A dual view of the 3d Heisenberg model and the abelian projection

Details A dual view of the 3d Heisenberg model and the abelian projection A dual view of the 3d Heisenberg model and the abelian projection

1999-05-06

arxiv.org/abs/hep-lat/9905007v1

Phys.Rev.D60:094511,1999

Physics

High Energy Physics

High Energy Physics - Lattice

LateX, 15 pages, 3 figures

Scientific paper

10.1103/PhysRevD.60.094511

The Heisenberg model in 3d is studied from a dual point of view. It is shown that it can have vortex configurations, carrying a conserved charge(U(1) symmetry). Vortices condens in the disordered phase. A disorder parameter $\leftangle\mu\rightangle$ is defined dual to the magnetization $\leftangle\vec n\rightangle$, which signals condensation of vortices, i.e. spontaneous breaking of the dual U(1) symmetry. This study sheds light on the procedure known as abelian projection in non abelian gauge theories.

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