Classification for the universal scaling of Néel temperature and staggered magnetization density of three-dimensional dimerized spin- 12 antiferromagnets

Inspired by the recent theoretical development relevant to the experimental data of TlCuCl3, particularly those associated with the universal scaling between the Néel temperature TN and the staggered magnetization density Ms, we carry out a detailed investigation of three-dimensional (3D) dimerized quantum antiferromagnets using the first-principles quantum Monte Carlo calculations. Through this study we wish to better understand the microscopic effects on these scaling relations of TN and Ms, hence to shed light on some of the observed inconsistency between the theoretical and the experimental results. Remarkably, for the considered 3D dimerized models, we find that the established universal scaling relations are not only valid, but can each be categorized within its kind by the amount of stronger antiferromagnetic couplings connected to each spin. Convincing numerical evidence is provided to support the validity of this classification scheme. Based on all the related results known in the literature, we further argue that the proposed categorization for the universal scaling investigated in our paper should be applicable for 3D dimerized spin systems with (certain kinds of) quenched disorder and (or) on lattice geometries other than those considered here. The relevance of the outcomes presented in this investigation to the experiments of TlCuCl3 is briefly discussed as well.