Ziff–Gulari–Barshad model
# Ziff–Gulari–Barshad model

The Ziff–Gulari–Barshad (ZGB) model is a simple Monte Carlo method for catalytic reactions of oxidation of carbon monoxide to carbon dioxide on a surface using Monte-Carlo methods which captures correctly the essential dynamics: the phase transition between two poisoned states (either $CO_2-$ or O-poisoned) and a steady-state in between. It is named after Robert M. Ziff, Erdogan Gulari, and Yoav Barshad, who published it in 1986.

## Model definition

The model consists of three steps:

* Adsorption of the reacting species CO and $O_2$
* The actual reaction step on the surface: CO + O → $CO_2$
* Desorption of the products.

The simplest implementation considers the catalyst as simple square two-dimensional lattice, but one can also consider other kinds of underlying lattices. When a gas-phase molecule touches an empty site, adsorption occurs immediately and the chemical reaction is also instantaneous. Furthermore, assumes that the composition of the gas phase remains constant.

### Results and other work

The model belongs to the universality class of directed percolation. The model was modified several times.

