| 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.
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