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

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

2000-02-23

arxiv.org/abs/cond-mat/0002361v2

Phys. Rev E 63, 46116 (2001)

Physics

Condensed Matter

Statistical Mechanics

19 pages with 7 figures

Scientific paper

10.1103/PhysRevE.63.046116

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 tricritical point. We study the phase transitions and the critical behavior of the model using mean field approximations, direct numerical simulations and field theory. A closed form for the dynamics of the kinks between the two absorbing phases near the tricritical point is obtained, providing an exact correspondence between the presence of conserved quantities and the symmetry of absorbing states. 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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