Order parameter: Difference between revisions
imported>John R. Brews (replace disambiguation link) |
imported>John R. Brews (soft mode) |
||
Line 4: | Line 4: | ||
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. Because the frequency drops with temperature, a 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]]. | ||
Line 10: | Line 10: | ||
==References== | ==References== | ||
{{reflist|refs= | {{reflist|refs= | ||
<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}} | |||
</ref> | |||
<ref name=Pismen> | <ref name=Pismen> | ||
{{cite book |title=Patterns and Interfaces in Dissipative Dynamics |author=L.M. Pismen |url=http://books.google.com/books?id=Wje3RXlQdaMC&pg=PA5&lpg=PA5 |pages=p. 5 |isbn=3540304304 |year=2006 |publisher=Springer}} | {{cite book |title=Patterns and Interfaces in Dissipative Dynamics |author=L.M. Pismen |url=http://books.google.com/books?id=Wje3RXlQdaMC&pg=PA5&lpg=PA5 |pages=p. 5 |isbn=3540304304 |year=2006 |publisher=Springer}} |
Revision as of 11:42, 19 September 2012
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.
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.