Universal scaling of Néel temperature, staggered magnetization density, and spin-wave velocity of three-dimensional disordered and clean quantum antiferromagnets

The Néel temperature, staggered magnetization density, as well as the spin-wave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first-principles nonperturbative quantum Monte Carlo simulations. In particular, we examine the validity of universal scaling relations that are related to these three studied physical quantities. These relations are relevant to experimental data and are firmly established for clean (regular) 3D dimerized spin-1/2 Heisenberg models. Remarkably, our numerical results show that the considered scaling relations remain true for the investigated model with the introduced disorder. In addition, while the presence of disorder may change the physical properties of regular dimerized models, hence leading to different critical theories, both the obtained data of Néel temperature and staggered magnetization density in our study are fully compatible with the expected critical behavior for clean dimerized systems. As a result, it is persuasive to conclude that the related quantum phase transitions of the considered disordered model and its clean analogues are governed by the same critical theory, which is not always the case in general. Finally, we also find smooth scaling curves even emerging when both the data of the investigated disordered model as well as its associated clean system are taken into account concurrently. This in turn implies that, while in a restricted sense, the considered scaling relations for 3D spin-1/2 antiferromagnets are indeed universal.