The Order Parameter: Amplitude and Phase

Abstract

The concept of an order parameter has appeared with the attempt to describe the orderdisorder transition of alloys, specifically, to define a degree of disorder (see Section 3.1.6). First elaborated by Gorsky and Bragg and Williams to describe order-disorder transitions in alloys, it has been developed in its modern form by Landau for the purpose of a phenomenological description of phase transitions. More specifically, it addresses the question of the description of the long-range order of the structural (crystallographic) or thermodynamic (magnetic, dielectric, etc) properties, which repeat uniformly in a given system. Related quantities are intensive thermodynamic variables. The opposite notion of shortrange order refers to spatial thermodynamic fluctuations; these are particularly important near a second-order phase transition A ↔ B (see Chapter 4). Fluctuations that develop in, say, the high temperature phase A, announce the order properties of B. An important related quantity is the spatial extent $ξ$ of these fluctuations, the coherence length. The same term of coherence length (or correlation length) is also used to conote the range of distortions induced in the order parameter of phase B by a local perturbation (Chapter 5, section 5.6), e.g., the extent of the central region of a defect, where the order parameter is ``broken'' (singular), the core of the defect.