Renormalization group of the Domany-Kinzel cellular automaton

TL;DR

This paper applies a dynamical renormalization group approach to analyze the critical behavior of the Domany-Kinzel cellular automaton, successfully deriving its phase diagram and correlation length exponent.

Contribution

It introduces a specific renormalization scheme that preserves absorbing states, providing new insights into the automaton's phase transitions and critical properties.

Findings

Phase diagram of the automaton obtained

Critical exponent for spatial correlation length determined

Method preserves absorbing state clusters during renormalization

Abstract

We apply the dinamically driven renormalization group to study the critical properties of the Domany-Kinzel probabilistic cellular automaton. To preserve the absorbing state clusters with at least one site occupied are renormalized into a one occupied site and clusters with all sites empty are renormalized into a one empty site. We have obtained the phase diagram as well as the critical exponent related to the spatial correlation length.