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

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.

4 pages, 4 figures

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Cited by in corpus (19)

• Critical phenomena in complex networks
• Epidemic spreading in evolving networks
• Condensation and Extreme Value Statistics
• Condensation in Temporally Correlated Zero-Range Dynamics
• Zero-Range Processes with Multiple Condensates: Statics and Dynamics
• Instability of condensation in the zero-range process with random interaction
• Condensation transitions in a model for a directed network with weighted links
• Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process
• Condensation Transition in Polydisperse Hard Rods
• Criticality and Condensation in a Non-Conserving Zero Range Process
• Instability in a Network Coevolving with a Particle System
• Steady states in a non-conserving zero-range process with extensive rates as a model for the balance of selection and mutation
• Particle Condensation in Pair Exclusion Process
• Structural phase transition in evolving networks
• Cluster-factorized steady states in finite range processes
• Arrival Times in a Zero-Range Process with Injection and Decay
• Maintenance of order in a moving strong condensate
• Condensation and Clustering in the Driven Pair Exclusion Process
• Particle hopping on a ladder: exact solution using multibalance