Disorder Operators and Their Descendants

I review the concept of a disorder operator , introduced originally by Kadanoff in the context of the two-dimensional Ising model. Disorder operators acquire an expectation value in the disordered phase of the classical spin system. This concept has had applications and implications to many areas of...

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Bibliographic Details
Published in:Journal of statistical physics Vol. 167; no. 3-4; pp. 427 - 461
Main Author: Fradkin, Eduardo
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2017
Springer
Springer Nature B.V
Subjects:
Fermions
Ising model
Mathematical and Computational Physics
Operators
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Two dimensional models
Disorder operators
Ising gauge theory
Ising models
Topological phases of matter
Duality transformations
Critical phenomena
Quantum spin chains
ISSN:0022-4715, 1572-9613
Online Access:Get full text
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Summary:I review the concept of a disorder operator , introduced originally by Kadanoff in the context of the two-dimensional Ising model. Disorder operators acquire an expectation value in the disordered phase of the classical spin system. This concept has had applications and implications to many areas of physics ranging from quantum spin chains to gauge theories to topological phases of matter. In this paper I describe the role that disorder operators play in our understanding of ordered, disordered and topological phases of matter. The role of disorder operators, and their generalizations, and their connection with dualities in different systems, as well as with majorana fermions and parafermions, is discussed in detail. Their role in recent fermion–boson and boson–boson dualities is briefly discussed.
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ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1737-7