Growth Exponent in the Domany-Kinzel Cellular Automaton

Details Growth Exponent in the Domany-Kinzel Cellular Automaton Growth Exponent in the Domany-Kinzel Cellular Automaton

2001-09-24

arxiv.org/abs/cond-mat/0109443v1

Eur. Phys. J. B, 16 (2000) pp. 501-505

Physics

Condensed Matter

Statistical Mechanics

13 pages, 6 figures

Scientific paper

In a roughening process, the growth exponent $\beta$ describes how the roughness $w$ grows with the time $t$: $w\sim t^{\beta}$. 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 $\beta$ shows 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 ($\beta \sim 0.83$) or non-symmetric ($\beta \sim 0.61$). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.

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