A model for magnetic systems in which atomic spins have to be aligned either parallel or antiparallel to a given direction. The Ising model was introduced, and solved in the case of one dimension, by E. Ising in 1925. Ising found that in one dimension, in the absence of an external magnetic field, there is no spontaneous magnetization at any temperature above absolute zero. The study of phase transitions in the Ising model in dimensions greater than one has been very important to the general understanding of phase transitions. In two dimensions, the Ising model was first solved exactly by L. Onsager in 1944. In three dimensions, approximation techniques, frequently involving renormalization have to be used.
Subjects: Chemistry — Physics.