Order parameter: Difference between revisions
imported>John R. Brews (soft mode) |
mNo edit summary |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | {{subpages}} | ||
{{TOC|right}} | {{TOC|right}} | ||
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]]. | 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== | ||
{{reflist|refs= | {{reflist|refs= | ||
<ref name=Boi> | |||
{{cite book |title=The Quantum Vacuum: A Scientific and Philosophical Concept, from Electrodynamics to String Theory and the Geometry of the Microscopic World |author=Luciano Boi |url=http://books.google.com/books?id=rAEVOLae_FoC&pg=PA85&lpg=PA85 |pages=p. 85 |isbn=1421402475 |year=2011 |publisher=John Hopkins University Press}} | |||
</ref> | |||
<ref name=Dove> | <ref name=Dove> | ||
{{cite book |title=Introduction to Lattice Dynamics |author= Martin T. Dove |url=http://books.google.com/books?id=jpe2aYwF3v0C&pg=PA111&lpg=PA111 |pages=p. 111 |isbn=0521392934 |year=1993 |edition=4th ed |publisher=Cambridge University Press}} | {{cite book |title=Introduction to Lattice Dynamics |author= Martin T. Dove |url=http://books.google.com/books?id=jpe2aYwF3v0C&pg=PA111&lpg=PA111 |pages=p. 111 |isbn=0521392934 |year=1993 |edition=4th ed |publisher=Cambridge University Press}} | ||
</ref> | |||
<ref name=Longo> | |||
{{cite book |title=The Two Cultures: Shared Problems |chapter=Comments on Chapter 5: "Creating the physical world ''ex nihilo''? On the quantum vacuum and its fluctuations |url=http://books.google.com/books?id=Kz38u2qT36kC&pg=PA93&lpg=PA93 |pages=p. 93 |author= Luciano Boi |editor=Ernesto Carafoli, Gian Antonio Danieli, Giuseppe O. Longo, eds |isbn=8847008689 |year=2009 |publisher=Springer}} | |||
</ref> | </ref> | ||
| Line 18: | Line 25: | ||
</ref> | </ref> | ||
}} | }}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 12:01, 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.