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

Fernandes, Henrique A.; Silva, Roberto da; Santos, E.D.; Gomes, Paulo F.; Arashiro, Everaldo

doi:10.1103/physreve.94.022129

Cited by 14 publications

(21 citation statements)

References 76 publications

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“…In contempt of its existence in theoretical studies, there are no experimental evidences of the continuous phase transition. This last transition has also being studied by several authors with results supporting that the critical point belongs to the directed percolation (DP) universality class [46][47][48].…”

Section: A the Ziff-gulari-barshad Modelmentioning

confidence: 74%

Phase diagrams of the ZGB model on random networks

Vilela¹,

Fernandes²,

Costa³

et al. 2020

Preprint

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In this work, we revisited the ZGB model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the Random Geometric Graph and the Erdös-Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius α and the linking probability p, respectively. In addition, the catalytic reactions of the ZGB model is governed by the parameter y, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters (y, α) and (y, p) and showed that the continuous phase transition is greatly affected by the number of neighbors per node while the discontinuous one remains present in the diagram throughout the interval of study.In this work, we have revisited the ZGB model in order to study the behavior of its phase transitions through extensive equilibrium Monte Carlo simulations on two different and well-known random networks: the Random Geometric Graph (RGG) and the Erdös-Rényi network (ERN). These two networks are used as prototype for communication patterns and the connections between their sites follow precise rules defined by their control parameters.This paper is organized as follows: in Sec. II we describe the ZGB model and its phase diagram, as well as the two random networks considered in this study. In Sec. III we show our main results and present the discussions about our findings. Finally, the conclusions are presented in Sec. IV.

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Section: A the Ziff-gulari-barshad Modelmentioning

confidence: 74%

Phase diagrams of the ZGB model on random networks

Vilela¹,

Fernandes²,

Costa³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The ZGB model possesses two phase transitions. The first one is a continuous phase transition and occurs at the critical point y 1 ∼ = 0.3874 [37,40]. The second transition is discontinuous and occurs at y 2 ∼ = 0.5256 [41].…”

Section: The Modelmentioning

confidence: 99%

“…As shown in Ref. [37], the dynamic and static critical exponents of the model can be obtained by using the Eq. ( 6) and performing TDMC simulations with two different initial conditions ρ(0) = ρ 0 : (i) the lattice is completely empty, i.e.…”

Section: Short-time Dynamics and Time-dependent Monte Carlo Simulatio...mentioning

confidence: 99%

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Highly detailed computational study of a surface reaction model with diffusion: Four algorithms analyzed via time-dependent and steady-state Monte Carlo simulations

Silva

Fernandes

2018

Computer Physics Communications

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In this work, we present an extensive computational study on the Ziff-Gulari-Barshad (ZGB) model extended in order to include the spatial diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the surface. In our approach, we consider two different protocols to implement the diffusion of the atoms/molecules and two different ways to combine the diffusion and adsorption processes resulting in four different algorithms. The influence of the diffusion on the continuous and discontinuous phase transitions of the model is analysed through two very well established methods: the time-dependent Monte Carlo simulations and the steady-state Monte Carlo simulations. We also use an optimization method based on a concept known as coefficient of determination to construct color maps and obtain the phase transitions when the parameters of the model vary. This method was proposed recently to locate nonequilibrium second-order phase transitions and has been successfully used in both systems: with defined Hamiltonian and with absorbing states. The results obtained via time-dependent Monte Carlo simulation along with the coefficient of determination are corroborated by traditional steady-state Monte Carlo simulations also performed for the four algorithms. Finally, we analyse the finite-size effects on the results, as well as, the influence of the number of runs on the reliability of our estimates.

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“…There is no general theory of non-equilibrium phase transitions like in equilibrium ones, so absorbing phase transitions have been studied in different models with different approaches. In this sense, network science has been increasingly more important as a tool to fully describe the different phenomena obtained from real-world observation involving non-equilibrium models [20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Topological transition in a coupled dynamic in random networks

Gomes,

Fernandes,

Costa

2021

Preprint

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In this work, we study the topological transition in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states, on the network known as random geometric graph (RGG). In that approach, each node has two cultural states and each link has also two states. There are six possible combinations of pairs (two nodes connected by one link) and half of them are categorized as a satisfying combination and the other half are unsatisfying one. The control parameter of the model dictates the probability of link and node updates. The system presents two phases: the absorbing phase is reached when all pairs of nodes become satisfying and, on the other hand, the active phase is present when there are both satisfying and unsatisfying pairs of nodes in the network. We found that, along with the unsatisfying pair density, the assortativity coefficient can also be used as an order parameter of the model. Additionaly, the assortativity coefficient gives an intuitive picture of the features on the topological transition of the network. We also calculated the components and cultural domains to add another view on the topological transition of the network.

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

Cited by 14 publications

References 76 publications

Phase diagrams of the ZGB model on random networks

Phase diagrams of the ZGB model on random networks

Highly detailed computational study of a surface reaction model with diffusion: Four algorithms analyzed via time-dependent and steady-state Monte Carlo simulations

Topological transition in a coupled dynamic in random networks

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