Local micromechanics in a mean-field model of glasses reveal key properties of its non-equilibrium RSB phase
Abstract
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 degree of freedoms, 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 non-equilibrium 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 non-equilibrium 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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BibTeX
@misc{suda2026local,
title = {{Local micromechanics in a mean-field model of glasses reveal key properties of its non-equilibrium RSB phase}},
author = {Makoto Suda and Edan Lerner and Eran Bouchbinder},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.23603},
eprint = {2607.23603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23603},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local micromechanics in a mean-field model of glasses reveal key properties of its non-equilibrium RSB phase
AU - Makoto Suda
AU - Edan Lerner
AU - Eran Bouchbinder
PY - 2026
DA - 2026/07/26
PB - arXiv
DO - 10.48550/arxiv.2607.23603
UR - https://arxiv.org/abs/2607.23603
AB - 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 degree of freedoms, 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 non-equilibrium 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 non-equilibrium 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.
ER -