Generalized Dielectric Breakdown Model

We propose a generalized version of the dielectric breakdown model (DBM) for generic breakdown processes. It interpolates between the standard DBM and its analog with quenched disorder (QDBM), as a temperaturelike parameter is varied. The physics of other well-known fractal growth phenomena such as invasion percolation and the Eden model are also recovered for some particular parameter values. Competition between different growing mechanisms leads to nontrivial effects and allows us to better describe real growth phenomena. Numerical and theoretical analyses are performed to study the interplay between the elementary mechanisms. In particular, we observe a continuously changing fractal dimension as temperature is varied, and report evidence of a phase transition at zero temperature in the absence of an external driving field; the temperature acts as a relevant parameter for the "self-organized" invasion percolation fixed point. This permits us to obtain insight into the connections between self-organization and standard phase transitions.