Flavio Nicoletti — Sapienza Università di Roma #
Low energy excitations in mean field spin glasses #
We discuss the properties of the energy Hessian spectrum of excitations of simple vector spin glasses at zero temperature. We consider two mean field models, the first defined on a fully-connected graph and the second on a sparse random graph. The models are shown to reproduce key features of the low energy modes of glassy systems: the vibrational density of states features a pseudo-gap at low frequency with quasi-localised excitations. We characterise the properties of soft modes with respect to the zero-temperature spin glass transition in an external magnetic field. We show that the zero-temperature transition is a delocalisation transition for soft modes, discussing the features of this phenomenon in the two different cases (dense and sparse).