Moment ratios and dynamic critical behavior of a reactive system with several absorbing configurations

Andrade, Marcelo Freitas de; Figueiredo, W.

doi:10.1103/physreve.83.031108

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…Up to now we have calculated only the ratio between the critical exponents β and ν ⊥ . In order to determine each one of these exponents, one can use the fact that some ratios between different moments of the order parameter do not depend upon the system size at the critical point, showing universal values [22,23]. In particular, we use the ratio…”

Section: Resultsmentioning

confidence: 99%

Two competitive contact processes with local interactions

2014

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We present a simple lattice model that consists of two competitive contact processes with local interactions on a one-dimensional lattice. The sites of the lattice can be empty or occupied by particles of type A or type B. The time evolution of the densities is governed by a master equation, whose transition among the states depends essentially on the spreading and annihilation rates of both particles. This is a competitive model where the stationary states are determined as a function of the spreading and annihilation rates. We employ mean-field approximations, at the level of one and two sites, and we obtain a phase diagram that shows four well distinguished phases, including a mixed one in which both particles coexist. Monte Carlo simulations show that this mixed phase no longer exists in the limit of large one-dimensional lattices. However, simulations of the model in two dimensions show that the mixed phase does not disappear as in the one-dimensional case. We also calculate some static critical exponents of the one-dimensional version of the model and we have shown that they belong to the directed percolation universality class.

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Section: Resultsmentioning

confidence: 99%

Two competitive contact processes with local interactions

2014

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“…Its success in describing the poisoning of the catalyst by carbon monoxide or oxygen led to many other approaches to the ZGB model [13]- [18] and related models [19]- [24]. In this context, we focus our attention in a model of competitive catalytic reactions between two monomers subjected to thermal effects and lateral energy interactions [25,26].…”

Section: Introductionmentioning

confidence: 99%

“…We explore in this work the sensitivity to the initial condition of a one-dimensional catalytic reaction model [25,26] that displays several absorbing configurations. This model takes into account effects of thermal fluctuations, as well as interactions between nearest neighbor monomers.…”

Section: Introductionmentioning

confidence: 99%

Non-universal spreading exponents in a catalytic reaction model

Andrade¹,

Figueiredo²

2011

J. Stat. Mech.

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We investigated the dependence of the spreading critical exponents and the ultimate survival probability exponent on the initial configuration of a nonequilibrium catalytic reaction model. The model considers the competitive reactions between two different monomers, A and B, where we take into account the energy couplings between nearest neighbor monomers, and the adsorption energies, as well as the temperature T of the catalyst. For each value of T the model shows distinct absorbing states, with different concentrations of the two monomers. Employing an epidemic analysis, we established the behavior of the spreading exponents as we started the Monte Carlo simulations with different concentrations of the monomers. The exponents were determined as a function of the initial concentration ρA, ini of A monomers. We have also considered initial configurations with correlations for a fixed concentration of A monomers. From the determination of three spreading exponents, and the ultimate survival probability exponent, we checked the validity of the generalized hyperscaling relation for a continuous set of initial states, random and correlated, which are dependent on the temperature of the catalyst.

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Absorbing states in a catalysis model with anti-Arrhenius behavior

Andrade

Figueiredo

2012

The Journal of Chemical Physics

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We study a model of heterogeneous catalysis with competitive reactions between two monomers A and B. We assume that reactions are dependent on temperature and follow an anti-Arrhenius mechanism. In this model, a monomer A can react with a nearest neighbor monomer A or B, however, reactions between monomers of type B are not allowed. We assume attractive interactions between nearest neighbor monomers as well as between monomers and the catalyst. Through mean-field calculations, at the level of site and pair approximations, and extensive Monte Carlo simulations, we determine the phase diagram of the model in the plane y(A) versus temperature, where y(A) is the probability that a monomer A reaches the catalyst. The model exhibits absorbing and active phases separated by lines of continuous phase transitions. We calculate the static, dynamic, and spreading exponents of the model, and despite the absorbing state be represented by many different microscopic configurations, the model belongs to the directed percolation universality class in two dimensions. Both reaction mechanisms, Arrhenius and anti-Arrhenius, give the same set of critical exponents and do not change the nature of the universality class of the catalytic models.

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Moment ratios and dynamic critical behavior of a reactive system with several absorbing configurations

Cited by 5 publications

References 24 publications

Two competitive contact processes with local interactions

Two competitive contact processes with local interactions

Non-universal spreading exponents in a catalytic reaction model

Absorbing states in a catalysis model with anti-Arrhenius behavior

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