Absorbing-state phase transition for driven-dissipative stochastic dynamics on ℤ

@article{Rolla2012AbsorbingstatePT,
  title={Absorbing-state phase transition for driven-dissipative stochastic dynamics on ℤ},
  author={Leonardo T. Rolla and Vladas Sidoravicius},
  journal={Inventiones mathematicae},
  year={2012},
  volume={188},
  pages={127-150}
}
We study the long-time behavior of conservative interacting particle systems in ℤ: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition. 

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References

SHOWING 1-10 OF 55 REFERENCES

Self-organized criticality.

Generalized Hammersley Process and Phase Transition for Activated Random Walk Models

TLDR
It is proved that there is a unique phase transition for the one-dimensional finite-range random walk and some variables that are sufficient to characterize fixation and at the same time are stochastically monotone in the model's parameters are identified.

Self-organized criticality: An explanation of the 1/f noise.

We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical

Steady State of Stochastic Sandpile Models

We study the steady state of the Abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be

Fluctuation-Induced First-Order Transition in a Nonequilibrium Steady State

We present the first example of a phase transition in a nonequilibrium steady state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion

Driving sandpiles to criticality and beyond.

TLDR
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation but casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the Abelian sandpile model at stationarity.

Paths to self-organized criticality

We present a pedagogical introduction to self-organized criticality (SOC), unraveling its connections with nonequilibrium phase transitions. There are several paths from a conventional critical point

Critical behavior of a two-species reaction-diffusion problem

TLDR
An algorithm is presented that enables us to simulate simultaneously the full range of densities rho between zero and some maximum density and the critical initial increase exponent takes the value straight theta (')=0.30(2), in agreement with the theoretical relationstraight theta(')=-eta/2 due to Van Wijland et al.

Critical behavior of a one-dimensional diffusive epidemic process.

TLDR
A finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension d=1 finds that the correlation exponent nu=2 as predicted by field-theoretical arguments.
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