Abstract
We study a recently introduced and exactly solvable mean-field model for the density of vibrational states of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness drawn from a distribution , subjected to a constant field and interacting bilinearly with a coupling of strength . We investigate the vibrational properties of its ground state at zero temperature. When is gapped, the emergent is also gapped, for small . Upon increasing , the gap vanishes on a critical line in the phase diagram, whereupon replica symmetry is broken. At small , the form of this pseudogap is quadratic, , and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough , a quartic pseudogap , 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.
- Received 28 December 2020
- Accepted 13 April 2021
DOI:https://doi.org/10.1103/PhysRevB.103.174202
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