TOPICAL REVIEW: The non-equilibrium phase transition of the pair-contact process with diffusion

@article{Henkel2004TOPICALRT,
  title={TOPICAL REVIEW: The non-equilibrium phase transition of the pair-contact process with diffusion},
  author={Malte Henkel and Haye Hinrichsen},
  journal={Journal of Physics A},
  year={2004}
}
The pair-contact process 2A ? 3A, 2A ? ? with diffusion of individual particles is a simple branching-annihilation process which exhibits a phase transition from an active to an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years, it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent… 
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The phase transition of the diffusive pair contact process revisited
Coupled two-species model for the pair contact process with diffusion.
TLDR
A two-species representation for the PCPD is introduced in which single particles B and particle pairs A are dynamically coupled according to the stochastic reaction processes B+B→A, A→A+B,–A→∅, and A→B-B, with each particle type diffusing independently.
Phase transition in an exactly solvable reaction-diffusion process.
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The model exhibits a phase transition at a particular point in the phase diagram which can be related to a condensation transition in a particular zero-range process and the corresponding critical exponents are determined.
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TLDR
To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, numerically a variation of the PCPD is studied by introducing a nonorder field associated with infinitely many absorbing states and it is found that a crossover from thePCPD to DP occurs due to the non order field.
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