Tolerance and Sensitivity in the Fuse Network

TL;DR

This paper investigates how the fuse network's breakdown process is affected by small noise in the threshold distribution, revealing a transition between sensitivity and insensitivity based on the distribution's properties.

Contribution

It identifies a critical threshold distribution exponent that determines the network's sensitivity to noise, linking it to a known localization-delocalization transition.

Findings

Network sensitivity depends on the threshold distribution's power law exponent.

A second-order transition separates sensitive and insensitive regimes.

The transition relates to a previously observed localization-delocalization phenomenon.

Abstract

We show that depending on the disorder, a small noise added to the threshold distribution of the fuse network may or may not completely change the subsequent breakdown process. When the threshold distribution has a lower cutoff at a finite value and a power law dependence towards large thresholds with an exponent which is less than $0.16\pm0.03$, the network is not sensitive to the added noise, otherwise it is. The transition between sensitivity or not appears to be second order, and is related to a localization-delocalization transition earlier observed in such systems.