Particle condensation in pair exclusion process

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size N. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the zero-range process by including a pair exclusion. Each particle is associated with its own partner and particles of a pair are forbidden to stay at the same site. The pair exclusion is weak in that a particle interacts with only a single one among all others. It turns out that such a weak interaction changes the nature of condensation drastically. There appear a number of mesoscopic condensates: the mass of a condensate scales as mcon ∼ N1/2 and the number of condensates scales as Ncon ∼ N1/2 with a logarithmic correction. These results are derived analytically through a mapping to a solvable model under a certain assumption and confirmed numerically.