CRITICAL-BEHAVIOR OF A PROBABILISTIC LOCAL AND NONLOCAL SITE-EXCHANGECELLULAR AUTOMATION

We study the critical behavior of a probabilistic automata network who se local rule consists of two subrules. The first one, applied synchro nously, is a probabilistic one-dimensional range-one cellular automato n rule. The second, applied sequentially, exchanges the values of a pa ir of sites. According to whether the two sites are first-neighbors or not, the exchange is said to be local or nonlocal. The evolution of t he system depends upon two parameters, the probability p characterizin g the probabilistic cellular automaton, and the degree of mixing m res ulting from the exchange process. Depending upon the values of these p arameters, the system exhibits a bifurcation similar to a second order phase transition characterized by a nonnegative order parameter, whos e role is played by the stationary density of occupied sites. When m i s very large, the correlations created by the application of the proba bilistic cellular automaton rule are destroyed, and, as expected, the behavior of the system is then correctly predicted by a mean-field-typ e approximation. According to whether the exchange of the site values is local or nonlocal, the critical behavior is qualitatively different as m varies.