You were probably told in high school that there are three phases of matter: solid, liquid, and gas. In reality, many more phases exist. But what exactly is a phase of matter? How can one phase be distinguished from another?
Basically, for a large collection of similar particles, a phase is a region in some parameter space in which the thermal equilibrium states possess some properties in common that can be distinguished from those in other phases. That means that some discontinuity of the properties occurs at the boundary between the phases.
Traditionally, the properties used to distinguish between phases of a system are expectation values of local observable quantities. By “local quantity,” I mean a function that depends only on the coordinates and momenta of the particles that are within some finite distance of a particular point in space. The density at a point is a local quantity; so...
