Universal spectrum of normal modes in low-temperature glasses

2015/06/30 by Silvio Franz, Giorgio Parisi, Pierfrancesco Urbani +1 · 9 citations
Materials Science · Physics and Astronomy · #Condensed matter physics #Jamming #Material Dynamics and Properties #Molecular vibration #Molecule #Normal mode #Phase transition #Physics #Quantum mechanics #Random lasers and scattering media #Soft modes #Spectrum (functional analysis) #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #Vibration #Vibrational spectrum #cond-mat.dis-nn #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1073/pnas.1511134112

published as PNAS 112, 14539-14544 (2015) · 6 pages, 3 figures, submitted to PNAS

arxiv created 2015/09/29 · openalex publication_date 2015/11/11 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.

Citations

• THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION
• Solution of 'Solvable model of a spin glass'
• Anharmonic and quasi-localized vibrations in jammed solids—Modes for mechanical failure
• The space of interactions in neural network models
• Anomalous low-temperature thermal properties of glasses and spin glasses
• Jamming at zero temperature and zero applied stress: The epitome of disorder
• Excess Vibrational Modes and the Boson Peak in Model Glasses
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Vibrations and Diverging Length Scales Near the Unjamming Transition
• On asymptotics of eigenvectors of large sample covariance matrix
• Soft modes in jammed hard spheres (I): Mean field theory of the isostatic transition

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• Spin-glass-like aging in colloidal and granular glasses
• Jamming transition as a paradigm to understand the loss landscape of deep neural networks