Critical fluctuations in spatial complex networks

TL;DR

This paper investigates how embedding complex networks in geometrical spaces affects critical fluctuations in the Ising model, revealing that spatial embedding can lead to deviations from mean-field behavior.

Contribution

It demonstrates that spatial embedding of complex networks can alter critical fluctuations, extending the Ginsburg criterion to complex topologies.

Findings

Spectral properties of networks influence critical fluctuations.

Embedding networks in space can break mean-field behavior.

Generalization of the Ginsburg criterion to complex networks.

Abstract

An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a break-down of this scenario can be obtained when complex networks are embedded in geometrical spaces. Through the analysis of the Ising model on annealed spatial networks, we reveal in particular the spectral properties of networks responsible for critical fluctuations and we generalize the Ginsburg criterion to complex topologies.