The random fuse network as a dipolar magnet
CEA, Service de Physique de la Matière Condensée BP12, 91680
2 Department of Physics, Harvard University - Cambridge, MA 02138, USA
3 CEA, Service de Physique Théorique - 91191 Gif-sur-Yvette, Cedex, France
Accepted: 9 January 2002
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.
PACS: 62.20.Mk – Fatigue, brittleness, fracture, and cracks / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems
© EDP Sciences, 2002