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The present work is an endeavour to determine analytically features of the stationary measure of a non-integrable zero-range process, and to investigate the possible existence of phase transitions for such a nonequilibrium model. The rates defining the model do not satisfy the constraints necessary for the stationary measure to be a product measure. Even in the absence of a drive, detailed balance with respect to this measure is violated. Analytical and numerical investigations on the complete graph demonstrate the existence of a first-order phase transition between a fluid phase and a condensed phase, where a single site has macroscopic occupation. The transition is sudden from an imbalanced fluid where both species have densities larger than the critical density, to a critical neutral fluid and an imbalanced condensate.
Comment: Lecture notes for the Luxembourg Summer School 2005
Comment: 18 pages, 8 figures 2 figures added, more accurate data at criticality
Comment: 10 pages, 3 figures, Latex, submitted to J. Phys. A (letters)
Comment: 23 pages, plain tex, revised and augmented
Comment: 30 pages,5 figures. Minor updates
Comment: 29 pages, 13 figures, 3 tables. A few minor changes
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