Condensation transition in a conserved generalized interacting zero-range process.

Abstract

A conserved generalized zero-range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability p. The steady-state particle distribution function P(n) is obtained using both analytical and numerical methods. The system goes through several phases as p is varied. In particular, a condensate phase appears for p_{l}<p<p_{c}, where the bounding values depend on the range of interaction, with p_{c}<0.5 in general. Analysis of P(n) in the condensate phase using a known scaling form shows there is universal behavior in the short-range process while the infinite range process displays nonuniversality. In the noncondensate phase above p_{c}, two distinct regions are identified: p_{c}<p≤0.5 and p>0.5; a scale emerges in the system in the latter and this feature is present for all ranges of interaction.