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

TL;DR

This study extensively analyzes how diffusion affects phase transitions in the Ziff-Gulari-Barshad surface reaction model using four algorithms and Monte Carlo simulations, introducing an optimization method for transition detection.

Contribution

It introduces four algorithms combining diffusion and adsorption processes and applies an optimization method to accurately locate phase transitions in the model.

Findings

Diffusion influences both continuous and discontinuous phase transitions.

The optimization method effectively maps phase boundaries.

Results are validated by both time-dependent and steady-state Monte Carlo simulations.

Abstract

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.