Statistical mechanics of dielectric breakdown

A statistical picture of dielectric breakdown in solids is presented and discussed in this paper. The morphology selection mechanism is described by the stochastic model or η model. The approach is formulated in terms of two functions α(η) and β(η), which play the role of a free energy and that of an inverse temperature, respectively. Numerical evidence for a description of the probability distribution of branched structures grown on a square lattice is reported.