Hungary

Menyhárd, Attila

doi:10.1007/978-3-211-77572-1_16

Tort and Insurance Law

DOI: 10.1007/978-3-211-77572-1_16

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Hungary

Attila Menyhárd

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“…A few models have appeared in the literature which have two equivalent absorbing states. Those are the model A and B of probabilistic cellular automa (PCA) introduced by Grassberger et al [12,13], nonequilibrium kinetic Ising models with two different dynamics (NKI) [14,15], and the interacting monomer-dimer model (IMD) [16,17]. The PCA and NKI models are single-component models, while the IMD model is a multi-component model.…”

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Critical behavior of an absorbing phase transition in an interacting monomer-dimer model

Park

1995

Physica A: Statistical Mechanics and its Applications

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We study a monomer-dimer model with repulsive interactions between the same species in one dimension. With infinitely strong interactions the model exhibits a continuous transition from a reactive phase to an inactive phase with two equivalent absorbing states. Static and dynamic Monte Carlo simulations show that the critical behavior at the transition is different from the conventional directed percolation universality class but is consistent with that of the models with the mass conservation of modulo 2. The values of static and dynamic critical exponents are compared with those of other models. We also show that the directed percolation universality class is recovered when a symmetry-breaking field is introduced.PACS numbers: 64.60.-i, 02.50.-r, 05.70.Ln, 82.65.Jv A monomer-dimer(MD) model was introduced by Ziff, Gulari, and Barshad to describe the oxidation of carbon monoxide on catalytic surface [1]. In this model, a monomer (CO) adsorbs onto a single vacant site, while a dimer (O 2 ) adsorbs onto a pair of adjacent vacant sites and then immediately dissociates. A nearest neighbor of adsorbates, comprised of a dissociated O atom and an CO atom, reacts and forms a CO 2 molecule and desorbs from the metal surface. In two dimensions, as the CO gas pressure is lowered, the system undergoes a first-order transition from a CO-saturated inactive phase into a reactive steady state and then a continuous transition into a O 2 -saturated inactive phase. This continuous transition is shown to be in the same universality class as the directed percolation (DP) [2,3,4]. In one dimension, there is only a first-order phase transition between two saturated phases.

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Critical behavior of an absorbing phase transition in an interacting monomer-dimer model

Park

1995

Physica A: Statistical Mechanics and its Applications

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“…Recently, a few models have appeared in the literature which are known to be in a different universality class from DP. Those are the model A and B of probabilistic cellular automa (PCA) introduced by Grassberger et al [27,28], branching annihilating random walks with an even number of offsprings (BAW) [29][30][31][32], nonequilibrium kinetic Ising models with two different dynamics (NKI) [33,34], and an interacting monomer-dimer model (IMD) [35].…”

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Dynamic scaling behavior of an interacting monomer-dimer model

1995

Phys. Rev. E

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We study the dynamic scaling behavior of a monomer-dimer model with repulsive interactions between the same species in one dimension. With infinitely strong interactions the model exhibits a continuous transition from a reactive phase to an inactive phase with two equivalent absorbing states. This transition does not belong to the conventional directed percolation universality class. The values of dynamic scaling exponents are estimated by Monte Carlo simulations for two distinct initial configurations, one near an absorbing

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Cited by 2 publications

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Critical behavior of an absorbing phase transition in an interacting monomer-dimer model

Critical behavior of an absorbing phase transition in an interacting monomer-dimer model

Dynamic scaling behavior of an interacting monomer-dimer model

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