1 research outputs found
The inactive-active phase transition in the noisy additive (exclusive-or) probabilistic cellular automaton
We investigate the inactive-active phase transition in an array of additive
(exclusive-or) cellular automata under noise. The model is closely related with
the Domany-Kinzel probabilistic cellular automaton, for which there are
rigorous as well as numerical estimates on the transition probabilities. Here
we characterize the critical behavior of the noisy additive cellular automaton
by mean field analysis and finite-size scaling and show that its phase
transition belongs to the directed percolation universality class of critical
behavior. As a by-product of our analysis, we argue that the critical behavior
of the noisy elementary CA 90 and 102 (in Wolfram's enumeration scheme) must be
the same. We also perform an empirical investigation of the mean field
equations to assess their quality and find that away from the critical point
(but not necessarily very far away) the mean field approximations provide a
reasonably good description of the dynamics of the PCA.Comment: 21 pages, 6 figures, 48 references. To appear in the Int. J. Mod.
Phys. C (2016