Scaling exponents of rough surfaces generated by the Domany-Kinzel cellular automaton

The critical behavior at the frozen-active transition in the Domany-Kinzel stochastic cellular automaton is studied via a surface growth process in (1+1) dimensions. At criticality, this process presents a kinetic roughening transition; we measure the critical exponents in simulations. Two update schemes are considered: in the symmetric scheme, the growth surfaces belong to the directed percolation (DP) universality class, except at one terminal point. At this point, the phase transition is discontinuous and the surfaces belong to the compact directed percolation universality class. The relabeling of space-time points in the nonsymmetric scheme alters significantly the surface growth, changing the values of the critical exponents. The critical behavior of rough surfaces at the nonchaotic-chaotic transition is also studied using the damage spreading technique; the exponents confirm DP values for the symmetric scheme.