Generalized dielectric breakdown model

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