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.

Non-equilibrium critical phenomena and phase transitions into absorbing states

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or to defect $(D)$ unconditionally. The players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect. In the limits $\stackrel{\ensuremath{\rightarrow}}{c}0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

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Evolutionary prisoner's dilemma game on a square lattice

Preface 1. Introduction 2. Cellular automata modeling 3. Statistical mechanics of lattice gas 4. Diffusion phenomena 5. Reaction-diffusion processes 6. Non-equilibrium phase transitions 7. Other models and applications Bibliography Glossary Index.

Cellular automata modeling of physical systems

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.

Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1405&context=physastro_pubs

Random and cooperative sequential adsorption

An irreversible kinetic surface-reaction model, based upon the reaction of carbon monoxide and oxygen on a catalyst surface, is presented. It is found by computer simulation that the adsorbed molecules on the surface undergo both first- and second-order kinetic phase transitions. These transitions correspond to the "poisoning" phenomenon seen on catalysts. Interesting transient and periodic behavior is also seen.

Erdagon Gulari

Papers

Kinetic phase transitions in an irreversible surface-reaction model.