In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
, an order operator or an order field is a
quantum field version of Landau's
order parameter whose expectation value characterizes
phase transition
In physics, chemistry, and other related fields like biology, 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 Sta ...
s. 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
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 a ...
. 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) and disordered phases happens at some temperature.
[Fradkin, E. J Stat Phys (2017) 167: 427. https://doi.org/10.1007/s10955-017-1737-7]
See also
*
Operator (physics)
An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they a ...
Books
*
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) Paperback '' (also available online
an
''
References
Quantum field theory
Statistical mechanics
Phase transitions
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