A Theory of Cooperative Phenomena

Abstract

A new method of approximation for order-disorder phenomena is developed. In Sec. A, the method is explained for the one-dimensional Ising lattice. Sections B and C cover the approximations already known, such as those of Bethe (Sec. B) and of Kramers-Wannier (Sec. C), which are shown to be derived as special cases of the method with suitable choices of variables. In Sec. D, an improved treatment is explained for the three-dimensional simple cubic Ising lattice. This approximation is found to agree with the rigorous expansion of the partition function up to the fourth moment by Kirkwood's moment method, so far as the disordered state is concerned. In Sec. E the general formula for the entropy is given. In Sec. H an improved treatment of the face-centered lattice (Ising model) is given.