Roughness exponent in the Domany-Kinzel cellular automaton

Abstract

We propose a method to detect phase transitions in discrete lattice models based on the roughness exponent. This approach is applied to the one-dimensional Domany-Kinzel cellular automaton (CA). Our results, obtained by numerical simulations, show that the roughness exponent method detects the frozen-active phase transition directly from the CA spatio-temporal configurations without any reference to thermodynamical potentials, order parameters or response functions.