Recently, progress has been made in 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 and not the quartic law. To address this inconsistency, we presented a new type of instability, which is different from the conventional one, and proposed that amorphous solids are marginally stable considering the new instability in the preceding study [M. Shimada, H. Mizuno and A. Ikeda, Soft Matter, 2020, 16, 7279]. In this study, we further extend and detail the results for these instabilities. By analyzing various examples of disorder, we demonstrate that real glasses in finite spatial dimensions can be marginally stable by the proposed novel instability.

中文翻译：

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有限空间中非晶态固体的新型弹性不稳定性

最近，在对非晶态固体中异常振动激发的理解上取得了进展。在最低频率区域，振动频谱遵循非德拜四次定律，该定律一直持续到零频率而没有任何频率间隙。这种无间隙的状态振动密度（vDOS）表明玻璃正处于不稳定的边缘。现在，边缘稳定性的这一特征已成为眼镜理论中的关键概念。特别是，基于边际稳定性的弹性理论可以预测无间隙vDOS。但是，该理论产生了二次定律，而不是二次定律。为了解决这种不一致问题，我们提出了一种新型的不稳定性，它不同于传统的不稳定性，并考虑到先前研究中的新不稳定性，提出了无定形固体在一定程度上是稳定的[M. Shimada，H。Mizuno和A.Ikeda，软物质，到2020年，16，7279]。在这项研究中，我们进一步扩展和详细说明了这些不稳定性的结果。通过分析各种疾病的例子，我们证明了有限的空间尺寸的真实眼镜可以通过提出的新型不稳定性而处于边际稳定状态。