Growth exponent in the Domany-Kinzel cellular automaton

In a roughening process, the growth exponent beta describes how the roughness omega grows with the time t: omega similar to t(beta). We determine the exponent beta of a growth process generated by the spatiotemporal patterns of the one-dimensional Domany-Kinzel cellular automaton. The values obtained for beta show a cusp at the frozen/active transition which permits determination of the transition line. The beta value at the transition depends on the scheme used: symmetric (beta similar or equal to 0.83) or non-symmetric (beta similar or equal to 0.61). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.