The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the Lattice Green's Function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to infinity. Finally, numerical results are obtained along different directions and a comparison is carried out with the perfect capacitances.

A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases) is carried out using the lattice Green's function. We show how to calculate the resistance between the origin and any other site using the lattice Green's function at the origin,

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Green's Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. This method can be applied directly to other lattice structures.

It is shown that the resistance between the origin and any lattice pointin an infinite perfect Simple Cubic (SC) is expressible rationally in terms of the known value ofThe resistance between arbitrary sites in a SC is also studied and calculated when one of the resistors is removed from the perfect lattice. Finally, the asymptotic behavior of the resistance for both the perfect and perturbed SC is also investigated.

An infinite regular three-dimensional network is composed of identical resistors each of resistance R joining adjacent nodes. What is the equivalent resistance between the lattice site i r r and the lattice j r r site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites.