magnitude (size of the spins in the spin language, or number of bosons in the boson language) as well as a phase (direction of the spins). In the particle language, the boson number can be tuned by the magnetic field. For this to occur, the system must be an XY magnet, i. e., must have uniaxial symmetry in the plane perpendicular to the applied magnetic field. Therefore only certain quantum magnets can be treated as BECs. We note that in real systems there will always be terms that break the uniaxial symmetry, such as dipole-dipole interactions and spin-orbit interactions. Consequently the theory is valid only when these terms are significantly smaller than the temperature. At very low temperatures any real quantum magnet will cross over to the Ising universality class.

Bosons can be achieved by creating and maintaining a large number of quasi-particles in a system. One special case is the creation of magnons at the induced magnetic-ordering phase. Figure 2 shows the phase diagram in the temperature-versus field plane of an induced antiferromagnetic ordering in a field whose magnetic ions are strongly correlated. Magnons can be created and, under special conditions, condensed into the ordered phase [@2; @8; @14].

