Phenomenological renormalization group for cellular automata

The phenomenological renormalization group method introduced by Barber (1983) for equilibrium spin models is extended to stochastic cellular automata exhibiting continuous phase transitions from a quiescent state to an active one. The method is applied to the Domany-Kinzel model (1984), which contains bond and site directed percolation in 1+1 dimensions as special cases. A new universality class with critical exponents close to, but definitely different from, the ones of directed percolation is predicted. Finite-size scaling analysis and Monte Carlo simulations provide further support to this result.