The description of superfluid 4He in terms of a disorder field theory developed in Part II can serve as a prototype for the treatment of many other physical systems. For this to be true, these systems have to possess the following fundamental properties.
1. There exists an ordered ground state.
2. The important fundamental exitations are of two types, namely,
a) soft long-wavelength exitations which only slightly disturb the order, and
b) line-like disturbances which drastically disturb the order in their immediate neighbourhood.
3. There exists a phase transition where the line-like disturbances condense and completely destroy the order everywhere in the system.
In superfluid 4He the long-wavelength exitations were the fluctuations of the phase angle, the line-like disturbances were the vortex lines, and the order which was destroyed in the phase transition was the superfluid order. We shall now discuss the second important physical system of this type: the crystalline solid. In thermal equilibrium at low temperature, this consists of a regular array of atoms which form the ordered ground state. If the crystal is perturbed weakly, the atoms perform long-wavelength oscillations. These are observable in the form of sound waves. If the crystal is perturbed strongly, for example via local external forces, one obtains what is called a plastically deformed state. To a good approximation such a state can be described by means of line-like defects. The most important ones are of two types called dislocations and disclinations. These are the crystalline analogues of the vortex lines in superfluid 4He. We shall develop a disorder field theory for these fundamental exitations in close analogy with the vortex lines in superfluid 4He. The phase transition in which defect lines condense and destroy the crystalline order will be identified with the melting process. The melting process is a first order transition and thus of a nature different from the superfluid transition. Still, we shall see that a number of quasi-universal features of this process can be understood by means of this disorder field theory.
