Higher-order moments at the critical point of the Ziff-Gulari-Barshad model

Leite, Vanessa Souza; Hoenicke, Gilberto Luiz; Figueiredo, W.

doi:10.1103/physreve.64.036104

Cited by 11 publications

(6 citation statements)

References 8 publications

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“…7 yields δ = 0.453 (9), in very good agreement with the standard value of δ = 0.4523 (10) for DP [33]. Moment ratios (or reduced cumulants) represent an alternative method for identifying the universality class of a continuous phase transition [34,35,36]. Here we analyze the critical moment ratio m = ρ 2 / ρ 2 .…”

Section: Resultssupporting

confidence: 67%

Contact process on a Voronoi triangulation

et al. 2008

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We study the continuous absorbing-state phase transition in the contact process on the VoronoiDelaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

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Section: Resultssupporting

confidence: 67%

Contact process on a Voronoi triangulation

et al. 2008

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“…Although the former is commonly used, some studies have considered ρ V as order parameter (see Ref. [66]). First, we considered a lattice of linear size L = 160 and explored the scenery in general by estimating r for different values of y (0.3 ≤ y ≤ 0.6 and ∆y = 10 −4 ) (see Fig.…”

Section: Resultsmentioning

confidence: 99%

Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models

et al. 2016

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In this paper we revisited the Ziff-Gulari-Barshad model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We use a method proposed recently to locate the nonequilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the continuous phase transition of the model, as well as its upper spinodal point, a pseudocritical point located near the discontinuous phase transition. The static critical exponents β, ν_{∥}, and ν_{⊥}, as well as the dynamic critical exponents θ and z for the continuous transition point, were also estimated and are in excellent agreement with results found in literature.

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“…Field theoretical and simulation results have unveiled that the critical exponents vary continuously with α for both cases of conserving and non-conserving parity of the number of particles [20,28,29]. To probe the fluctuations of the order parameter has been considered one relevant action aiming to fully characterize the critical behavior of non-equilibrium phase transitions [30][31][32][33][34][35][36]. It has been well established that the relative fluctuation of the order parameter becomes scale invariant at the transition with its critical value being a universal quantity.…”

Section: Introductionmentioning

confidence: 99%

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

et al. 2016

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We study the critical order parameter fluctuations of the absorbingstate phase-transition exhibited by branching and annihilating random walkers performing anomalous diusion in a linear chain. The diusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α. We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diusion. Anomalous diusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α. We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit 5 2 / α = on which the active state predominates for any finite branching probability.

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Higher-order moments at the critical point of the Ziff-Gulari-Barshad model

Cited by 11 publications

References 8 publications

Contact process on a Voronoi triangulation

Contact process on a Voronoi triangulation

Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

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