Order parameter

In the theory of complex systems, an order parameter, more generally an order parameter field describes a collective behavior of the system, an ordering of components or subsystems on a macroscopic scale. In particular, the magnitude of the order parameter may determine the phase of a physical system.

The idea of an order parameter first arose in the theory of phase transitions, for example the transition of a solid material from a paraelectric phase to a ferroelectric phase. Such a transition occurs in some materials and is described as the lowering in frequency of a particular atomic lattice vibration with the lowering of temperature, a so-called soft mode. Because the frequency drops with temperature, a ferroelectric solid experiencing this vibration becomes frozen in time with a non-zero amplitude of this vibration that implies a reduction in crystal symmetry and net electric dipole moment. The order parameter in this instance is the amplitude of the frozen mode.

A more recent application of this idea is the Higgs boson, which lowers the symmetry of the QCD vacuum to produce the observed sub-atomic particles of the Standard Model. The Higgs field is the order parameter breaking "electroweak gauge symmetry" (the "Higgs mechanism") causing a phase transition.