# Order operator

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{{Short description|Operator characterizing the phase of a system}}
{{more citations needed|date=August 2014}}
In [quantum field theory](/source/quantum_field_theory), an '''order operator''' or an '''order field''' is a [quantum field](/source/quantum_field) version of Landau's [order parameter](/source/order_parameter) whose expectation value characterizes [phase transition](/source/phase_transition)s. There exists a dual version of it, the disorder operator or [disorder field](/source/disorder_field), whose expectation value characterizes a phase transition by indicating the prolific presence of defect or vortex lines in an ordered phase.

The '''disorder operator''' is an [operator](/source/Operator_(mathematics)) that creates a [discontinuity](/source/Discontinuity_(mathematics)) of the ordinary order operators or a [monodromy](/source/monodromy) for their values. For example, a ['t Hooft operator](/source/'t_Hooft_loop) is a disorder operator. So is the [Jordan–Wigner transformation](/source/Jordan%E2%80%93Wigner_transformation). The concept of a disorder observable was first introduced in the context of 2D [Ising spin lattices](/source/Ising_model), where a phase transition between spin-aligned ([magnetized](/source/magnetized)) and disordered phases happens at some temperature.<ref>Fradkin, E. J Stat Phys (2017) 167: 427. https://doi.org/10.1007/s10955-017-1737-7</ref>

==See also==
* [Operator (physics)](/source/Operator_(physics))

==Books==
* [Kleinert, Hagen](/source/Hagen_Kleinert), ''[Gauge Fields](/source/gauge_field) in [Condensed Matter](/source/condensed_matter)'', Vol. I,  " [SUPERFLOW](/source/superfluidity)  AND [VORTEX LINES](/source/vortex_line)", pp.&nbsp;1–742, Vol. II,  "[STRESSES](/source/Stress_(physics)) AND [DEFECTS"](/source/Crystallographic_defect), pp.&nbsp;743–1456,  [https://archive.today/20060514143926/http://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)];  Paperback {{ISBN|9971-5-0210-0}} '' (also available online: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html Vol. I] {{Webarchive|url=https://web.archive.org/web/20080527174206/http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html |date=2008-05-27 }} and [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents2.html Vol. II] {{Webarchive|url=https://web.archive.org/web/20080527174211/http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents2.html |date=2008-05-27 }})''

==References==
{{Reflist}}

Category:Quantum field theory
Category:Statistical mechanics
Category:Phase transitions

{{quantum-stub}}

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