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Bagnoli F, Boccara N, Rechtman R. Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. Phys Rev E Stat Nonlin Soft Matter Phys. 2001;63(4):046116doi: 10.1103/PhysRevE.63.046116.
Bagnoli, F., Boccara, N., & Rechtman, R. (2001). Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. Physical review. E, Statistical, nonlinear, and soft matter physics, 63(4), 046116. https://doi.org/10.1103/PhysRevE.63.046116
Bagnoli, F, et al. "Nature of phase transitions in a probabilistic cellular automaton with two absorbing states." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 63,4 (2001): 046116. doi: https://doi.org/10.1103/PhysRevE.63.046116
Bagnoli F, Boccara N, Rechtman R. Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Apr;63(4):046116. doi: 10.1103/PhysRevE.63.046116. Epub 2001 Mar 29. PMID: 11308921.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Apr;63(4):046116. doi: 10.1103/PhysRevE.63.046116. Epub 2001 Mar 29.

Nature of phase transitions in a probabilistic cellular automaton with two absorbing states.

Physical review. E, Statistical, nonlinear, and soft matter physics

F Bagnoli, N Boccara, R Rechtman

Affiliations

  1. Dipartimento di Matematica Applicata, Università di Firenze, via Santa Marta 3, I-50139 Florence, Italy. [email protected]

PMID: 11308921 DOI: 10.1103/PhysRevE.63.046116

Abstract

We present a probabilistic cellular automaton with two absorbing states, which can be considered a natural extension of the Domany-Kinzel model. Despite its simplicity, it shows a very rich phase diagram, with two second-order and one first-order transition lines that meet at a bicritical point. We study the phase transitions and the critical behavior of the model using mean field approximations, direct numerical simulations and field theory. The second-order critical curves and the kink critical dynamics are found to be in the directed percolation and parity conservation universality classes, respectively. The first-order phase transition is put in evidence by examining the hysteresis cycle. We also study the "chaotic" phase, in which two replicas evolving with the same noise diverge, using mean field and numerical techniques. Finally, we show how the shape of the potential of the field-theoretic formulation of the problem can be obtained by direct numerical simulations.

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