TABLE OF CONTENTS The order-disorder transition and ferromagnetism have their origins in quite different manifestations of atomic interactions and are exhibited in quite different kinds of material. But, as shown in chapter 9, both can be described by the Ising model with considerable success. In fact, there are other phenomena that are different from either magnetism or order-disorder that can also be described by similar models. These include adsorption of atoms or molecules on surfaces, absorption of gases in solids, and the attachment of impurities to dislocation cores. A simple description of such phenomena is provided by the lattice gas model, and this model is easily shown to be equivalent to the Ising model. The fact that the same model can describe such varied systems implies that there are some important similarities among them that do not depend on the specific nature of the systems or the interaction energies involved. This, in fact, turns out to be the case and is most clearly apparent in the neighborhood of critical points. The statistical mechanics of the lattice gas is described in appendix 7, and specific applications are given in chapter 12. Here, the model and its connection to the Ising model are described.
Divide the system into cells such that, at most, only one molecule can occupy a given cell and a cell can either be occupied or empty. This is described by defining a parameter that is unity if a cell is occupied by a molecule and zero otherwise. Also,...
