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29 March 2024
 
  » arxiv » cond-mat/0109443

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Growth Exponent in the Domany-Kinzel Cellular Automaton
A.P.F. Atman ; J.G. Moreira ;
Date 24 Sep 2001
Journal Eur. Phys. J. B, 16 (2000) pp. 501-505
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractIn a roughening process, the growth exponent $eta$ describes how the roughness $w$ grows with the time $t$: $wsim t^{eta}$. We determine the exponent $eta$ of a growth process generated by the spatiotemporal patterns of the one dimensional Domany-Kinzel cellular automaton. The values obtained for $eta$ shows a cusp at the frozen/active transition which permits determination of the transition line. The $eta$ value at the transition depends on the scheme used: symmetric ($eta sim 0.83$) or non-symmetric ($eta sim 0.61$). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.
Source arXiv, cond-mat/0109443
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