优化诱导随机矩阵中复制对称破缺的谱特征
Spectral Signatures of Replica Symmetry Breaking in Optimization-Induced Random Matrices
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中文总结 AI 辅助
研究由吉布斯测度生成的优化诱导矩阵系综，探讨诱导谱与玻璃态吉布斯几何结构的关系。通过密集张量优化模型发现，单个诱导矩阵主导主体消除玻璃态结构，两个矩阵差异的谱能呈现玻璃态几何结构，帕里西理论和蒙特卡罗方法证实了该机制。
中文摘要 AI 辅助
我们研究了由吉布斯测度生成的优化诱导矩阵系综。赋予构型权重的相同淬火无序也提供了在这些构型上观察到的矩阵元素。对于玻璃态吉布斯测度，这引发了一个自然问题：诱导谱是否继承了潜在的玻璃态吉布斯几何结构？在一个密集张量优化模型中，我们找到了一个选择性答案。单个诱导矩阵有一个通用的主导主体，它消除了玻璃态结构。由相同无序中独立热样本构建的两个矩阵的差异则不然：其谱给出了玻璃态吉布斯几何结构的清晰图像，由样本间相互重叠分布编码。帕里西理论和蒙特卡罗方法在简单相和玻璃态相中证实了这一机制。
英文摘要
We study optimization-induced matrix ensembles generated by Gibbs measures. The same quenched disorder that weights configurations also supplies the matrix entries observed on them. For glassy Gibbs measures this raises a natural question: does the induced spectrum inherit the underlying glassy Gibbs geometry? In a dense tensor optimization model we find a selective answer. A single induced matrix has a universal leading bulk that washes out the glassy organization. The difference of two matrices built from independent thermal samples in the same disorder does not: its spectrum gives an explicit image of the glassy Gibbs geometry, encoded by the distribution of mutual overlaps between samples. Parisi theory and Monte Carlo confirm this mechanism across simple and glassy phases.
