5 Phase transitions

In the remaining of the course, we are going to study phase transitions. This is

a discrete change in the properties of a system, characterized by discontinuities

in some of the variables describing the system. Macroscopically, these often

correspond to some rather drastic changes, such as freezing and boiling.

We have already met some examples of phase transitions before, such as

Bose–Einstein condensation. However, in this chapter, we are mainly going to

focus on two examples — the liquid-gas transition, and the Ising model. At first

sight, these two examples should be rather unrelated to each other, but it turns

out they behave in a very similar way. In fact, it seems like all phase transitions