Crossover from directed percolation to mean field behavior in the diffusive contact process

@article{Messer2008CrossoverFD,
  title={Crossover from directed percolation to mean field behavior in the diffusive contact process},
  author={Andrea Messer and Haye Hinrichsen},
  journal={arXiv: Statistical Mechanics},
  year={2008}
}
Recently Dantas, Oliveira and Stilck [J. Stat. Mech. (2007) P08009] studied how the one-dimensional diffusive contact process crosses over from the critical behavior of directed percolation to an effective mean field behaviour when the diffusion rate is sent to infinity. They showed that this crossover can be described in terms of a crossover exponent $\phi$, finding the boundaries 3 <= $\phi$ <= 4 in one spatial dimension. In the present work we refine and extend this result up to four spatial… 
Crossovers from parity conserving to directed percolation universality.
  • G. Ódor, N. Menyhárd
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method and the resulting models show a diversity within the DP universality class in one dimension.
Forest fire modeling using cellular automata and percolation threshold analysis
  • Sangil Pak, T. Hayakawa
  • Environmental Science, Computer Science
    Proceedings of the 2011 American Control Conference
  • 2011
TLDR
A new method is proposed to derive the critical probability, below which forest fires do not expand to infinitely large area, using percolation theory and mean-field approximation.

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