Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs.

@article{Bizhani2012DiscontinuousPT,
  title={Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs.},
  author={Golnoosh Bizhani and Maya Paczuski and Peter Grassberger},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={86 1 Pt 1},
  pages={011128}
}
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first-order behaviors in two different classes of models: The first are generalized epidemic processes that describe in their spatially embedded version--either on or off a regular lattice--compact or fractal cluster growth in random media at zero temperature. A random… CONTINUE READING
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