Universal spectrum of normal modes in low-temperature glasses

By Silvio Franz, Giorgio Parisi, Pierfrancesco Urbani, Francesco Zamponi. 2015

168 citations recorded by the source corpus.

Significance The vibrational spectrum of glasses displays an anomalous excess of soft, low-frequency modes with respect to crystals. Such modes are responsible for many anomalies in thermodynamic and transport properties of low-temperature glasses. Many distinct proposals have been formulated to understand their origin but none of them results from the analytic solution of a microscopically grounded model. Here we solve analytically the spectrum of a simple model that belongs to the same universality class of glasses, and identify two distinct mechanisms that are responsible for the soft modes. 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.

Subfields: Acoustics and Ultrasonics, Condensed Matter Physics, Materials Chemistry, AI for Physical Sciences

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Citations in the corpus

The jamming transition as a paradigm to understand the loss landscape of deep neural networks (2018, background): “[55] Silvio Franz, Giorgio Parisi, Pierfrancesco Urbani, and”
A jamming transition from under- to over-parametrization affects generalization in deep learning (2018, background): “It generalized a previous seminal analogy established between the loss landscape of the perceptron (the simplest network without hidden neurons) and the energy landscape of spherical particles [18], and specified the universality class to which deep learning corresponds to.”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, methodology): “A similar situation appears in the replica approach to the problem: The original 1RSB calculation under the replica approach of the force distribution for hard sphere glasses done in (Parisi and Zamponi, 2010) led to a trivial scaling θ1RSB = 0, (132) while the non-zero exponent was only obtained wh”
Universality of jamming of nonspherical particles (2018, background): “In the full RSB phase, the eigenvalue distribution function is gapless, and thus, the system is indeed marginally stable (26).”
Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, background): “In [ 16 ] the spectrum of the Hessian matrix of the energy minima in the UNSAT phase of the perceptron has been computed showing that it captures essential features of the vibrations of low temperature glasses.”