Universal scalings of N\'eel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets

TL;DR

This study uses quantum Monte Carlo simulations to verify that universal scaling relations for key physical quantities hold true in both disordered and clean three-dimensional quantum antiferromagnets, suggesting a shared critical theory.

Contribution

It demonstrates that universal scaling relations apply to disordered 3D quantum antiferromagnets, indicating the same critical behavior as clean systems despite disorder effects.

Findings

Scaling relations remain valid with disorder

Critical behavior matches clean dimerized systems

Universal scalings observed across models

Abstract

The N\'eel temperature, staggered magnetization density, as well as the spinwave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first principles non-perturbative 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 N\'eel temperature and staggered magnetization density in our study are fully compatible with the expected critical behaviour 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 counterparts are governed by the same critical theory, which is not always the case in general. Finally, we also find smooth scalings even emerging when both the data of the investigated disordered model as well as its associated clean system are taken into account. This in turn implies that, while in a restricted sense, the considered scaling relations for 3D spin-1/2 antiferromagnets are indeed universal.