Dynamic scaling behavior of an interacting monomer-dimer model

H, Park; Mh, Kim

doi:10.1103/physreve.52.5664

Cited by 51 publications

(27 citation statements)

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“…In this section, we discuss the dynamic critical behavior of the IMD model via Monte Carlo simulations. Some of the results reported previously [19] are much improved using new efficient algorithms and some new results for various interface dynamics are presented.…”

Section: Dynamic Critical Behavior Of the Imd Modelmentioning

confidence: 99%

“…A common feature of these models is that the absorbing phase consists of a single absorbing state.Only a few models have been studied that are not in the DP universality class. Those are the models A and B of probabilistic cellular automata (PCA) [13,14], nonequilibrium kinetic Ising models with two different dynamics (NKI) [15][16][17], and interacting monomer-dimer models (IMD) [18,19]. Numerical investigations show that critical behaviors of these models are different from DP but form a non-DP universality class.…”

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confidence: 99%

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Critical phenomena of nonequilibrium dynamical systems with two absorbing states

et al. 1998

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We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase that belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only. ͓S1063-651X͑98͒06806-8͔

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Section: Dynamic Critical Behavior Of the Imd Modelmentioning

confidence: 99%

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confidence: 99%

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

et al. 1998

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“…The first model belonging to a non-DP, and now believed to belong to the BAWe universality class was a probabilistic cellular automaton studied by Grassbeger et al [13]. Recently, a number of models belonging to BAWe universality, such as certain kinetic Ising models [14], the interacting monomer-dimer model (MDM) [15,16], three species monomer-monomer model [17], and modified DomanyKinzel model [18] introduced by Hinrichsen [19] attracted much attention. While for DP universality models series expansion treatment proved to be most effective in estimating critical values (see references above), so far models in BAWe universality relied exclusively on Monte Carlo simulations.…”

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Critical Behavior of the Contact Process with Parity Conservation

Inui

Tretyakov

1998

Phys. Rev. Lett.

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We introduce a parity conserving version of the contact process, which can be treated using a series expansion technique. Both Padé approximants for the series and numerical simulations for the derivative of the order parameter show that the critical exponent b is consistent with the conjecture b 1. Dynamical Monte Carlo simulations confirm that the model belongs to the branching annihilating random walk with an even number of offsprings universality class. [S0031-9007 (98)06309-1] PACS numbers: 64.60.Ak, 05.40. + j, 64.60.Ht Contact process (CP) [1,2] is a nonequilibrium model exhibiting an extinction-survival second order dynamical phase transition. The basic CP introduced by Harris [1]has a unique absorbing state and belongs to the directed percolation (DP) universality class [3][4][5]. Many other nonequilibrium models such as A-model [6,7], branching annihilating random walk [8,9] with an odd number of offsprings, and Reggon field theory [10] are believed to belong to the same universality class as the basic contact process, which is often regarded as a minimal example of a broad class of interacting particle systems, similarly to the role of the Ising system in equilibrium critical phenomena.Another important universality class for nonequilibrium models is branching annihilating random walk with even offsprings universality class (BAWe) [11,12]. The first model belonging to a non-DP, and now believed to belong to the BAWe universality class was a probabilistic cellular automaton studied by Grassbeger et al. [13]. Recently, a number of models belonging to BAWe universality, such as certain kinetic Ising models [14], the interacting monomer-dimer model (MDM) [15,16], three species monomer-monomer model [17], and modified DomanyKinzel model [18] introduced by Hinrichsen [19] attracted much attention. While for DP universality models series expansion treatment proved to be most effective in estimating critical values (see references above), so far models in BAWe universality relied exclusively on Monte Carlo simulations.Although the DP universality class is very wide and includes models with rather simple rules, no model in it has been solved exactly [20]. Guttmann and Enting [21] suggested that DP models will never be solved exactly in the sense of being expressed in terms of D-finite functions due to an absence of pattern in series expansion coefficients. Furthermore, based on numerical data Jensen and Guttmann [5] conjectured that critical exponents for DP should not be expected to be simple rational fractions.On the other hand, Jensen conjectured that combinations of critical exponents of BAWe can be represented as b͞n Ќ 1 2 and n Ќ ͞n k 7͞4 [11]. Intuitively, it would suggest that BAWe universality is "simpler" than DP universality; one could even speculate concerning the possibility of an exact solution.In this Letter, we introduce a extended CP, which while belonging to BAWe universality allows a series expansion treatment. We use the series expansion technique [22][23][24] in order to clarify the value o...

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“…In the non-equilibrium Ising model with combined spin-flip and spin exchange dynamics (NEKIM) [19,20] the kinks have local parity conserving symmetry as well as the absorbing state is symmetrically doubly degenerated. The three species monomer-monomer [21] (3MM) and the interacting monomer-dimer (IMD) models [23,24] are multi component models with parity conservations and symmetric absorbing phases.…”

Section: Introductionmentioning

confidence: 99%

Damage spreading for one-dimensional, nonequilibrium models with parity conserving phase transitions

Ódor

Menyhárd

1998

Phys. Rev. E

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The damage spreading (DS) transitions of two one-dimensional stochastic cellular automata suggested by Grassberger (A and B) and the kinetic Ising model of Menyhárd (NEKIM) have been investigated. These non-equilibrium models exhibit non-directed percolation universality class continuous phase transition to absorbing states, exhibit parity conservation (PC) law of kinks and have chaotic to non-chaotic DS phase transitions, too. The relation of the critical point and the damage spreading point has been explored with numerical simulations. For model B the two transition points are well separated and directed percolation universality was found both for spin damage and kink damages in spite of the conservation of damage variables modulo 2 in the latter case. For model A and NEKIM the two transition points coincide with drastic effects on the damage of spin and kink variables showing different time dependent behaviours. While the kink DS transition of these two models shows regular PC class universality, the spin damage of them exhibits a discontinuous phase transition with compact clusters and PC-like spreading exponents. In the latter case the static exponents determined by finite size scaling are consistent with that of the spins of the NEKIM model at the PC transition point. The generalised hyper-scaling law is satisfied. Detailed discussion is given concerning the dependence of DS on initial conditions especially for the A model case, where extremely long relaxation time was found.

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Dynamic scaling behavior of an interacting monomer-dimer model

Cited by 51 publications

References 36 publications

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

Critical Behavior of the Contact Process with Parity Conservation

Damage spreading for one-dimensional, nonequilibrium models with parity conserving phase transitions

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