Low-frequency vibrational spectrum of mean-field disordered systems

Eran Bouchbinder, Edan Lerner, Corrado Rainone, Pierfrancesco Urbani, and Francesco Zamponi
Phys. Rev. B 103, 174202 – Published 7 May 2021

Abstract

We study a recently introduced and exactly solvable mean-field model for the density of vibrational states D(ω) of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness κ drawn from a distribution p(κ), subjected to a constant field h and interacting bilinearly with a coupling of strength J. We investigate the vibrational properties of its ground state at zero temperature. When p(κ) is gapped, the emergent D(ω) is also gapped, for small J. Upon increasing J, the gap vanishes on a critical line in the (h,J) phase diagram, whereupon replica symmetry is broken. At small h, the form of this pseudogap is quadratic, D(ω)ω2, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough h, a quartic pseudogap D(ω)ω4, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.

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  • Received 28 December 2020
  • Accepted 13 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.174202

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Eran Bouchbinder1, Edan Lerner2, Corrado Rainone2,*, Pierfrancesco Urbani3, and Francesco Zamponi4

  • 1Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
  • 2Institute of Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands
  • 3Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France
  • 4Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France

  • *c.rainone@uva.nl

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Vol. 103, Iss. 17 — 1 May 2021

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