Low energy excitations of mean-field glasses

TL;DR

This paper investigates the spectral properties of linear excitations around energy minima in a mean-field disordered model, revealing a pseudogap and localization phenomena, with implications for understanding glassy energy landscapes.

Contribution

It provides new insights into the nature of excitations in mean-field glasses, highlighting the existence of a pseudogap and localization effects near typical and ultra-stable minima.

Findings

Spectra of excitations are ungapped with a pseudogap.

Deeper minima show increased localization and fewer excitations.

Ultra-stable minima have an energy gap and lack localized excitations.

Abstract

We study the linear excitations around typical energy minima of a mean-field disordered model with continuous degrees of freedom undergoing a Random First Order Transition (RFOT). Contrary to naive expectations, the spectra of linear excitations are ungapped and we find the presence of a pseudogap corresponding to localized excitations with arbitrary low excitation energy. Moving to deeper minima in the landscape, the excitations appear increasingly localized while their abundance decreases. Beside typical minima, there also exist rare ultra-stable minima, with an energy gap and no localised excitations.