FIRST-ORDER TRANSITION IN THE BREAKDOWN OF DISORDERED MEDIA

We study the approach to global breakdown in disordered media driven b y increasing external forces. We first analyze the problem by mean-fie ld theory, showing that the failure process can be described as a firs t-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the pre dictions of the mean-field theory using numerical simulations of discr ete models. Widely distributed avalanches and the corresponding mean-f ield scaling are explained by the long-range nature of elastic interac tions. We discuss the analogy of our results to driven disordered firs t-order transitions and spinodal nucleation in magnetic systems.