Perturbation of infinite networks of resistors

Details Perturbation of infinite networks of resistors Perturbation of infinite networks of resistors

2001-07-17

arxiv.org/abs/cond-mat/0107362v1

American Journal of Physics 70, 153-159 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 4 figures, submitted to American Journal of Physics

Scientific paper

10.1119/1.1419104

The resistance between arbitrary nodes of infinite networks of resistors is studied when the network is perturbed by removing one bond from the perfect lattice. A connection is made between the resistance and the lattice Green's function of the perturbed network. Solving Dyson's equation the Green's function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results are presented for a square lattice. Our method of the lattice Green's function in studying resistor networks can also be applied in the field of random walks as well as electrical and mechanical breakdown phenomena in insulators, thin films and modern ceramics.

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