The Models of Ising and Heisenberg

Abstract

The theoretical description of phase transitions is very difficult. We have already explained some reasons for this in the preceding sections. Only a few models can be treated in the framework of statistical mechanics without large numerical efforts. One is due to Lenz (1920), and was later on worked out in detail by his pupil Ising (1925). Originally, it was invented for the phase transition of ferromagnets at the Curie temperature; however, in the course of time it was realized that with only slight changes the model can also be applied to other phase transitions, like order-disorder transitions in binary alloys. Furthermore, the model may be applied to several modern problems of many-particle physics, for instance for the description of so-called spin glasses. These are metals having amorphous instead of crystalline structures, which have the interesting property of nonvanishing entropy at T = O. Recently, it has been realized that Ising’s idea (in modified form) could also explain pattern recognition in schematic neural networks. Thus, this model gains more and more importance for the development of models for the human brain.