The coherent potential method in the diffusion problem on a random substitution lattice

Based on the balance equation, we consider the diffusion problem on a hyperlattice with randomly distributed inaccessible sites. Using diagram methods, we find a self-consistent expression for the configurationally averaged Green's function in the coherent potential approximation. We show that this approach is applicable in a broad range of concentrations of accessible sites. Using this approximation, we find the exact asymptotic form of the static diffusion coefficient for a low concentration of blocked sites. This allows making good estimates of the percolation threshold in the random-site diffusion problem on an arbitrary hyperlattice.