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In quantum field theory, an order operator or an order field is a quantum field version of Landau's order parameter whose expectation value characterizes phase transitions. There exists a dual version of it, the disorder operator or 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 that creates a discontinuity of the ordinary order operators or a monodromy for their values. For example, a 't Hooft operator is a disorder operator. So is the Jordan–Wigner transformation.
- Kleinert, Hagen, Gauge Fields in Condensed Matter, Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1--742, Vol. II, "STRESSES AND DEFECTS", pp. 743-1456, World Scientific (Singapore, 1989)[permanent dead link]; Paperback ISBN 9971-5-0210-0 (also available online: Vol. I and Vol. II)
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