Reentrant phase diagram of branching annihilating random walks with one and two offspring

Kwon, Sungchul; Park, Hyunggyu

doi:10.1103/physreve.52.5955

Cited by 43 publications

(39 citation statements)

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“…A pair of adjacent vacancies is required for a dimer to adsorb, so a state with alternating sites occupied by monomers can be identified with an absorbing state. The PC class phase transition of the r A = r B = 0 infinite repulsive case has been investigated in (Hwang et al, 1998;Kim and Park, 1994;Kwon and Park, 1995;Park et al, 1995;Park and Park, 1995). As one can see the basic reactions are similar to those of the MM model (eq.…”

Section: Pc Class Surface Catalytic Modelsmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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Section: Pc Class Surface Catalytic Modelsmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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“…Pair annihilation is allowed only between identical particles (A i + A i → ∅). In the branching process, a particle A i creates two identical particles in its neighborhood (A i → A i + 2A j ), with rate σ for i = j and rate σ ′ /(N − 1) for i = j.For N = 1, this model exhibits an absorbing transition of directed Ising type (Z 2 symmetry) at finite branching rate [10][11][12][13]. The N species generalization imposes the permutation symmetry S N between species.…”

mentioning

confidence: 99%

“…For N = 1, this model exhibits an absorbing transition of directed Ising type (Z 2 symmetry) at finite branching rate [10][11][12][13]. The N species generalization imposes the permutation symmetry S N between species.…”

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“…The survival probability never decays (δ = 0). When two offspring are placed both to the left or both to the right side of the parent particle with equal probability (dynamic branching) [12], S(t) decays with a nontrivial scaling exponent.…”

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“…With hardcore interaction, S(t) depends crucially on where to create two offspring with respect to their parent. When two offspring are divided by their parent (static branching) [12], they have no chance to meet each other. The survival probability never decays (δ = 0).…”

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Does Hard Core Interaction Change Absorbing-Type Critical Phenomena?

2000

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It has been generally believed that hardcore interaction is irrelevant to absorbing type critical phenomena because the particle density is so low near an absorbing phase transition. We study the effect of hardcore interaction on the N species branching annihilating random walks with two offspring and report that hardcore interaction drastically changes the absorbing type critical phenomena in a nontrivial way. Through Langevin equation type approach, we predict analytically the values of the scaling exponents, ν ⊥ = 2, z = 2, α = 1/2, β = 2 in one dimension for all N > 1. Direct numerical simulations confirm our prediction. When the diffusion coefficients for different species are not identical, ν ⊥ and β vary continuously with the ratios between the coefficients.The study of nonequilibrium systems with trapped (absorbing) states has been very active in recent years [1]. Models displaying absorbing phase transitions describe a wide range of phenomena, in particular, epidemic spreading, catalytic chemical reactions, and transport in disordered media. Furthermore, the absorbing transition is one of the simplest and natural extensions of the well-established equilibrium phase transition to nonequilibrium systems, which are still poorly understood.The concept of universality, which plays a key role in equilibrium critical phenomena, was shown to be applicable also to nonequilibrium absorbing transitions. Critical behavior near an absorbing transition is determined by properties such as dimensionality and symmetry, and is not affected by details of the system. Finding a new universality class is difficult, and only a few classes of absorbing transitions are known [1].Hardcore interaction between particles or kinks has been believed to be irrelevant to absorbing type critical phenomena, because the particle density is so low near an absorbing transition that the probability of multiple occupations at a site should be too small to be significant. This conventional belief leads to recent successes of field theoretical techniques using bosonic type operators [2][3][4][5][6]. However, it is well known that hardcore interaction does changes the asymptotic decay behavior of the particle density in many multi-species diffusion-reaction models near an annihilation fixed point [7]. Since many absorbing transition models can be mapped onto diffusionreaction ones, it may seem natural to ask a question whether hardcore constraint changes the absorbing type universality classes in multi-species models. Despite recent efforts using fermionic formulation incorporating hardcore interactions [8,9], the effect of hardcore interactions is barely understood both analytically and numerically.In this Letter, we study the N species branching annihilating random walks with two offspring (N -BAW(2)), introduced recently by Cardy and Täuber [6]. The model was solved exactly for all N > 1, using renormalization group techniques in bosonic type formulation which ignores hardcore interactions. We employ Langevin equation type approach incorporat...

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Scaling Relations in Absorbing Phase Transitions with a Conserved Field in One Dimension

Lee

2009

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Reentrant phase diagram of branching annihilating random walks with one and two offspring

Cited by 43 publications

References 23 publications

Universality classes in nonequilibrium lattice systems

Universality classes in nonequilibrium lattice systems

Does Hard Core Interaction Change Absorbing-Type Critical Phenomena?

Scaling Relations in Absorbing Phase Transitions with a Conserved Field in One Dimension

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