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Density of excess modes below the first phonon mode in four-dimensional glasses |
| Lijin Wang(王利近)1,†, Ding Xu(胥鼎)2,‡, and Shiyun Zhang(张世允)2,§ |
1 School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China;
2 Department of Physics, University of Science and Technology of China, Hefei 230026, China |
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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.
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Received: 22 February 2024
Revised: 02 April 2024
Accepted manuscript online: 12 April 2024
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PACS:
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64.70.Q-
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(Theory and modeling of the glass transition)
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64.70.kj
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(Glasses)
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| 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
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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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