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

computer physics communications

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