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.
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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.
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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