Resistance networks with resistances from statistical distributions: exploring how characteristic parameters scale with distance from current input node

A random resistance network is a simple yet powerful model to study a multitude of fascinating physical phenomena in condensed matter and statistical physics, owing to the fact that the network models are easily simulated since only scalar quantities are involved. We study a random resistance network constituting of a square lattice wherein the magnitudes of the resistances are obtained from different statistical distributions (all about a fixed mean value), for example, completely random, Gaussian distribution and exponential disorder, as well as resistance fractures. Using these resistance networks, characteristic parameters of the lattice such as equivalent resistance between nodes, optimal current paths, nodal current values etc. are studied. In a particular configuration, where the input current enters the lattice centrally and exits from the four corners of the lattice, the characteristic parameters are studied at large distances for perturbations restricted to varying distances from the central node, to understand the scaling of perturbations with distance from current input node. Computational experiments are carried out and the results are obtained numerically. Analysis carried out aims to explore a broader physical understanding of the results obtained.