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]] 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. 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. | ||
Revision as of 10:36, 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. 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.
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.