Percolative conduction in anisotropic media: A renormalization-group approach

Abstract

We apply renormalization-group transformations to a square random resistor lattice with conductance anisotropy. The bulk conductance of the lattice is studied as the bond probability and degree of anisotropy are varied. The transformations yield qualitatively correct results, although differences from numerical simulations increase as the degree of anisotropy is increased. The bulk conductance of the lattice becomes isotropic near the percolation threshold but only in an asymptotic region which shrinks as the lattice becomes more anisotropic. Near the percolation threshold the anisotropy in the macroscopic conductance vanishes as ${(p-p_c)}^{\lambda }$, where $\lambda =0.86\mathrm{}\pm 0.1$.