ABSTRACT

The purpose of this chapter is to explain how phase transitions can occur in principle. Thus, we shall define precisely what we mean by a phase transition, and examine how it is possible for a phase transition to occur in a simple model of a magnet-the Ising model. The Ising model is the drosophila of statistical mechanics, and we will not shrink from using it as an example to illustrate many of the general ideas that we shall develop. We shall also explore some of the wider and more complex issues associated with phase transitions, using other examples. In particular, we shall focus on ergodicity breaking, using disordered systems as an example. Throughout this chapter, we shall aim to be descriptive: our goal is to examine the possibilities that may occur, rather than to show how they occur in practice. The following chapter will present some calculational techniques whose results illustrate the general considerations given here.