玻璃平均场模型中的局部微观力学揭示其非平衡RSB相的关键性质
Local micromechanics in a mean-field model of glasses reveal key properties of its non-equilibrium RSB phase
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中文总结 AI 辅助
研究玻璃平均场模型非平衡RSB相，通过定义微观力学响应函数，建立力单极刚度与全局磁化率关系，实现集体自由度具体描述，可由单极响应统计计算振动谱并提取软玻璃模式特征标度。
中文摘要 AI 辅助
最近提出的玻璃平均场模型在某些参数范围内具有平衡的零温度复制对称破缺（RSB）转变。在此范围内，复制对称相中的模型解由有效自洽随机势表示，向RSB相的转变以谱边缘局域模式和赝能隙四次振动谱的出现为特征。这些性质在非平衡条件下的模型数值解中得以保留。受计算机玻璃近期进展启发，定义了微观力学响应函数，建立了力单极刚度与全局磁化率之间的精确关系，所得微观力学可观测量构成模型集体自由度的具体实现，还表明模型振动谱可仅从单极响应统计计算得出，并提取出与有限维实验室玻璃中玻色子峰相关的软玻璃模式的特征频率/刚度标度。
英文摘要
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.
