广义TAP自由能最大值的大偏差
Large deviations for the maximum of the generalized TAP free energy
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中文总结 AI 辅助
该论文研究Ising混合p自旋模型中广义TAP自由能最大值的大偏差，通过新插值与Huang-Sellke策略确定超对称公式为TAP最大值存在的大偏差指数，还为Ising模型Parisi公式提供构造性证明。
中文摘要 AI 辅助
我们研究了Chen、Panchenko和Subag为Ising混合p自旋模型引入的广义TAP自由能最大值的大偏差。上界使用了一种新的Guerra型插值，该插值可能对其他自旋玻璃模型也有用；下界遵循Huang和Sellke的策略。我们证明，超对称临界点在其自身球面上的正重叠处没有竞争者，因此它们构成一个球形码，这将退火计数转化为存在概率的下界。这确定了物理学家提出的超对称公式是TAP最大值存在的大偏差指数，而非普通退火复杂度。所得速率函数是底部原子质量中受约束Parisi值的Legendre变换。在TAP祖先上方的带中重复相同论证，将在严格稳定性假设下为Ising模型的Parisi公式提供构造性证明。
英文摘要
We study large deviations of the maximum of the generalized TAP free energy introduced by Chen, Panchenko, and Subag for the Ising mixed $p$-spin model. The upper bound uses a new Guerra-type interpolation that may also be useful for other spin-glass models. The lower bound follows the strategy of Huang and Sellke. We show that supersymmetric critical points have no competitor at positive overlap on their own sphere. As such, they form a spherical code, which turns the annealed count into a lower bound on the probability of existence. This identifies the supersymmetric formula proposed by physicists with the large-deviation exponent for the existence of TAP maxima, rather than with the ordinary annealed complexity. The resulting rate function is the Legendre transform of a constrained Parisi value in the bottom-atom mass. The same argument, iterated in bands above TAP ancestors, would give a constructive proof of the Parisi formula for the Ising model under a technical strict stability assumption.
