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The Zero-Range Process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here a non-conserving Zero-Range Process is introduced which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterised by mesocondensates each of which contains a subextensive number of particles. The model is closely related to that of rewiring networks, in which rewiring of links between nodes takes place, and where analogous properties are predicted. |
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