Large-Cell Renormalization-Group Approach to Long-Range Hopping on Energetically Disordered Lattices

We describe an approach for computing the conductivity associated with long-range hopping on energetically disordered lattices. Using a numerically exact supercell procedure we compute the distribution ρL(γ) of block conductances γL associated with conducting cubes of edge length L that are randomly chosen from the disordered system of interest. This distribution of block conductances is then used in a self-consistent numerical calculation to obtain the renormalized bulk conductivity. The approach displays a surprisingly fast approach to the infinite-system limit, allowing finite-size effects to be minimized. In this paper we use this approach to study transport in a series of binary lattices containing a random distribution of two enegetically inequivalent ions. Specific examples considered include variations of the nearest-neighbor site percolation problem, long-range hopping on more general binary lattices, and the trapping-to-percolation transition that occurs in such systems.