Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model

TL;DR

This paper investigates the critical behavior of the Ziff-Gulari-Barshad surface-reaction model near its second-order phase transition, providing precise critical point and exponents, confirming its universality class as directed percolation.

Contribution

The study offers highly accurate critical point and dynamical exponents for the ZGB model, establishing its transition as part of the directed percolation universality class.

Findings

Critical point p_1 = 0.3873682 ± 0.0000015

Transition belongs to directed percolation universality class

Precise dynamical critical exponents z, δ, η

Abstract

We study the dynamic behavior of the Ziff-Gulari-Barshad (ZGB) irreversible surface-reaction model around its kinetic second-order phase transition, using both epidemic and poisoning-time analyses. We find that the critical point is given by p_1 = 0.3873682 \pm 0.0000015, which is lower than the previous value. We also obtain precise values of the dynamical critical exponents z, \delta, and \eta which provide further numerical evidence that this transition is in the same universality class as directed percolation.