Universal scaling of three-dimensional dimerized quantum antiferromagnets on bipartite lattices

Using the first principles quantum Monte Carlo (QMC) calculations, we investigate the previously established universal scaling between the N\'eel temperature $T_N$ and the staggered magnetization density $M_s$ of three-dimensional (3D) dimerized quantum antiferromagnets. Particularly, the calculations are done on both the stacked honeycomb and the 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 third type of bond is introduced. Interestingly, while the data of models with two types of bonds obtained here fall on top of the universal scaling curves determined previously, the effects due to microscopic details do appear. 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 $T_N$ and $M_s$ can be classified by the coordinate number of the underlying lattice geometries. The findings presented here broaden the applicability of the associated classification schemes formerly discovered. In particular, these results are not only interesting from a theoretical point of view, but also can serve as useful guidelines for the relevant experiments.