Phase diagram of a probabilistic cellular automaton with three-site interactions.

Abstract

We study a (1+1)-dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel stochastic-cellular automaton (DKCA), but in which the update of a given site depends on the state of three sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter p(3) representing the probability for a site to be active at time t, given that it and its nearest neighbors were active at time t-1. We study phase transitions and critical behavior for the activity and for damage spreading, using one- and two-site mean-field approximations, and simulations, for p(3)=0 and p(3)=1. We find evidence for a line of tricritical points in the (p(1),p(2),p(3)) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For p(3)=0, the phase diagram is similar to the DKCA, but the damage-spreading transition exhibits a reentrant phase. For p(3)=1, the growth-exponent method reproduces the two absorbing states, first- and second-order phase transitions, bicritical point, and damage-spreading transition recently identified by Bagnoli et al. [Phys. Rev. E 63, 046116 (2001)].