These models differ by the constrains given to the orientation of the electron's spins (arrows). If all spins are aligned in one direction, the material becomes a ferromagnet. Below the magnetic transition temperature, adjacent spins affect each other's behaviour, but as the temperature rises, they move more independently. The Ising model refers to spins with only two directions (z-axis); up or down. In the case of the XY model, the spin follows x- and y- axis on a plane, and in the Heisenberg model, spins take various directions, much like how clock hands point in a number of directions.