Is small-world network disordered?

TL;DR

This paper investigates the critical behavior of a quenched Ising model on small-world networks, finding strong self-averaging behavior contrary to predictions of non self-averaging at criticality.

Contribution

It demonstrates that despite the relevance of disorder, small-world networks exhibit self-averaging behavior at the critical point, challenging existing renormalization group predictions.

Findings

Strong self-averaging observed at criticality

Contradicts previous predictions of non self-averaging behavior

Highlights unique critical properties of small-world networks

Abstract

Recent renormalization group results predict non self averaging behaviour at criticality for relevant disorder. However, we find strong self averaging(SA) behaviour in the critical region of a quenched Ising model on an ensemble of small-world networks, despite the relevance of the random bonds at the pure critical point.