Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 427–461 | Cite as

Disorder Operators and Their Descendants

  • Eduardo FradkinEmail author


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.


Disorder operators Critical phenomena Ising models Ising gauge theory Quantum spin chains Topological phases of matter Duality transformations 



I am grateful to Paul Fendley for many enlightening discussions on parafermions and for sharing his unpublished results with me. This work was supported in part by the National Science Foundation through the Grant DMR 1408713 at the University of Illinois.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Physics and Institute for Condensed Matter TheoryUniversity of IllinoisUrbanaUSA

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