Directed percolation conjecture for cellular automata revisited

Abstract

The directed percolation (DP) hypothesis for stochastic, range-4 cellular automata with acceptance rule $y\le {\sum }_{j=-4}^4{s}_{i-j}\le 6$, 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.

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

References in corpus (1)

• Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.

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