OrdnungParameter

Ordnungsparameter, often written as Ordnungsparameter or Ordnungparameter in German, is a concept in physics that describes the degree of order in a system undergoing a phase transition. It is zero in the high-symmetry, disordered phase and nonzero in the ordered phase, signaling spontaneous symmetry breaking.

In the framework of Landau theory, the order parameter is treated as a field that characterizes the broken symmetry. The free energy is expressed as a function of this parameter, and a phase transition occurs when the minimum of the free energy shifts from zero to a finite value. Near the critical point, the order parameter typically follows a power-law behavior with a characteristic critical exponent.

Common examples include the magnetization M in a ferromagnet as the order parameter for magnetic ordering, the superconducting order parameter which is a complex scalar describing the condensate of Cooper pairs, and the superfluid or Bose-Einstein condensate order parameter that represents the macroscopic wavefunction. In crystalline solids, the amplitude of a density modulation associated with a charge or spin density wave can serve as an order parameter, reflecting the breaking of translational symmetry.

In some systems, particularly those with topological order, no conventional local order parameter exists; order is then described by nonlocal properties or topological invariants rather than a traditional order parameter.

The concept of an order parameter is central to classifying phase transitions and understanding symmetry breaking and universality. It can be spatially and temporally varying, allowing the description of domains, interfaces, and critical fluctuations.