Condensation transition in a conserved generalized interacting zero-range process

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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 pₗ < p < pc, where the bounding values depend on the range of interaction, with pc < 0.5 in general. Analysis of P(n) in the condensate phase using a known scaling form shows there is universal behaviour in the short range process while the infinite range process displays non-universality. In the non-condensate phase above pc, two distinct regions are identified: pc < 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.