Nonphononic spectrum of two-dimensional structural glasses

The scaling form and system-size dependence of the low-frequency wing of the nonphononic vibrational spectrum of two-dimensional structural glasses have been debated in recent literature. Here we provide numerical evidence that the prefactor $A_{\mathrm{g}}$ of the low-frequency nonphononic vibrational spectrum – the latter grows from zero frequency ($\omega \text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0$) as $A_{\mathrm{g}}{\omega }^{\beta }$ – is system-size dependent, and that the exponent $\beta$ exhibits a similar glass-formation-protocol and system-size dependence as seen in three-dimensional structural glasses.