On the resistance of an infinite square network of identical resistors – Theoretical and experimental comparison

Abstract

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,

Infinite Body Centered Cubic Network of Identical Resistors

“…It is worth mentioning that for other cubic networks (i.e., sc and face centered cubic, fcc) the resistance approaches a nite value for large separation between the two sites [30,33,37], whereas for the innite square lattice it goes to innity [30,34].…”

Exact Evaluation of the Resistance in an Infinite Face-Centered Cubic Network

“…which is the LGF at the origin in an infinite SC lattice, while the resistance in an infinite square network diverges for large separation between the two sites [36]. Table Caption Table 1: Calculated values of F(2n,0,0;3) Table 1:…”

Remarks on the Lattice Green Function for the Anisotropic Face Centered Cubic Lattice

“…Nowadays, GF is one of the most important concepts in many branches of physics, as many quantities in solid state physics can be expressed in terms of the LGF. In the following there are some examples: statistical model of ferromagnetism such as the Ising model [5], the Heisenberg model [6], spherical model [7], random walk theory [8,9], diffusion [10], band structure [11], and in recent * corresponding author; e-mail: drjasad@yahoo.com years it becomes an important tool in analyzing infinite electric networks [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”