An Algorithm-Independent Definition of Damage Spreading—Application to Directed Percolation

@article{Hinrichsen1997AnAD,
  title={An Algorithm-Independent Definition of Damage Spreading—Application to Directed Percolation},
  author={Haye Hinrichsen and Joshua S. Weitz and Eytan Domany},
  journal={Journal of Statistical Physics},
  year={1997},
  volume={88},
  pages={617-636}
}
We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner that does not depend on the particular dynamic procedure that is being used. The formalism can be used for any spin-model or cellular automaton, with sequential or parallel update rules. At this point we present its application to the Domany–Kinzel cellular automaton in one dimension, this being the simplest model in which damage spreading… 
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References

SHOWING 1-10 OF 56 REFERENCES
On damage-spreading transitions
We study the damage-spreading transition in a generic one-dimensional stochastic cellular automaton with two inputs (Domany-Kinzel model). Using an original formalism for the description of the
Are damage spreading transitions generically in the universality class of directed percolation?
We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martinset al. is in the same universality class as directed percolation. We
Evidence for a new phase in the Domany-Kinzel cellular automaton.
TLDR
A generalized version (including anisotropy) of the stochastic one-dimensional cellular automaton studied by Domany and Kinzel is considered, which recovers Wolfram-like deterministic cellular automata as particular cases and recognizes the Glauber dynamics, for example, as a special case of a CA.
Comparative study of damage spreading in the Ising model using heat-bath, glauber, and metropolis dynamics
AbstractWe study the time evolution of two configurations of the Ising model submitted to heat-bath (HB), Glauber (G), and two types of Metropolis (M and $$\tilde M$$ ) dynamics, analyzing the damage
Time-dependent thermodynamic properties of the Ising model from damage spreading
The relationship between damage spreading and static thermodynamic properties in the Ising model developed by Coniglioet al. is here extended to include time-dependent thermodynamic quantities. We
Time-dependent perturbation theory for nonequilibrium lattice models.
We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation
Directed compact percolation: cluster size and hyperscaling
Exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice. The corresponding relation for the moment generating
...
...