The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$, and 3 dimensions. At the critical point an algebraic decay of the form $\sim r^{-{\eta }_t}$ is found, with a decay exponent being approximately ${\eta }_t\approx 2+2d$. In $d=1$ the results are related to dimer-dimer correlations in the random antiferromagnetic $XX$ chain and have been tested by numerical calculations using free-fermionic techniques.

中文翻译：

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随机横向场伊辛模型的横向自旋相关性

随机横向场Ising模型在有限维晶格中的临界行为由无限无序固定点控制，该无序固定点已经通过使用强无序重归一化组（SDRG）方法进行了计算。在这里，我们扩展这些研究并通过SDRG方法的数值实现来计算连接的横向自旋相关函数。$d=\mathrm{1个}，\mathrm{2个}$，以及3个维度。在临界点上，形式的代数衰减$〜{\mathrm{[R}}^{-{\eta }_{Ť}}$ 被发现，其衰减指数约为 ${\eta }_{Ť}\approx \mathrm{2个}+\mathrm{2个}d$。在$d=\mathrm{1个}$ 结果与随机反铁磁中的二聚体-二聚体相关性有关 $XX$ 链，并已通过使用自由铁离子技术的数值计算进行了测试。