Lattice gauge theories and spin models

The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2+1) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2+1) dimens...

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Bibliographic Details
Published in:Physical review. D 2016-10, Vol.94 (8), Article 085029
Main Authors: Mathur, Manu, Sreeraj, T. P.
Format: Article
Language:English
Subjects:
Gauge theory
Ising model
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Summary:The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2+1) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2+1) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.94.085029