Exact results for kinetics of catalytic reactions

The kinetics of an irreversible catalytic reaction on a substrate of arbitrary dimension is examined. In the limit of infinitesimal reaction rate (reaction-controlled limit), we solve the dimer-dimer surface reaction model (or voter model) exactly in arbitrary dimension $D$. The density of reactive interfaces is found to exhibit a power-law decay for $D<\mathrm{}2\mathrm{}$ and a slow logarithmic decay in two dimensions. We discuss the relevance of these results for the monomer-monomer surface reaction model.