A recently formulated mean-field model of glasses features an equilibrium, zero-temperature Replica-Symmetry-Breaking (RSB) transition in some parameter range. In this range, the model's solution in the Replica-Symmetric phase is expressed in terms of an effective, self-consistent random potential for uncoupled degrees of freedom, where the transition to the RSB phase is characterized by the emergence of spectral-edge localized modes and a pseudogapped quartic vibrational spectrum, resulting in a finite spin-glass susceptibility. These properties are preserved in numerical solutions of the model under nonequilibrium conditions, i.e., upon an instantaneous quench. Inspired by recent advances in computer glasses, we define a micromechanical response function—the linear response to local force monopoles—in the framework of the mean-field model. We establish exact relations between the force monopole stiffness and global susceptibilities, which suggest a close correspondence between the nonequilibrium RSB phase of the model and the above-mentioned effective random potential description. As such, the obtained micromechanical observables constitute a concrete realization of the collective degrees of freedom of the model, offering a bridge between a glassy mean-field model and finite-dimensional glasses. We show that the model's vibrational spectrum can be computed solely from the monopole response statistics and, by employing a marginal stability criterion, we extract a characteristic frequency/stiffness scale of soft glassy modes, which is related to the boson peak in finite-dimensional, laboratory glasses.

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• Bifurcations
• Many-body localization
• Nonequilibrium & irreversible thermodynamics
• Phase transitions
• Disordered systems
• Glasses
• Nonequilibrium systems
• Finite-size scaling
• Mean field theory
• Random matrix theory
• Replica theory