Anomalous vibrational properties in the continuum limit of glasses

TL;DR

This study investigates the low-frequency vibrational modes in Lennard-Jones glasses, revealing coexistence of phonon and localized modes in the continuum limit, and highlights the impact of potential truncation schemes on these vibrational properties.

Contribution

It demonstrates that realistic Lennard-Jones glasses exhibit vibrational properties similar to harmonic models, clarifies the influence of potential truncation, and explains this sensitivity through linear stability analysis.

Findings

Vibrational properties of LJ glasses converge to coexistence of phonon and localized modes.

Low-frequency vibrations are sensitive to potential truncation schemes.

The sensitivity is explained by linear stability analysis.

Abstract

The low-temperature thermal properties of glasses are anomalous with respect to those of crystals. These thermal anomalies indicate that the low-frequency vibrational properties of glasses differ from those of crystals. Recent studies revealed that, in the simplest model of glasses, i.e., the harmonic potential system, phonon modes coexist with soft localized modes in the low-frequency (continuum) limit. However, the nature of low-frequency vibrational modes of more realistic models is still controversial. In the present work, we study the Lennard-Jones (LJ) system using large-scale molecular-dynamics (MD) simulation and establish that the vibrational property of the LJ glass converges to coexistence of the phonon modes and the soft localized modes in the continuum limit as in the case of the harmonic potential system. Importantly, we find that the low-frequency vibrations are rather sensitive to the numerical scheme of potential truncation which is usually implemented in the MD simulation, and this is the reason why contradictory arguments have been reported by previous works. We also discuss the physical origin of this sensitiveness by means of a linear stability analysis.