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

Дата и время публикации : 2000-02-23T17:05:25Z

Авторы публикации и институты :
Franco Bagnoli
Nino Boccara
Raul Rechtman

Ссылка на журнал-издание: Phys. Rev E 63, 46116 (2001)
Коментарии к cтатье: 19 pages with 7 figures
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech

Краткий обзор статьи: 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.

Category: Physics