A model which consists of a lattice of “spin” variables with two characteristic properties: (1) each of the spin variables independently takes on either the value +1 or the value −1; and (2) only pairs of nearest neighboring spins can interact. The study of this model (introduced by Ernst Ising in 1925) in two dimensions, where many exact calculations have been carried out explicitly, forms the basis of the modern theory of phase transitions and, more generally, of cooperative phenomena.