Low energy excitations of mean-field glasses

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.

Field theory for zero temperature soft anharmonic spin glasses in a field

“…Here we follow the very same construction. Moreover, we note that vectorial models for O(M ) spins have been used recently in [26,27] to model the density of states in zero temperature amorphous solids. The model in Eq.…”

“…The model in Eq. ( 1) differs from [26,27] because of two points: (i) we consider real (unbounded) spins subjected to a random anharmonic (quartic) local potential which is essential for the physical behavior close to the mean field spin glass transition at zero temperature, and (ii) we include, as in [18], the adjacency matrix c and use the M → ∞ limit as a way to generate a field theory expansion at fixed and finite spatial dimension. For d → ∞ and M = 1 the model reduces to the KHGPS model as much as in the same limit the Edwards-Anderson model [28] gives the Sherrington-Kirkpatrick model [29].…”