Density of excess modes below the first phonon mode in four-dimensional glasses

doi:10.1088/1674-1056/ad3dd1

Abstract Glasses are known to possess low-frequency excess modes beyond the Debye prediction. For decades, it has been assumed that evolution of low-frequency density of excess modes $D(\omega)$ with frequency $\omega$ follows a power-law scaling: $D(\omega)\sim \omega^{\gamma}$. However, it remains debated on the value of $\gamma$ at low frequencies below the first phonon-like mode in finite-size glasses. Early simulation studies reported $\gamma=4$ at low frequencies in two- (2D), three- (3D), and four-dimensional (4D) glasses, whereas recent observations in 2D and 3D glasses suggested $\gamma=3.5$ in a lower-frequency regime. It is uncertain whether the low-frequency scaling of $D(\omega)\sim \omega^{3.5}$ could be generalized to 4D glasses. Here, we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses. It is found that the system size dependence of $D(\omega)$ below the first phonon-like mode varies with spatial dimensions: $D(\omega)$ increases in 2D glasses but decreases in 3D and 4D glasses as the system size increases. Furthermore, we demonstrate that the $\omega^{3.5}$ scaling, rather than the $\omega^{4}$ scaling, works in the lowest-frequency regime accessed in 4D glasses, regardless of interaction potentials and system sizes examined. Therefore, our findings in 4D glasses, combined with previous results in 2D and 3D glasses, suggest a common low-frequency scaling of $D(\omega)\sim \omega^{3.5}$ below the first phonon-like mode across different spatial dimensions, which would inspire further theoretical studies.

Keywords: vibrational density of states excess modes four-dimensional glasses scaling computer simulation

Received: 22 February 2024
Revised: 02 April 2024
Accepted manuscript online: 12 April 2024

PACS:	64.70.Q-	(Theory and modeling of the glass transition)
	64.70.kj	(Glasses)

Fund: We acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 12374202 and 12004001), Anhui Projects (Grant Nos. 2022AH020009, S020218016, and Z010118169), and Hefei City (Grant No. Z020132009).

Corresponding Authors: Lijin Wang, Ding Xu, Shiyun Zhang
E-mail: lijin.wang@ahu.edu.cn;dingxu@mail.ustc.edu.cn;zsy12@mail.ustc.edu.cn

Cite this article:

Lijin Wang(王利近), Ding Xu(胥鼎), and Shiyun Zhang(张世允) Density of excess modes below the first phonon mode in four-dimensional glasses 2024 Chin. Phys. B 33 076401

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Density of excess modes below the first phonon mode in four-dimensional glasses

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