论文标题
量子自旋系统应用的反射阳性措施的现场单调性特性
Site-monotonicity properties for reflection positive measures with applications to quantum spin systems
论文作者
论文摘要
我们在局部空间的乘积上考虑了一个一般的统计力学模型，并证明，如果相应的度量为反射阳性，则具有两点函数保持的几种位点自声调属性。 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 Cesàro sum -- and we derive site-monotonicity properties for the probability that一个环连接了各种随机循环模型的两个顶点，包括旋转O（n）模型的循环表示，双二聚体模型，循环O（n）模型，晶格排列，从而扩展了\ textit {lees and taggi（2019）}的先前结果。
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 Cesàro 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)}.
