Non-equilibrium critical phenomena and phase transitions into absorbing states

By H. Hinrichsen. 2000

1,423 citations recorded by the source corpus.

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-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

Subfields: Condensed Matter Physics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd6d9af9032ede040d16318ab268dbf3899f3f55

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Citations in the corpus

Colloquium: Criticality and dynamical scaling in living systems (2017, methodology): “(1) by a field ρ(x, t) and to introduce a diffusive coupling term (Henkel et al., 2008; Hinrichsen, 2000; Ódor, 2008).”
Non-equilibrium steady states: fluctuations and large deviations of the density and of the current (2007, background): “The matrix ansatz of section VI (which gives the weights of the microscopic configurations in the steady state) has been generalized to describe the steady state of several other systems [12, 62, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124]”
Evolutionary games on graphs (2006, methodology): “The general properties of these so-called heteroclinic cycles and their relevance to ecological models were described and discussed in a more general context by May and Leonard (1975) and Hofbauer and Sigmund (1988). The above numerical investigations suggest that the stationary solutions of the pai”
The nonperturbative functional renormalization group and its applications (2020, background): “The most common ones are absorbing phase transitions, which separate an active fluctuating steady-state from one, or several, absorbing states, with no fluctuations [457–459].”
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics (2009, result): “In this respect, it is worth pointing out that some studies did use this perspective: thus, it has been shown that the extinction transitions when the temptation parameter varies within the Prisoner’s Dilemma game and the evolutionary dynamics is stochastic fall in the directed percolation universal”
UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS (2004, methodology): “Instead of going into the details we refer the interested readers to the reviews [7, 8, 90].”
Universality classes in nonequilibrium lattice systems (2002, background): “There are many introductory works available now on directed percolation sKinzel, 1983; Grassberger, 1996; Marro and Dickman, 1999; Hinrichsen, 2000ad.”
The density-matrix renormalization group (2004, background): “These transitions are characterized by universal critical exponents, quite analogously to equilibrium phase transitions ssee Hinrichsen, 2000 for a reviewd.”
Recent advances in percolation theory and its applications (2015, background): “ space. It accounts for one of the most prominent universality classes of nonequilibrium phase transitions, playing a similar role as the Ising universality class in equilibrium statistical mechanics [239]. Directed percolation models exhibit a continuous phase transition with a fascinating property”
An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “In particular, for 1D, this model makes a connection to the critical behavior of the directed percolation universality class for absorbing-state phase transitions [37].”
Evolutionary game theory: Theoretical concepts and applications to microbial communities (2010, background): “The broader class of absorbing-state transitions has recently been reviewed [129].”