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 < 2 and a slow logarithmic decay in two dimensions. We discuss the relevance of these results for the monomer-monomer surface reaction model. PACS numbers: 05.40.+j, 68.10.Jy, 82.20.Mj In modeling heterogeneous catalysis [1], the monomermonomer surface reaction model plays an important role, at least from the theoretical point of view since an appealing simplicity of this model allows one to examine several issues analytically. In particular, investigations of the monomer-monomer model clarified the role of fluctuations [2][3][4][5][6][7][8], interfacial roughening [9], diffusion of the adsorbants [10], and surface disorder [11]. In the simplest situation (no diffusion, no disorder, etc.), it was found that single-species clusters grow with time when the dimensionality D of the substrate is sufficiently small, D ≤ 2. However, the details of the coarsening like the decay rate of the density of reactive interfaces remain uncertain in two dimensions, -simulations [5,12,13] revealed a very slow decay which could be logarithmic or power law with a small exponent. In this paper, we clarify these questions by computing analytically kinetic characteristics of an idealized version of the monomer-monomer model, the voter model. We then expand these results and perform numerical simulations for the full model.The monomer-monomer surface reaction process can be schematically represented by the following kinetic steps:A and B particles impinge upon a surface, with respective rates k A and k B , and adsorb onto vacant sites V to form a monolayer of adsorbed particles, A V and B V . Nearest-neighbor pairs of dissimilar adsorbed particles, A V B V , react and desorb with rate k r , leaving behind two vacancies. For k A = k B , the adsorption imbalance leads to the quick saturation of the surface by the majority species. For k A = k B and for dimensions D ≤ 2, there is a fluctuation-induced coarsening of the surface into growing A and B adsorbed islands. This nontrivial case of equal adsorption rates will be considered in the following. Furthermore, in theoretical analysis we will restrict ourselves to the reaction-controlled limit, k r ≪ k A = k B , which was found to provide qualitatively the same behavior as the general case [4,6] but more amenable to theoretical treatment. In the reaction-controlled limit, the substrate quickly becomes completely covered and then stays covered forever, since in units of the typical, i.e. adsorption, time interval unoccupied sites are refilled instantaneously. The kinetics of the monomer-monomer surface reaction model is conveniently described by a mapping onto the Ising model with mixed zero-temperature voter dynamics and infinite-temperature...

We investigate coarsening and persistence in the voter model by introducing the quantity $P_n(t)$, defined as the fraction of voters who changed their opinion n times up to time t. We show that $P_n(t)$ exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations. Exact results are obtained for the average number of opinion changes, , and the autocorrelation function, $A(t)\equiv \sum (-1)^n P_n\sim t^{-d/2}$ in arbitrary dimension d. These exact results are complemented by a mean-field theory, heuristic arguments and numerical simulations. For dimensions d>2, the system does not coarsen, and the opinion changes follow a nearly Poissonian distribution, in agreement with mean-field theory. For dimensions d<=2, the distribution is given by a different scaling form, which is characterized by nontrivial scaling exponents. For unequal opinion concentrations, an unusual situation occurs where different scaling functions correspond to the majority and the minority, as well as for even and odd n.Comment: 25 pages, 4 postscript figures, revtex, postscript file available from http://arnold.uchicago.edu/~eb