A Theory of Cooperative Phenomena
Abstract
A new method of approximation for orderdisorder phenomena is developed. In Sec. A, the method is explained for the onedimensional Ising lattice. Sections B and C cover the approximations already known, such as those of Bethe (Sec. B) and of KramersWannier (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 threedimensional 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 facecentered lattice (Ising model) is given.
 Publication:

Physical Review
 Pub Date:
 March 1951
 DOI:
 10.1103/PhysRev.81.988
 Bibcode:
 1951PhRv...81..988K