Non-equilibrium critical phenomena and phase transitions into absorbing states

@article{Hinrichsen2000NonequilibriumCP,
  title={Non-equilibrium critical phenomena and phase transitions into absorbing states},
  author={Haye Hinrichsen},
  journal={Advances in Physics},
  year={2000},
  volume={49},
  pages={815 - 958}
}
This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing… 
Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations.
TLDR
This work theoretically addresses a nonequilibrium universal phenomena scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition and proposes how this physics could be explored within gases of interacting atoms excited to Rydberg states.
Non-equilibrium phase transitions
Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models.
  • U. Basu, P. K. Mohanty
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
A model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density is introduced and it is shown that both the density of active sites and the survival probability vanish as the particle density is decreased below half.
Absorbing state phase transitions with a non-accessible vacuum
We analyse from the renormalization group perspective a universality class of reaction–diffusion systems with absorbing states. In this class, models where the vacuum state is not accessible are
Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states
We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a
Explosive phase transitions in percolation processes
Percolation processes are well studied in physics. In theoretical physics, directed percolation (DP) is a representative of a well-known universality class of continuous phase transitions [1]. DP has
Simplest nonequilibrium phase transition into an absorbing state.
TLDR
Different versions of these models are studied and it is confirmed that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display nontrivial behavior, with critical exponents differing from their mean-field values, representing a universality class.
Directed Percolation and Other Systems with Absorbing States
We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states.
Phase Transitions and Scaling in Systems Far From Equilibrium
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful
Absorbing-state phase transitions with extremal dynamics.
TLDR
The absorbing BS model is revisited, obtaining refined estimates for the threshold and critical exponents in one dimension and an extremal version of the usual contact process is studied, using mean-field theory and simulation.
...
...

References

SHOWING 1-10 OF 505 REFERENCES
Phase Structure of Systems with Infinite Numbers of Absorbing States
Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to
Nonequilibrium phase transitions in systems with infinitely many absorbing states.
  • Jensen, Dickman
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
TLDR
One of the models exhibiting a continuous phase transition from an active state to an absorbing state in which the system is trapped is used to illustrate how finite-size scaling concepts may be used to enhance computer-simulation studies of the critical behavior.
Theory of Branching and Annihilating Random Walks.
TLDR
A new universality class has been observed in d = 1 for even values of m, when the number of particles is locally conserved modulo 2, and another issue which clearly requires theoretical explanation is the occurrence of a transition at a finite value of σm.
Numerical analysis of a Langevin equation for systems with infinite absorbing states
One-dimensional systems with an infinite number of absorbing states exhibit a phase transition that is not fully understood yet. Their static critical exponents are universal and belong in the
Critical phenomena of nonequilibrium dynamical systems with two absorbing states
We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit
Smooth phases, roughening transitions, and novel exponents in one-dimensional growth models
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the
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
On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state
It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlögl's first reaction) exhibit nevertheless a second order phase transition
Critical phenomena in nonequilibrium phase transitions
We discuss a number of models associated with phase transitions in purely kinetic models where detailed balance does not hold as in thermal equilibrium systems. These models include some of the
...
...