Robust criticality of Ising model on rewired directed networks

TL;DR

This paper demonstrates that preferential rewiring in directed networks induces robust critical behavior in the Ising model, contrasting with the single critical point in non-rewired networks, due to heterogeneities and core formation.

Contribution

It introduces a model showing how rewiring leads to persistent criticality in directed networks, supported by mean-field analysis and Monte Carlo simulations.

Findings

Rewiring causes divergence in susceptibility at high temperatures.

Mean-field equations are valid only at low temperatures.

Core formation influences global system behavior.

Abstract

We show that preferential rewiring, which is supposed to mimick the behaviour of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behaviour. For the non-rewired random graph version, due to a constant number of links out-going from each site, we write a simple mean-field-like equation describing the behaviour of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behaviour is traced back to the formation of a relatively small core of agents which influence the entire system.