AI 中文总结
该研究推导了横场模型的通用相关不等式，结合已有结果明确了量子自旋玻璃的高低场重叠相，还证明了重叠量的集中性并确定了量子SK模型压强的高场渐近行为。
AI 中文摘要
我们研究具有对相互作用的横场模型类，包括量子居里-外斯模型、横场伊辛模型，以及基于Sherrington-Kirkpatrick（SK）模型和Edwards-Anderson模型的量子自旋玻璃。我们的主要结果是基于高斯卷积估计的通用相关不等式，该不等式由Ding-Song-Sun不等式的推广和Brascamp-Lieb凸性技术的应用推导得到。这些结果适用于足够强的横场，对于量子自旋玻璃，可得到无副本序的高场区域。结合此前已确立的低场副本对称性破缺区域，这给出了截然不同的低场和高场重叠相。作为本文推导的基础函数积分的对数索伯列夫不等式的推论，我们证明了自重叠和副本重叠的集中性，并确定了量子SK模型中压强的高场渐近行为。
英文摘要
We study the class of transversal field models with pair interactions, including the quantum Curie-Weiss and the transversal field Ising model, as well as quantum spin glasses based on the Sherrington-Kirkpatrick (SK) and Edwards-Anderson models. Our main result is a general correlation inequality based on a Gaussian convolution estimate, which is derived from an extension of the Ding-Song-Sun inequality and an application of Brascamp-Lieb convexity techniques. The results apply for sufficiently strong transversal fields and, for quantum spin glasses, yield a high-field regime without replica order. Combined with the previously established low-field replica-symmetry-breaking regime, this gives distinct low- and high-field overlap phases. As a corollary of the logarithmic Sobolev inequalities for the underlying functional integrals derived here, we show the concentration of the self- and replica-overlap, and determine the high-field asymptotics of the pressure in the quantum SK model.
Comments22 pages
