Marginal Stability of Soft Anharmonic Mean Field Spin Glasses

Crystalline solids can be understood in terms of their lattice symmetries which control, at low energies their phononic spectrum. Conversely, what happens with disordered solids such as glasses is very much not well understood. Such amorphous systems present a gapless spectrum of harmonic excitations together with an abundance of non-linear excitations giving rise to avalanches and two-level systems. We discuss the solution of the glass phase of a mean-field model, recently introduced, and show that it is marginally stable by means of two different mechanisms: soft linear excitations —appearing in a gapless spectrum of the Hessian of the energy landscape— and pseudogapped non-linear excitations —corresponding to nearly degenerate two level systems (TLS). In this model TLS appear in a dynamical way and are the result of interactions between degrees of freedom.