Heterogeneous catalysis processes had been traditionally studied with the aid of mean-field rate equations. However, evidence has mounted in recent years that phenomena associated with microscopic length scales, such as local fluctuations in concentrations and excluded volume effects, are relevant to the dynamics. History dependent kinetics, bistability, and dynamic phase transitions are among the many consequences of microscopic effects. The classical approach of rate equations fails to explain these results. The recently introduced lattice models for heterogeneous catalysis provide with a more appropriate microscopic way of analysis. We explain these models and focus on the kinetic effects arising from fluctuations in the number of reacting molecules. Our method consists of the studying of catalysis on complete graphs, i.e., lattices where all sites are connected to each other. We illustrate the method for the process A+B→AB and show that its upper critical dimensions is dc=2. We also discuss some of the many open problems in the field.
