ABSTRACT
The Ginzburg-Landau theory is the version of Landau mean-field theory which applies to non-homogeneous systems. The order parameter can be position-dependent, either in the presence of an external field or due to the boundary conditions imposed on the system. At very low temperature, some materials become superconducting: they do not resist the flow of an electric current and they repel external magnetic fields. In 1950, Ginzburg and Landau proposed a phenomenological theory of superconductivity inspired by Landau theory of second order phase transitions. This chapter presents an advanced discussion of the thermodynamics of magnetic systems. It addresses the rich behaviour of a superconductor in the presence of magnetic fields. Situations where the external magnetic field is just at the critical value correspond to the coexistence line of a first order phase transition, and the two phases, normal and superconducting, can coexist.
