Landau Theory of Phase Transitions

The Landau theory of phase transitions constitutes the phenomenological framework for mesoscopic thermodynamics in the meanfield approximation, in which a “mean force”, acting throughout the system, represents the complex microscopic interactions. In this chapter, the classification of phase transitions is introduced through the concept of the order parameter, and a comprehensive description of a generalized Landau expansion of the free energy, in powers of the order parameter, is presented. Special attention is directed toward weakly first-order, second-order, and tricritical phase transitions. Several apparently very distinct systems, such as fluids, liquid crystals, and ferromagnets, are considered to demonstrate the universality of the theory. Incorporation of fluctuations in the thermodynamic properties leads to the introduction of mesoscopic susceptibility and correlation length. These properties, in turn, facilitate the definition of the "local" (coordinate-dependent) Landau-Ginzburg free-energy functional. The limitations of meanfield theories are expressed through the Ginzburg criterion, and a meanfield description of the relaxation of thermodynamic properties to equilibrium is provided.