Phase transitions and their accompanying concepts of criticality and universality are a foundation stone of statistical physics. Gapped spin-dimer systems are an ideal testbed to study criticality because a quantum phase transition can be induced by a magnetic field resulting in a phase equivalent to the XY spin model. It was proposed that BaCuSi2O6, a quasi-2D spin-dimer system consisting of stacked bilayers, undergoes a dimensional reduction, from 3D to 2D, thereby realizing an effective 2D-XY spin model. In this thesis, we investigate the magnetic excitations and order in BaCuSi2O6 and Ba0.9Sr0.1CuSi2O6 using a combination of experimental techniques and analyze the collected data by modern statistical methods. We find that BaCuSi2O6 contains three different bilayer types, which cause an anomalous scaling regime previously misinterpreted as dimensional reduction. Furthermore, we verify that the bilayers in Ba0.9Sr0.1CuSi2O6 are equivalent and that this system therefore displays 3D scaling without any hallmarks of 2D physics.