Directed-percolation conjecture for cellular automata

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Abstract

The directed-percolation (DP) hypothesis for stochastic, range-4 cellular automata with an acceptance rule y ≤ ∑j=-44 si-j ≤ 6, in the cases of y : {1, ⋯ , 5}, Si {0,1} 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 for y <4 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 university; but in the cases of y > 1 the transitions become first order.

Original languageEnglish
Pages (from-to)2231-2238
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number3
Publication statusPublished - 1996

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Directed Percolation
cellular automata
Cellular Automata
One Dimension
acceptability
Renormalization Group
Mean Field
Anomaly
Two Dimensions
anomalies
First-order
Range of data
Simulation
simulation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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