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Critical phase in non-conserving zero-range processes and equilibrium networks

A. G. Angel·M. R. Evans·E. Levine·D. Mukamel
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Abstract

Zero-range processes, in which particles hop between sites on a lattice, are closely related to equilibrium networks, in which rewiring of links take place. Both systems exhibit a condensation transition for appropriate choices of the dynamical rules. The transition results in a macroscopically occupied site for zero-range processes and a macroscopically connected node for networks. Criticality, characterized by a scale-free distribution, is obtained only at the transition point. This is in contrast with the widespread scale-free real-life networks. Here we propose a generalization of these models whereby criticality is obtained throughout an entire phase, and the scale-free distribution does not depend on any fine-tuned parameter.

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A. G. Angel, M. R. Evans, E. Levine, D. Mukamel. 2005-03-18. Critical phase in non-conserving zero-range processes and equilibrium networks. https://doi.org/10.1103/physreve.72.046132

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