Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution

Silvio Franz 1 Giorgio Parisi 2 Pierfrancesco Urbani 3 Francesco Zamponi 4

Proceeding of the national academy of sciences, National Academy of Sciences, 2015, 112, pp.14539

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 towards a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. Dipartimento di Fisica and INFM
  • 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681
  • 4. ETH Zurich