Continuum limit of the vibrational properties of amorphous solids

Hideyuki Mizuno, Hayato Shiba, Atsushi Ikeda

Research output: Contribution to journalArticlepeer-review

135 Citations (Scopus)


The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

Original languageEnglish
Pages (from-to)E9767-E9774
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number46
Publication statusPublished - 2017 Nov 14


  • Amorphous solids
  • Continuum limit
  • Non-Debye law
  • Phonons
  • Soft localized modes

ASJC Scopus subject areas

  • General


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