Order parameter

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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.[1]

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.[2] 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.[3][4]

References

  1. L.M. Pismen (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, p. 5. ISBN 3540304304. 
  2. Martin T. Dove (1993). Introduction to Lattice Dynamics, 4th ed. Cambridge University Press, p. 111. ISBN 0521392934. 
  3. Luciano Boi (2011). The Quantum Vacuum: A Scientific and Philosophical Concept, from Electrodynamics to String Theory and the Geometry of the Microscopic World. John Hopkins University Press, p. 85. ISBN 1421402475. 
  4. Luciano Boi (2009). “Comments on Chapter 5: "Creating the physical world ex nihilo? On the quantum vacuum and its fluctuations”, Ernesto Carafoli, Gian Antonio Danieli, Giuseppe O. Longo, eds: The Two Cultures: Shared Problems. Springer, p. 93. ISBN 8847008689.