Abstract
The boundaries between the three phases of the Domany-Kinzel probabilistic cellular automaton are determined with high accuracy via the gradient method. The difficulties the extrapolation to the thermodynamic limit are circumvented and the critical exponents are also presented.
This is a preview of subscription content, log in via an institution to check access.
References
S. Wolfram,Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).
D. Stauffer,J. Phys. A 24:909 (1991).
E. Domany and W. Kinzel,Phys. Rev. Lett. 53:311 (1984); W. Kinzel,Z. Phys. B 58:229 (1985).
M. L. Martins, H. F. Verona de Rezende, C. Tsallis, and A. C. N. de Magalhães,Phys. Rev. Lett. 66:2045 (1991).
G. A. Kohring and M. Schreckenberg,J. Phys. I (Paris)2:2033 (1992).
J. Cook and B. Derrida,J. Phys. A,23:1523 (1990).
B. Sapoval, M. Rosso, and J.-F. Gouyet,J. Phys. Lett. (Paris)46:L749 (1985).
L. R. da Silva and H. J. Herrmann,J. Stat. Phys. 52:463 (1988).
N. Boissin and H. J. Herrmann,J. Phys. A 24:L43 (1991).
G. G. Batrouni and A. Hansen,J. Phys. A 25:L1059 (1992).
M. L. Martins, G. F. Zebende, T. J. P. Penna, and C. Tsallis, preprint (1993).
Author information
Authors and Affiliations
Additional information
Communicated by D. Staffer
Rights and permissions
About this article
Cite this article
Zebende, G.F., Penna, T.J.P. The Domany-Kinzel cellular automaton phase diagram. J Stat Phys 74, 1273–1279 (1994). https://doi.org/10.1007/BF02188230
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02188230