标题： 站点单调性性质及其在量子自旋系统中的应用 显示英文标题

标题： Site-monotonicity properties for reflection positive measures with applications to quantum spin systems

摘要： 我们考虑一个在局部空间乘积上的通用统计力学模型，并证明如果相应的测度是反射正的，那么两点函数的几种站点单调性性质成立。 作为这样一个一般定理的应用，我们推导出量子海森堡反铁磁体和$XY$模型的自旋-自旋关联的站点单调性性质，我们证明这样的自旋-自旋关联在所有坐标均为奇数的顶点上是逐点一致正的——改进了之前仅对Cesàro和成立的正性结果——并且我们推导出在各种随机环模型中，环连接两个顶点的概率的站点单调性性质，包括自旋O(N)模型的环表示、双钉模型、环O(N)模型、格子排列，从而扩展了\textit{Lees和Taggi (2019)}的先前结果。 显示英文摘要

摘要： We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application of such a general theorem, we derive site-monotonicity properties for the spin-spin correlation of the quantum Heisenberg antiferromagnet and $XY$ model, we prove that such spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates -- improving previous positivity results which hold for the Ces\`aro sum -- and we derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model, lattice permutations, thus extending the previous results of \textit{Lees and Taggi (2019)}.