Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice

DOI10.1088/1751-8113/42/46/465001zbMATH Open1179.82077arXiv0903.3111OpenAlexW2083980274MaRDI QIDQ3650330

Author name not available (Why is that?)

Publication date: 14 December 2009

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: Our study is based on the work of Stinchcombe [1974 emph{J. Phys. C} extbf{7} 179] and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi [1974 emph{Phys. Rev. B} extbf{9} 4575] for the regular lattice.

Full work available at URL: https://arxiv.org/abs/0903.3111

zbMATH Keywords

Bethe lattice percolation threshold

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)