J. Phys. I France
Volume 3, Numéro 1, January 1993
Page(s) 21 - 28
DOI: 10.1051/jp1:1993113
J. Phys. I France 3 (1993) 21-28

Ordered cellular automata in one dimension

P.-M. Binder, D. Y. K. Ko, A. L. Owczarek and C. J. Twining

Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, G.B.

(Received 5 October 1992, accepted 9 October 1992)

We study a probabilistic one-dimensional majority-rule two-state cellular automaton and examine the stability of ordered magnetised states in systems of size L as the neighbourhood radius R varies. We find that a scaling $R \sim \ln L$ is sufficient for an ordered phase to be metastable, i.e., to survive for times much longer than the typical critical fluctuation. The lattice magnetisation obeys a scaling relation which agrees with results from mean-field analysis.

05.50 - 64.60 - 75.10

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