Algorithmic Mapping Criticality into Self Organized Criticality

Abstract

Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties of these models are usually obtained by fine-tuning one or more control parameters, as for instance the temperature. We present a method for the parallel evolution of the model for all the values of the control parameter, although its implementation is in general limited to a fixed number of values. This algorithm facilitates the sketching of phase diagrams and can be useful in deriving the critical properties of the model. Since the criticality here emerges from the asymptotic distribution of some quantities, without tuning of parameters, our method is a mapping from a probabilistic cellular automaton with critical behavior to a self organized critical model with the same critical properties.