Ultrastable 2D glasses and packings explained by local centrosymmetry

TL;DR

This paper shows that ultrastable 2D glasses and packings have high local centrosymmetry, which explains their exceptional mechanical properties and lack of certain vibrational modes, based on recent numerical data.

Contribution

It demonstrates the high degree of local centrosymmetry in ideal ultrastable 2D glasses and packings, linking this to their mechanical robustness and vibrational characteristics.

Findings

High inversion-symmetry order parameter in ultrastable glasses

Centrosymmetry explains high shear modulus and absence of boson peak

Bond-orientational order poorly correlates with vibrational properties

Abstract

Using the most recent numerical data by Bolton-Lum \emph{et al.} [Phys. Rev. Lett. 136, 058201 (2026)], we demonstrate that ideal ultrastable glasses in the athermal limit (or ultrastable ideal 2D disk packings) possess a remarkably high degree of local centrosymmetry. In particular, we find that the inversion-symmetry order parameter for local force transmission introduced in Milkus and Zaccone, [Phys. Rev. 93, 094204 (2016)], is as high as $F_{IS}= 0.84522$, to be compared with $F_{IS}=1$ for perfect centrosymmetric crystals free of defects, and with $F_{IS} \sim 0.3-0.5$ for standard random packings. This observation provides a clear, natural explanation for the ultra-high shear modulus of ideal packings and ideal glasses, because the high centrosymmetry prevents non-affine relaxations which decrease the shear modulus. The same mechanism explains the absence of boson peak-like soft vibrational modes. These results also confirm what was found previous work, i.e. that the bond-orientational order parameter is a very poor correlator for the vibrational and mechanical