An alternative method to characterize first- and second-order phase transitions in surface reaction models

TL;DR

This paper introduces a novel time-dependent Monte Carlo simulation method to accurately identify and characterize phase transitions in surface reaction models, specifically applied to the ZGB model.

Contribution

It presents a new approach based on optimizing the coefficient of determination to locate non-equilibrium phase transitions and estimate critical exponents.

Findings

Successfully characterized second-order phase transition and upper spinodal point.

Estimated critical exponents in agreement with existing literature.

Validated the method's effectiveness for surface reaction models.

Abstract

In this work, we revisited the Ziff-Gulari-Barshad (ZGB) model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We used a method proposed recently to locate the non-equilibrium 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 second-order phase transition of the model, as well as its upper spinodal point, a pseudo-critical point located near the first-order transition. The static critical exponents $\beta $, $\nu_{\parallel }$, and $\nu_{\perp }$, as well as the dynamic critical exponents $\theta $ and $z$ for the second-order point were also estimated and are in excellent agreement with results found in literature.