Generalized Dielectric Breakdown Model

TL;DR

This paper introduces a generalized Dielectric Breakdown Model that interpolates between different growth processes, revealing new phase transition phenomena and fractal dimension variations influenced by a temperature-like parameter.

Contribution

It develops a unified framework connecting various fractal growth models and uncovers a novel phase transition at zero temperature, enhancing understanding of self-organization in growth phenomena.

Findings

Fractal dimension varies continuously with temperature.

Evidence of a zero-temperature phase transition.

Temperature influences self-organized invasion percolation.

Abstract

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, as a temperature like parameter is varied. The physics of other well known fractal growth phenomena as Invasion Percolation and the Eden model are also recovered for some particular parameter values. The competition between different growing mechanisms leads to new non-trivial effects and allows us to better describe real growth phenomena. Detailed numerical and theoretical analysis 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 an evidence of a novel phase transition at zero temperature in 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 new insight into the connections between self-organization and standard phase transitions.