Novel elastic instability of amorphous solids in finite spatial dimensions

Recent progress has advanced the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic law, \textit{not} the quartic law. To address this inconsistency, our preceding paper~[M. Shimada, H. Mizuno, and A. Ikeda, Soft Matter, {\bf 16}, 7279, 2020] presented a new type of instability, which is different from the well-established, conventional one and proposed that amorphous solids are marginally stable in the sense of the former. In this paper, we report further extended and detailed results for these instabilities. Through the analyses of various examples of disorder, we demonstrate that real glasses in finite spatial dimensions can be marginally stable by this novel instability.