AI 中文总结
研究伊辛自旋玻璃自由能上大偏差的TAP态，证明其存在性、局域化及边缘稳定性，并给出速率代价条件。
AI 中文摘要
我们通过Chen、Panchenko和Subag的广义TAP自由能$F_{\mathrm{TAP}}$研究混合$p$-自旋伊辛自旋玻璃自由能的上大偏差。对于每个收敛半径大于1的混合，$\max F_{\mathrm{TAP}}$和$\log Z_N$在速度$N$下具有相同的大偏差；证明结合了他们的带定理与Ramsey定理。对于满足$\sum_p 2^p\beta_p^2<\infty$的凸混合，水平$f$处的上偏差由广义TAP临界点承载，这些临界点以自由能速率存在，无需Boursier的严格Plefka条件。在指数阶更小的事件之外，水平$f$处的近极大点位于约束Parisi障碍的接触集附近，遵循Auffinger-Chen场定律，其Hessian体接近反射Pastur定律，该定律的边缘非正，并且在障碍二阶平坦的接触处恰好消失。当每个接触都属于这种类型时，固定的稳定性边际需要付出速率代价。
英文摘要
We study upper large deviations of the free energy of mixed $p$-spin Ising spin glasses through the generalized TAP free energy $F_{\mathrm{TAP}}$ of Chen, Panchenko and Subag. For every mixture with radius of convergence greater than one, $\max F_{\mathrm{TAP}}$ and $\log Z_N$ have the same large deviations at speed $N$; the proof combines their band theorem with Ramsey's theorem. For convex mixtures with $\sum_p 2^pβ_p^2<\infty$, upper deviations at level $f$ are carried by generalized TAP critical points, which exist at the free-energy rate without Boursier's strict Plefka condition. Outside an event of smaller exponential order, near-maximizers at level $f$ lie near the contact set of a constrained Parisi obstacle, follow the Auffinger-Chen field law, and have Hessian bulk near a reflected Pastur law whose edge is nonpositive and vanishes exactly at contacts where the obstacle is flat to second order. Where every contact is of this kind, a fixed stability margin costs rate.
Comments164 pages, 4 figures, 2 tables
