combines real-space renormalization and effective-medium approximation techniques. We use it to investigate two-, three-, and four-dimensional bond-disordered conductance networks. REMA provides excellent predictions for the network conductivity $g\left(p\right)\mathrm{}$ over the entire range of fraction $p$ of conducting bonds in two and three dimensions. REMA reproduces the exact bond percolation threshold of the square lattice and predicts bond percolation thresholds for the simple cubic lattices in three and four dimensions which differ only by about 6% and 1%, respectively, from the best available estimates. It also provides good estimates of the conductivity critical exponents $t$ and $s$ in both two and three dimensions.