Non-Gaussian Fluctuations in Biased Resistor Networks: Size Effects versus Universal Behavior

TL;DR

This study investigates resistance fluctuation distributions in biased resistor networks, revealing size-dependent non-Gaussian behavior that becomes universal near criticality, especially in highly disordered systems, with implications for thin film conductors.

Contribution

It demonstrates that non-Gaussian resistance fluctuations are size-dependent and universal near the conductor-insulator transition in disordered networks, highlighting the influence of network shape and disorder level.

Findings

Non-Gaussian fluctuations vanish with increasing size in most systems.

Highly disordered networks show persistent non-Gaussianity in large sizes.

Distribution shape depends on network anisotropy and disorder level.

Abstract

We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and biased processes of breaking and recovery of the elementary resistors. The fluctuations of the network resistance are calculated by Monte Carlo simulations which are performed for different values of the applied current, for networks of different size and shape and by considering different levels of intrinsic disorder. The distribution of the resistance fluctuations generally exhibits relevant deviations from Gaussianity, in particular when the current approaches the threshold of electrical breakdown. For two-dimensional systems we have shown that this non-Gaussianity is in general related to finite size effects, thus it vanishes in the thermodynamic limit, with the remarkable exception of highly disordered networks. For these systems, close to the critical point of the conductor-insulator transition, non-Gaussianity persists in the large size limit and it is well described by the universal Bramwell-Holdsworth-Pinton distribution. In particular, here we analyze the role of the shape of the network on the distribution of the resistance fluctuations. Precisely, we consider quasi-one-dimensional networks elongated along the direction of the applied current or trasversal to it. A significant anisotropy is found for the properties of the distribution. These results apply to conducting thin films or wires with granular structure stressed by high current densities.