Order parameter: Difference between revisions
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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 (chemistry)|phase]] of a physical system.<ref name=Pismen/> | 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 (chemistry)|phase]] of a physical system.<ref name=Pismen/> | ||
The idea of an order parameter first arose in the theory of [[phase transition]]s, 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''.<ref name=Dove/> 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. | The idea of an order parameter first arose in the theory of [[phase transition]]s, 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''.<ref name=Dove/> 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 [[Quantum chromodynamics|QCD vacuum]] to produce the observed sub-atomic particles of the [[Standard Model]]. The Higgs field is the order parameter breaking "electroweak | A more recent application of this idea is the [[Higgs boson]], which lowers the symmetry of the [[Quantum chromodynamics|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.<ref name=Boi/><ref name=Longo/> | ||
==References== | ==References== | ||
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Latest revision as of 11:01, 29 September 2024
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
- ↑ L.M. Pismen (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, p. 5. ISBN 3540304304.
- ↑ Martin T. Dove (1993). Introduction to Lattice Dynamics, 4th ed. Cambridge University Press, p. 111. ISBN 0521392934.
- ↑ 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.
- ↑ 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.