论文标题
平均场自旋眼镜的新兴自动流动
An Emergent Autonomous Flow for Mean-Field Spin Glasses
论文作者
论文摘要
我们研究对称和不对称的自旋玻璃模型的动力学尺寸$ n $。分析是在双重经验过程的角度：这既包含旋转，又包含在特定时间（不了解相关历史记录）的每个自旋感觉。可以证明，在大$ n $限制中，双重经验过程的动态在有限的时间间隔内成为确定性和自主性。这与众所周知的事实并不矛盾：SK旋转玻璃动力学是非马克维亚人（在$ n $ limit中），因为经验过程的拓扑与不同时间的单个旋转相关性。在大$ n $限制中，双经验过程的密度的演变接近非本地自动pde操作员$φ_T$。由于紧急动态是自主的，因此在将来的工作中，人们将能够应用PDE技术来分析$φ_T$的分叉。 SK Glauber动力学的初步数值结果表明，当流动运算符的稳定固定点$φ_T$不稳定时，就会发生“玻璃动力学相变”。
We study the dynamics of symmetric and asymmetric spin-glass models of size $N$. The analysis is in terms of the double empirical process: this contains both the spins, and the field felt by each spin, at a particular time (without any knowledge of the correlation history). It is demonstrated that in the large $N$ limit, the dynamics of the double empirical process becomes deterministic and autonomous over finite time intervals. This does not contradict the well-known fact that SK spin-glass dynamics is non-Markovian (in the large $N$ limit) because the empirical process has a topology that does not discern correlations in individual spins at different times. In the large $N$ limit, the evolution of the density of the double empirical process approaches a nonlocal autonomous PDE operator $Φ_t$. Because the emergent dynamics is autonomous, in future work one will be able to apply PDE techniques to analyze bifurcations in $Φ_t$. Preliminary numerical results for the SK Glauber dynamics suggest that the `glassy dynamical phase transition' occurs when a stable fixed point of the flow operator $Φ_t$ destabilizes.
