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
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatom ...
version of Landau's
order parameter
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 s ...
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
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 sp ...
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
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, m ...
) 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
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, that arise from electromagnetic forces between atoms and electrons. More gen ...
'', 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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