Finite-size effects in the nonphononic density of states in computer glasses
Edan Lerner
Abstract
The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency $\ensuremath{\omega}$ in structural glasses, $\mathcal{D}(\ensuremath{\omega})$, was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, $\mathcal{D}(\ensuremath{\omega})$ increases from zero frequency as ${\ensuremath{\omega}}^{4}$, independent of spatial dimension and of microscopic details. However, it has been shown [Lerner and Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)] that the preparation protocol employed to create glassy samples may affect the form of their resulting $\mathcal{D}(\ensuremath{\omega})$: glassy samples rapidly quenched from high-temperature liquid states were shown to feature $\mathcal{D}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}<4$, presumably limiting the degree of universality of the ${\ensuremath{\omega}}^{4}$ law. Here we show that exponents $\ensuremath{\beta}<4$ are seen only in small glassy samples quenched from high-temperature liquid states---whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations---while larger glassy samples made with the same protocol feature the universal ${\ensuremath{\omega}}^{4}$ law. Our results demonstrate that observations of $\ensuremath{\beta}<4$ in the nonphononic density of states stem from finite-size effects, and we thus conclude that the ${\ensuremath{\omega}}^{4}$ law should be featured by any sufficiently large glass quenched from a melt.