Phase-transition study of a one-dimensional probabilistic site-exchange cellular automaton

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Abstract
The effect of mixing on one-dimensional probabilistic cellular automaton with totalistic rule has been investigated by different methods. The evolution of system depends on two parameters, the probability p and the degree of mixing m. The two-dimensional phase space of parameters has been explored by simulation. The results are compared to multiple-point-correlation approximation. By increasing the mixing, the order of the phase transition has been found to change from second order to first order. The tricritical point has been located and estimates are given for the β exponent. Short- and long-range mixing are compared.