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(ω)with frequency ω follows a power-law scaling:D(ω)～ωγ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finite-size glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)～ω3 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(ω)below the first phonon-like mode varies with spatial dimensions:D(ω)increases in 2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω3.5 scaling,rather than the ω4 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(ω)～ω3.5 below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.
基金项目
National Natural Science Foundation of China(12374202)
National Natural Science Foundation of China(12004001)
Anhui Projects(2022AH020009)
Anhui Projects(S020218016)
Anhui Projects(Z010118169)
Hefei City(Z020132009)
Hefei Advanced Computing Center,Beijing Super Cloud Computing Center()
High-Performance Computing Platform of Anhui University()
NETL
NSTL
万方数据