ABSTRACT
This chapter explains how phase transitions can occur in principle. It examines how phase transition is possible for a phase transition to occur in a simple model of a magnet-the Ising model. The chapter explores some of the wider and more complex issues associated with phase transitions, using other examples. It focuses on ergodicity breaking, using disordered systems as an example. The goal of statistical mechanics is to compute the partition function Z. In order for uniform bulk behaviour to exist, the forces in the system must satisfy certain properties, and the thermodynamic limit must be taken carefully. The casual reader of any textbook or research paper on phase transitions and statistical mechanics cannot help being struck by the frequency of the term “model”. The phase transition literature is replete with models: the Ising model, the Heisenberg model, the Potts model, the Baxter model, the F model, and even such unlikely sounding names as the non-linear sigma model!.
