Unveiling the ZGB model with $CO$ desorption: a single model with two universality classes?

Abstract

We study the behavior of the phase transitions of the Ziff-Gullari-Barshad (ZGB) model when the $CO$ molecules are adsorbed on the catalytic surface with a rate $y$ and desorbed from the surface with a rate $k$. We employ large-scale nonequilibrium Monte Carlo simulations along with an optimization technique based on the coefficient of determination, in order to obtain an overview of the phase transitions of the model in the whole spectrum of $y$ and $k$: ($0\leq y\leq 1$ and $0\leq k\leq 1$) with precision $\Delta y=\Delta k=0.001$. Sucessive refinements reveal a region of points belonging to the directed percolation universality class whereas the exponents $\theta $ and $\beta /\nu_{\parallel }$ obtained agree with those of this universality class. On the other hand, the effects of allowing the $CO$ desorption from the lattice on the discontinuous phase transition point of the original ZGB model suggest the emergence of an Ising-like point previously predicted in Ref. \cite{tome1993}. We show that such a point appears after a sequence of two lines of pseudo-critical points which leads to a unique peak of the coefficient of determination curve in $y_{c}=0.554$ and $k_{c}=0.064$. In this point, the exponent $\theta $ agrees with the value found for Ising model.