Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Novel elastic instability of amorphous solids in finite spatial
  dimensions   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 \textit{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, {\bf 16}, 7279, 2020]. 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.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph