Directed-percolation conjecture for cellular automata
Géza Ódor, Attila Szolnoki · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1996
The directed-percolation (DP) hypothesis for stochastic, range-4 cellular automata with an acceptance rule y\ensuremath{\le}${\mathit{tsum}}_{\mathit{j}=\mathrm{\ensuremath{-}}4}^{4}$${\mathit{s}}_{\mathit{i}\mathrm{\ensuremath{-}}\mathit{j}}$\ensuremath{\le}6, in the cases of y6, was investigated in one and two dimensions. Simulations, as well as mean-field renormalization-group and coherent-anomaly calculations, show that in one dimension the phase transitions for y4 are continuous and belong to the DP class, while for y=4,5 they are discontinuous. The same rules in two dimensions for y=1 show (2+1)-dimensional DP universality; but in the cases of y>1 the transitions become first order. \textcopyright{} 1996 The American Physical Society.