  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.
