Condensation and clustering in the driven pair exclusion process

We investigate particle condensation in a driven pair exclusion process on one- and two-dimensional lattices under the periodic boundary condition. The model describes a biased hopping of particles subject to a pair exclusion constraint that each particle cannot stay at a same site with its pre-assigned partner. The pair exclusion causes a mesoscopic condensation characterized by the scaling of the condensate size m _con ~ N ^β and the number of condensates N _con ~ N ^α with the total number of sites N. Those condensates are distributed randomly without hopping bias. We find that the hopping bias generates a spatial correlation among condensates so that a cluster of condensates appears. Especially, the cluster has an anisotropic shape in the two-dimensional system. The mesoscopic condensation and the clustering are studied by means of numerical simulations.