Correlation function studies on the Domany–Kinzel cellular automaton

The Domany–Kinzel cellular automaton is a simple and yet very rich model to study phase transitions in nonequilibrium systems. This model exhibits three characteristic phases: frozen, active and chaotic. In this paper we discuss the behavior of the equal-time two-point correlation functions and that of the associated correlation lengths as one crosses the phase boundary both for the frozen–active and active–chaotic transitions. We have investigated in detail how the correlation lengths diverge as one approaches the phase boundary from both sides. The divergence of the correlation length coupled with the previous studies on the divergence of the susceptibility, suggests that the fluctuation–dissipation theorem holds true in the Domany–Kinzel cellular automaton model. Time dependence of the correlation functions is also discussed.