Using the first-principles quantum Monte Carlo calculations, we investigate the previously established universal scaling, as well as the corresponding classification schemes, for the Néel temperature TN and the staggered magnetization density Ms of three-dimensional dimerized quantum antiferromagnets. Particularly, the calculations are done on both the stacked honeycomb and cubic lattices. In addition to simulating models with two types of antiferromagnetic couplings (bonds) like those examined in earlier studies, here a tunable parameter controlling the strength of the third type of bond is introduced. Interestingly, while minor effects due to microscopic details appear, the data for the studied models with two types of bonds do fall on top of the universal scaling curves determined previously. Moreover, the most striking result suggested in our study is that with the presence of three kinds of bonds in the investigated models, the considered scaling relations between TN and Ms can be classified by the coordination number of the underlying lattice geometries. The findings presented here broaden the applicability of the associated classification schemes formerly discovered. In particular, these results not only are interesting from a theoretical point of view but also can serve as useful guidelines for the relevant experiments.
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