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It is now well established that structural glasses possess disorder- andfrustration-induced soft quasilocalized excitations, which play key roles invarious glassy phenomena. Recent work has established that in modelglass-formers in three dimensions, these non-phononic soft excitations mayassume the form of quasilocalized, harmonic vibrational modes whose frequencyfollows a universal density of states $D(\omega)\!\sim\!\omega^4$,independently of microscopic details, and for a broad range of glasspreparation protocols. Here we further establish the universality of thenon-phononic density of vibrational modes by direct measurements in modelstructural glasses in two dimensions and four dimensions. We also investigatetheir degree of localization, which is generally weaker in lower spatialdimensions, giving rise to a pronounced system-size dependence of thenon-phononic density of states in two dimensions, but not in higher dimensions.Finally, we identify a fundamental glassy frequency scale $\omega_c$ abovewhich the universal $\omega^4$ law breaks down.

Universal non-phononic density of states in 2D, 3D and 4D glasses