Landau Theory of Phase Transitions

Abstract

We start this Chapter with an introduction of a concept of an order parameter (OP) as a hidden variable responsible for symmetry changes during the transition. To identify equilibrium thermodynamic states in an open system, we choose the Gibbs free energy as a function of temperature, pressure, and order parameter (the Landau potential). Using the concept of the order parameter, the phase transition is considered as a mathematical bifurcation or a catastrophe of the Landau potential. The “catastrophic” approach helps us to classify the phase transitions and see how different forms of the Landau potential are applicable to different cases of phase transitions. We also look at the special lines and points of the phase diagram from the point of view of the “catastrophic” changes of the order parameter. With this Chapter we start building the beams and columns configuration of field-theoretic method (FTM) in Fig. P.1. We conclude the Chapter with the analysis of the external field on the phase transition, using the properties of conjugation between the field and the order parameter. Although it is important to know the shortcomings of the Landau theory, e.g., it excludes effects of the fluctuations, it is imperative to say here that this theory not only presents a correct general picture of the phase transitions, but it will also provide for us a reasonable approach to the complicated dynamical problem, which, in many cases, has not been surpassed by other approaches.