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.
B. D. Bookout and P. E. Parris, "Large-Cell Renormalization-Group Approach to Long-Range Hopping on Energetically Disordered Lattices," Physical Review B (Condensed Matter), vol. 48, no. 17, pp. 12637-12644, American Physical Society (APS), Nov 1993.
The definitive version is available at https://doi.org/10.1103/PhysRevB.48.12637
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© 1993 American Physical Society (APS), All rights reserved.