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

The electric resistance between two arbitrary lattice points in infinite d- dimensional hypercubic lattices with second nearest neighbor) 2nd NN) resistors is calculated by using lattice Green's function. The resistance for square, and simple cubic lattices with 2nd 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