Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
TL;DR: In this article, a review of recent developments in nonequilibrium statistical physics is presented, focusing on phase transitions from fluctuating phases into absorbing states, and several examples of absorbing-state transitions which do not belong to the directed percolation universality class are discussed.
read more
Abstract: This review addresses recent developments in nonequilibrium 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 nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Recent advances in percolation theory and its applications
TL;DR: In this paper, a variety of percolation models have been introduced some of which have completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, dimensionality and the type of the underlying rules and networks.
261
Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
TL;DR: In this paper, a review of spatially confined, non-equilibrium physics in nanoporous media is presented. And a particular emphasis is put on texture formation upon crystallisation in nanopore-confined condensed matter, a topic both of high fundamental interest and of increasing nanotechnological importance.
257
First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
Juan P. Garrahan,Robert L. Jack,Vivien Lecomte,Estelle Pitard,K. van Duijvendijk,F. van Wijland +5 more
TL;DR: In this article, the dynamics of kinetically constrained models of glass formers were investigated by analyzing the statistics of trajectories of the dynamics, or histories, using large deviation function methods, and it was shown that these models exhibit a first-order dynamical transition between active and inactive dynamical phases.
256
Directed percolation phase transition to sustained turbulence in Couette flow
TL;DR: In this article, it was shown that the onset of turbulence is a second-order phase transition and falls into the directed percolation universality class, and that the complex laminar-turbulent patterns distinctive for the onset time of turbulence in basic shear flows are characterized by universal critical exponents.
Applications of field-theoretic renormalization group methods to reaction-diffusion problems
TL;DR: In this paper, the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems is reviewed, with a focus on the generic directed percolation universality class and the most prominent exception to this class: even-offspring branching and annihilating random walks.
References
•Book
Stochastic processes in physics and chemistry
N.G. van Kampen,William P. Reinhardt +1 more
- 01 Jan 1981
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
•Book
Exactly solved models in statistical mechanics
Rodney Baxter
- 01 Jan 1982
TL;DR: In this article, exactly solved models of statistical mechanics are discussed. But they do not consider exactly solvable models in statistical mechanics, which is a special issue in the statistical mechanics of the classical two-dimensional faculty of science.
8.8K
Density matrix formulation for quantum renormalization groups
TL;DR: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented and it is shown that this formulation is optimal in a certain sense.
8.3K
•Book
Introduction to percolation theory
Dietrich Stauffer,Amnon Aharony +1 more
- 01 Jan 1992
TL;DR: In this article, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
7.4K
Theory of Dynamic Critical Phenomena
TL;DR: The renormalization group theory has been applied to a variety of dynamic critical phenomena, such as the phase separation of a symmetric binary fluid as mentioned in this paper, and it has been shown that it can explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions.
6.8K