The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. In certain magnets, the magnetic dipoles are only free to rotate in a 2D plane, a system which can be adequately described by the so-called xy-model.