Self-organized criticality as an absorbing-state phase transition

@article{Dickman1998SelforganizedCA,
  title={Self-organized criticality as an absorbing-state phase transition},
  author={Ronald Dickman and Alessandro Vespignani and Stefano Zapperi},
  journal={Physical Review E},
  year={1998},
  volume={57},
  pages={5095-5105}
}
We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving field h - are set to their critical values. The critical values of epsilon and h are both equal to zero. The first is due to the absence of saturation (no bound on energy) in the sandpile model, while the second result is common to other absorbing-state… 

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References

SHOWING 1-2 OF 2 REFERENCES
NATO Advanced Study Institute.
  • M. Wolbarsht
  • Engineering, Medicine
    IEEE transactions on medical imaging
  • 1986
At the beginning of this symposium, Dr. K. Smith presented the basic laws of photobiology. However, as the laser is a special type of light source, so indeed, the laws of photobiology take a special
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