Surface-state-mediated interactions influence the spatial distribution of adatoms at surfaces. These indirect interactions are the driving force for the creation of superlattices of individual adsorbed atoms when the adatom concentration, the sample temperature, and the adatom diffusion barrier are in a subtle balance, as it has been first reported for Ce adatoms on Ag(1 1 1). The conditions for the formation of such superlattices are discussed. Specifically, the adatom concentration is shown to modify considerably the electronic structure of the Ag(1 1 1) surface. With increasing temperature the superlattice undergoes a direct transition from a two-dimensional solid to a two-dimensional liquid. Such superlattices, consisting of magnetic adatoms, may be interesting as model systems for the study of direct and indirect magnetic interactions in two dimensions. © 2009 Elsevier Ltd. All rights reserved.