Makoto Suda (Department of Earth Science, Tohoku University, Japan), Edan Lerner (Institute for Theoretical Physics, University of Amsterdam, The Netherlands), Eran Bouchbinder (Chemical and biological Physics Department, Weizmann Institute of Science, Israel)
Glasses feature a broad range of universal vibrational and mechanical phenomena, including nonphononic vibrational spectra, soft localized modes, plastic instabilities and elasto-plastic yielding transitions, all linked to the underlying disorder-induced, complex energy landscape. A major theoretical challenge is to develop a minimal model that can unifiedly predict these diverse glassy phenomena. We study a recently-introduced Hamiltonian mean-field model, which has already been shown to predict the universal nonphononic DG(ω)~ω4tail of the vibrational density of state populated by soft localized modes and a boson peak at higher vibrational frequency ω populated by delocalized modes [1, 2, 3], focusing on its mechanical properties. We formulate a micromechanical framework --- based on the linear response to local force monopoles --- and show using exact mean-field relations that a well-defined monopole response requires a finite spin-glass susceptibility, which is self-consistently related to the DG(ω)~ω4 tail distribution. We use this micromechanical framework to identify the emergent plastic degrees of freedom in the model, which in turn allow to extract a characteristic frequency scale that is shown to be intrinsically linked to the boson peak frequency across a wide range of quenched disorder levels. Finally, we show that when the model is strongly driven by external forces, it naturally predicts an oscillatory yielding transition and mechanical memory formation [4], which mirror corresponding findings in computer and lab glasses. These result demonstrate the generic `glassiness' and unifying nature of the mean-field model.
References:
[1] E. Bouchbinder, E. Lerner, C. Rainone, P. Urbani, F. Zamponi, Phys. Rev. B 103, 174202 (2021)
[2] C. Rainone, P. Urbani, F. Zamponi, E. Lerner, E. Bouchbinder, SciPost Phys. Core 4, 008 (2021)
[3] A. Moriel, E. Lerner, E. Bouchbinder, Phys. Rev. Res. 6, 023053 (2024)
[4] M. Suda, E. Lerner, E. Bouchbinder, Phys. Rev. Lett. 135, 258201 (2025)