Infinite 3D Cubic Lattices of Identical Resistors

We expressed the resistance between the origin and any lattice point in an infinite perfect Simple Cubic (i.e., SC) network rationally in terms of the known value of the Lattice Green's Function at the origin (i.e., ), and . On the other hand, we investigated the asymptotic behavior of the resistance. Finally, some numerical results has been calculated.

SUBSTITUTIONAL SINGLE RESISTOR IN AN INFINITE SQUARE LATTICE APPLICATION TO LATTICE GREEN'S FUNCTION

The resistance between two arbitrary lattice sites in an infinite square lattice of identical resistors is studied when the lattice is perturbed by substituting a single resistor using lattice Green's function. The relation between the resistance and the lattice Green's function for the perturbed lattice is derived. 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 and experimental results are presented.