The Random Fuse Network as a Dipolar Magnet
Statistical Mechanics
2009-11-07 v2 Disordered Systems and Neural Networks
Abstract
We introduce an approximate mapping between the random fuse network (RFN) and a random field dipolar Ising model (RFDIM). The state of the network damage is associated with a metastable spin configuration. A mean-field treatment, numerical solutions, and heuristic arguments support the broad validity of the approximation and yield a generic phase diagram. At low disorder, the growth of a single unstable `crack' leads to an abrupt global failure. Beyond a critical disorder, the conducting network sustains significant damage before the coalescence of cracks results in global failure.
Cite
@article{arxiv.cond-mat/0106012,
title = {The Random Fuse Network as a Dipolar Magnet},
author = {Marc Barthelemy and Rava da Silveira and Henri Orland},
journal= {arXiv preprint arXiv:cond-mat/0106012},
year = {2009}
}
Comments
6 pages, 2 figures