  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.
