Ordnungparameters

Ordnungparameter, in English often called order parameter, is a macroscopic quantity that indicates the degree of order in a system and serves to distinguish different phases. In many systems the order parameter is zero in the disordered, high-symmetry phase and becomes nonzero when order emerges as a control parameter such as temperature is changed. The concept is central to descriptions of phase transitions and spontaneous symmetry breaking.

In statistical mechanics and condensed matter physics, the order parameter is often the expectation value of a local or global operator. In Landau theory, the free energy is expressed as a function of the order parameter, with symmetry constraints determining which terms are allowed. Close to a continuous phase transition, the order parameter follows a power law in the reduced temperature, OP ~ (T_c − T)^β, with β a critical exponent that depends on the universality class.

Concrete examples include: ferromagnetism, where magnetization M serves as the order parameter; superconductivity, described by a complex scalar order parameter ψ = |ψ| e^{iφ} representing the superconducting condensate; crystallization, where a density modulation can act as an order parameter; and nematic liquid crystals, where orientational order is captured by a tensor order parameter.

Some systems exhibit more complex or nonlocal order, such as topological order, where no local order parameter exists. In quantum systems, order parameters can be nonlocal or related to correlation functions, and in practice may be inferred from measurements such as scattering data or spectroscopic probes.

Applications of the order parameter concept include mapping phase diagrams, interpreting experimental results, and guiding theoretical frameworks for phase transitions. The idea has limitations, and not all phase transitions are driven by a conventional local order parameter.