Universal properties of three-dimensional random-exchange quantum antiferromagnets

The thermal and ground state properties of a class of three-dimensional (3D) random-exchange spin-1/2 antiferromagnets are studied using first principles quantum Monte Carlo method. Our motivation is to examine whether the newly discovered universal properties, which connect the N\'eel temperature and the staggered magnetization density, for the clean 3D quantum dimerized Heisenberg models remain valid for the random-exchange models considered here. Remarkably, similar to the clean systems, our Monte Carlo results indicate that these universal relations also emerge for the considered models with the introduced antiferromagnetic randomness. The scope of the validity of these universal properties for the 3D quantum antiferromagnets is investigated as well.