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

TL;DR

This paper introduces a generalized model of zero-range processes and equilibrium networks where criticality and scale-free distributions are maintained across an entire phase, not just at a transition point, unlike traditional models.

Contribution

It proposes a new generalized framework that sustains criticality throughout a phase, eliminating the need for fine-tuning parameters to achieve scale-free distributions.

Findings

Criticality is maintained across an entire phase in the generalized model.

Scale-free distributions are independent of fine-tuned parameters.

The model bridges the gap between theoretical criticality and real-world 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.