Fig. 3.

The vDOSs at different $p$ in the 3D model system. $g(\omega )$ is plotted against the scaled frequency $\widehat{\omega }=\omega /{\omega }_{\ast }$ for several different $p$. Inset is the same as the main image, but for the reduced vDOSs $g/{\widehat{\omega }}^2$. Around ${\omega }_{\text{BP}}=\mathrm{\hspace{0.17em}0.21}{\omega }_{\ast }$, the vDOSs are collapsed onto the non-Debye scaling law $g(\omega )={\alpha }_{\text{BP}}{\widehat{\omega }}^2$ with ${\alpha }_{\text{BP}}=\mathrm{\hspace{0.17em}0.66}$.