Tolerance and sensitivity in the fuse network

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+or-0.03, the network is not sensitive to the added noise, otherwise it is. The transition between sensitivity and insensitivity appears to be second order, and is related to a localization-delocalization transition observed earlier in such systems.
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