AI 中文总结
本研究求解混合球形(p+s)-自旋玻璃的渐近动力学方程，确定其老化相图，得到渐近能量的解析表达式，发现不同有效温度老化态间的相变，数值积分验证了预测的老化态。
AI 中文摘要
我们确定了从随机构型淬火到零温度的混合球形(p+s)-自旋玻璃的老化相图。通过求解Cugliandolo和Kurchan的渐近动力学方程，我们发现具有1个、2个以及连续多个有效温度的老化态之间存在相变，包括离散与连续层级共存的相。我们得到了动力学渐近达到的能量的解析表达式。在结合两两相互作用与高阶相互作用的模型中，当相互作用阶数足够分离（s>3）时，存在一个完全连续的相，其中梯度下降弛豫收敛到算法能量下界；而在仅含高阶相互作用（p≥3）的混合模型中，能量弛豫始终严格高于该下界。动力学方程的数值积分与预测的两步及混合离散-连续老化态一致。
英文摘要
We determine the aging phase diagram of mixed spherical $(p+s)$-spin glasses quenched from random configurations to zero temperature. Solving the asymptotic dynamical equations of Cugliandolo and Kurchan, we find transitions between aging states with one, two, and continuously many effective temperatures, including phases in which discrete and continuous hierarchies coexist. We obtain analytic expressions for the energies reached asymptotically by the dynamics. In models combining pairwise and higher-order interactions, and sufficiently separated interaction orders ($s>3$), a fully continuous phase exists, where the gradient descent relaxation converges to the algorithmic energy lower bound. Instead, in mixed models with only high-order interactions ($p\ge3$) the energy relaxation remains strictly above it. Numerical integration of the dynamical equations is consistent with the predicted two-step and mixed discrete--continuous aging states.
Comments5 + 2 pages, 4 figures
