Two-point resistance on hypercubic lattices with second nearest neighbor resistors

Abstract

The electric resistance between two arbitrary lattice points in infinite d- dimensional hypercubic lattices with second nearest neighbor) 2^nd NN) resistors is calculated by using lattice Green's function. The resistance for square, and simple cubic lattices with 2^nd NN resistors is discussed in detail. For large separation between lattice points the finite limiting value of the resistance for a simple cubic lattice with second nearest neighbor resistors is calculated.

Keywords: Green’s function, hypercubic lattices, resistance.