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, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also 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 and lattice permutations, thus extending the previous results of Lees and Taggi (2019).

我们考虑局部空间乘积的一般统计力学模型，并证明，如果相应的量度为正反射，则两点函数的几个站点单调性成立。作为应用，我们推导了量子海森堡反铁磁体和XY的自旋-自旋相关性的位点单调性在模型中，我们证明了自旋-自旋相关性在具有所有奇数坐标的顶点上点向均匀一致，从而改善了先前对Cesàro和求正的结果。我们还推导了站点单调性属性，以了解在各种随机回路模型中回路连接两个顶点的概率，包括自旋O（N）模型，双二聚体模型，回路O（N）模型和晶格的回路表示排列，从而扩展了Lees和Taggi（2019）的先前结果。