New universality for spatially disordered cellular automata and directed percolation

Abstract

Stochastic cellular automata (SCA) with fixed, but randomly chosen, probabilities (spatial disorder) are studied in D dimensions. For zero disorder, the present SCA reduce to directed percolation in (D+1) space-time, but finite spatial disorder is incompatible with the critical exponents of directed percolation. Monte Carlo calculations of the SCA on several disordered structures in D=1 and D=2 yield new universal exponents. I also discuss the phase diagram of ``diluted'' SCA, which contains a multicritical point and the SCA analog of a ``Griffiths phase'' with nonexponential relaxation.