Equivalence of Cellular Automata to Ising Models and Directed Percolation

@article{Domany1984EquivalenceOC,
  title={Equivalence of Cellular Automata to Ising Models and Directed Percolation},
  author={Eytan Domany and Wolfgang Kinzel},
  journal={Physical Review Letters},
  year={1984},
  volume={53},
  pages={311-314}
}
Time development of cellular automata in $d$ dimensions is mapped onto equilibrium statistical mechanics of Ising models in $d+1$ dimensions. Directed percolation is equivalent to a cellular automaton, and thus to an Ising model. For a particular case of directed percolation we find ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=2$, ${\ensuremath{\nu}}_{\ensuremath{\perp}}=1$, ${\ensuremath{\eta}}_{\ensuremath{\perp}}=0$. 

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