Ring correlations in random networks

TL;DR

This paper investigates how rings in two-dimensional random network glasses are correlated based on their separation, revealing that true correlations decay within about three rings when using geometrical distance.

Contribution

It introduces a correction to measure ring correlations using geometrical distance, extending the Aboav-Weaire law to larger scales in 2D networks.

Findings

Correlations decay beyond three rings separation.

Topological measures can produce pseudo-long-range correlations.

Geometrical distance provides a more accurate correlation measure.

Abstract

We examine the correlations between rings in random network glasses in two dimensions as a function of their separation. Initially, we use the topological separation (measured by the number of intervening rings), but this leads to pseudo-long-range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring. This effect is associated with the non-circular nature of the shells. It is, therefore, necessary to use the geometrical distance between ring centers. Hence we find a generalization of the Aboav-Weaire law out to larger distances, with the correlations between rings decaying away when two rings are more than about 3 rings apart.