quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

, an order operator or an order field is a

quantum field In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

version of Landau's

order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

whose expectation value characterizes

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

s. There exists a dual version of it, the disorder operator or

disorder field Disorder may refer to randomness, non-order, or no intelligible pattern. Disorder may also refer to: Healthcare * Disorder (medicine), a functional abnormality or disturbance * Mental disorder or psychological disorder, a psychological pattern a ...

, 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 In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity. As the name implies, the fundamental meaning of ''mono ...

for their values. For example, a 't Hooft operator is a disorder operator. So is the

Jordan–Wigner transformation The Jordan–Wigner transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators. It was proposed by Pascual Jordan and Eugene Wigner for one-dimensional lattice models, but now two-dimensional ana ...

. The concept of a disorder observable was first introduced in the context of 2D Ising spin lattices, where a phase transition between spin-aligned (

magnetized Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...

) and disordered phases happens at some temperature.Fradkin, E. J Stat Phys (2017) 167: 427. https://doi.org/10.1007/s10955-017-1737-7

Books

* Kleinert, Hagen, '' Gauge Fields in

Condensed Matter Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...

'', Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1–742, Vol. II, " STRESSES AND DEFECTS", pp. 743–1456,
World Scientific (Singapore, 1989)
Paperback '' (also available online

an

''

References

Quantum field theory Statistical mechanics Phase transitions {{quantum-stub