In
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 a ...
, 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 an ...
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 ...
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 ...
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
Operator may refer to:
Mathematics
* A symbol indicating a mathematical operation
* Logical operator or logical connective in mathematical logic
* Operator (mathematics), mapping that acts on elements of a space to produce elements of another ...
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 '' ...
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-dimensiona ...
. 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]
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 sub ...
'', Vol. I, "
SUPERFLOW AND
VORTEX LINES
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wit ...
", 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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