Perturbed Infinite 3D Simple Cubic Network of Identical Capacitors

Abstract

The eective capacitance between the origin and any other lattice site, in an innite 3D simple cubic network consisting of identical capacitors, is evaluated in terms of the lattice Green function of the network. The perfect case is reviewed shortly, while the perturbed case (a capacitor is removed) is studied in two cases. Numerical values of the eective capacitance are presented and the asymptotic behavior is studied for the both cases.