Critical Behavior of an Interacting Monomer-Dimer Model

Kim, Mann Ho; Park, Hyunggyu

doi:10.1103/physrevlett.73.2579

Cited by 126 publications

(158 citation statements)

References 19 publications

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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%

“…The reactions always take place at domain boundaries, hence the Z 2 symmetric A and B saturated phases are absorbing. The interacting monomer-dimer model (IMD) (Kim and Park, 1994) is a generalization of the simple monomer-dimer model (Ziff et al, 1986), in which particles of the same species have nearest-neighbor repulsive interactions. The IMD is parameterized by specifying that a monomer (A) can adsorb at a nearest-neighbor site of an already-adsorbed monomer (restricted vacancy) at a rate r A k A with 0 ≤ r A ≤ 1, where k A is an adsorption rate of a monomer at a free vacant site with no adjacent monomer-occupied sites.…”

Section: Pc Class Surface Catalytic Modelsmentioning

confidence: 99%

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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%

Section: Pc Class Surface Catalytic Modelsmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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“…In terms of the domain wall, there is a single absorbing state (vacuum) with parity conservation in the number of domain walls, since spin flips change it only in pairs. Other examples in the DI class includes the interacting monomer-dimer model [21], the branching-annihilating random walks with an even number of offspring [12,22], and generalized versions of the contact process [5,23]. There also exist models in the DI universality class that have infinitely many absorbing states [24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Universality class of absorbing transitions with continuously varying critical exponents

Noh

Park

2004

Phys. Rev. E

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The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a new type of critical phenomena distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory effect. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations show that the GPCPD displays novel type critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We suggest that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

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“…In one spatial dimension, parity conservation allows the particles to be considered as kinks between oppositely oriented domains [7,8]. Using this interpretation, the process can be regarded as a directed percolation process with two Z 2 -symmetric absorbing states (DP2) [9].…”

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confidence: 99%

Binary spreading process with parity conservation

2001

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Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure

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Critical Behavior of an Interacting Monomer-Dimer Model

Cited by 126 publications

References 19 publications

Universality classes in nonequilibrium lattice systems

Universality classes in nonequilibrium lattice systems

Universality class of absorbing transitions with continuously varying critical exponents

Binary spreading process with parity conservation

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