Abstract
The basic concepts of the Landau theory of phase transitions are introduced through working examples. A number of rules governing the application of the theory to second and first-order transitions are given. The approach to magnetostructural transitions in magnetic mulltiferroic materials is detailed. Examples of transitions induced by replica of the same order-parameter in superconducting and liquid crystal systems, are described. The theory of reconstructive transitions is outlined and illustrated by the examples of the graphite-diamond transition and by the phase diagram of iron. An extention of the phenomenological approach to incommensurate structures to the crystal-amorphous transition is proposed (see also the chapter by Perez-Mato et al. for further discussion and applications).
Highlights
In the pioneering article of Landau [1] the phenomenological theory of phase transitions intended to establish the mutual compatibility of the symmetry and physical characteristics of a phase transition: Relationship between the symmetry of the phases, consistency between the nature of the symmetry change and the nature of the physical quantities behaving anomalously across the transition
In its initial formulation the theory considered the simple case of continuous transitions induced by a single irreducible representation between group-subgroup related phases, it proved subsequently to apply, providing suitable extensions, to discontinuous transitions [2], to transitions associated with several order-parameters [2], or to reconstructive transitions involving a loss of the group-subgroup relationship [3]
The theory was used to describe almost all types of phase transitions occurring in hard or soft condensed matter physics, such as structural and magnetic transitions in crystalline materials [4], the superconducting [5] and superfluid [6] transitions, the liquidsolid [7] and liquid-vapour [8] transitions, and the variety of transitions disclosed in liquid crystals [9] and complex fluids [10]
Summary
In the pioneering article of Landau [1] the phenomenological theory of phase transitions intended to establish the mutual compatibility of the symmetry and physical characteristics of a phase transition: Relationship between the symmetry of the phases, consistency between the nature of the symmetry change and the nature of the physical quantities behaving anomalously across the transition. This aim was achieved by means of introducing the concepts of order-parameter and Landau free-energy. After introducing the basic concepts of the Landau theory (Sec. 2) and some rules governing its application (Sec. 3), we describe recent extensions and selected applications of the theory: Application to multiferroic materials (Sec. 4), to unconventional superconductors and liquidcrystal systems (Sec. 5), to reconstructive transitions (Sec. 6), and to the formation of the amorphous state (Sec. 7)
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