arXiv:cond-mat/9506139·v1·cond-mat

Directed percolation conjecture for cellular automata revisited

Géza Ódor · Attila Szolnoki

Abstract

The directed percolation (DP) hypothesis for stochastic, range-4 cellular automata with acceptance rule $y \leq \sum_{j = - 4}^{4} s_{i - j} \leq 6$ , in cases of $y < 6$ was investigated in one and two dimensions. Simulations, mean-field renormalization group and coherent anomaly calculations show that in one dimension the phase transitions for $y < 4$ are continuous and belong to the DP class for $y = 4, 5$ they are discontinuous. The same rules in two dimensions for $y = 1$ show $2 + 1$ dimensional DP universality; but in cases of $y > 1$ the transitions become first order.

Comments: 20 pages + 6 figures, RevTex, submitted to Phys. Rev. E