Growth exponent in the Domany-Kinzel cellular automaton

Abstract.

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