An extinction-survival-type phase transition in the probabilistic cellular automaton p182?q200

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction?survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

[1]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

[2]  Roughening transition in a one-dimensional growth process. , 1995, Physical review letters.

[3]  J. R. G. Mendonça,et al.  Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Grinstein,et al.  Statistical mechanics of probabilistic cellular automata. , 1985, Physical review letters.

[5]  J. Lebowitz,et al.  Statistical mechanics of probabilistic cellular automata , 1990 .

[6]  P. Rujan,et al.  Cellular automata and statistical mechanical models , 1987 .

[7]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[8]  A Vespignani,et al.  Avalanche and spreading exponents in systems with absorbing states. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Tânia Tomé.  Spreading of damage in the Domany-Kinzel cellular automaton: A mean-field approach , 1994 .

[10]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems , 1999, Encyclopedia of Complexity and Systems Science.

[11]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[12]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[13]  I. Jensen.  Low-density series expansions for directed percolation: I. A new efficient algorithm with applications to the square lattice , 1999, cond-mat/9906036.

[14]  Eytan Domany,et al.  Equivalence of Cellular Automata to Ising Models and Directed Percolation , 1984 .

[15]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[16]  J. Ricardo G. de Mendoncca.  Precise Critical Exponents for the Basic Contact Process , 1999 .

[17]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[18]  Stephen Wolfram,et al.  Cellular Automata And Complexity , 1994 .

[19]  G. Ódor.  Universality classes in nonequilibrium lattice systems , 2002, cond-mat/0205644.

[20]  H. Fuks.  Solution of the density classification problem with two cellular automata rules , 1997, comp-gas/9703001.

[21]  F Bagnoli,et al.  Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  LETTER TO THE EDITOR: Precise critical exponents for the basic contact process , 1999 .

[23]  W. Kinzel.  Phase transitions of cellular automata , 1985 .