Abstract
We study the phase transitions of a family of nine-neighbor, two-state, totalistic, probabilistic cellular automata with one absorbing phase in order to assess the extent to which a simple mean-field approximation of cellular automata (CA) is valid. The focus is put on the order of the transition and the existence of universality classes for space dimensions 1 < d < 4. In particular, our numerical results show significant discrepancies with the critical behavior of directed percolation, a system usually believed to be the prototype of two-state probabilistic CA with one absorbing phase. The problem of the definition of universality classes is then discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
for a review article on directed percolation see: W. Kinzel, Ann. Israel Phys. Soc. 5, 425, 1983.
W. Kinzel, Z. Phys. B 58, 229, 1985.
H. Chate and P. Manneville, Phys. Rev. Lett. 58, 112, 1987.
H. Chate and P. Manneville, Physica 32D, 409, 1988; Europhys. Lett. 6, 591, 1988.
P. Bergé, Nucl. Phys. B (Proc. Suppl) 2, 247, 1987; S. Ciliberto and P. Bigazzi, Phys. Rev. Lett. 60, 286, 1988; F. Daviaud, M. Dubois and P. Bergé, Europhys. Lett., in press.
Y. Pomeau, Physica 23D, 3, 1986.
R. Bidaux, N. Boccara and H. Chaté, Phys. Rev. A 39, 3094, 1989.
S. Wolfram, Theory and Applications of Cellular Automata, World Scientific, Singapore, 1986.
See e.g.: N. Boccara, Symétries Brisées, Hermann, Paris, 1976.
H. Chaté and R. Bidaux, to be published.
H. Chaté and P. Manneville, “Collective behaviors in classical many-body dynamical systems”, in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bidaux, R., Boccara, N., Chaté, H. (1989). Phase Transitions of Two-State Probabilistic Cellular Automata with One Absorbing Phase. In: Manneville, P., Boccara, N., Vichniac, G.Y., Bidaux, R. (eds) Cellular Automata and Modeling of Complex Physical Systems. Springer Proceedings in Physics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75259-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-75259-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75261-2
Online ISBN: 978-3-642-75259-9
eBook Packages: Springer Book Archive