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arXiv · hep-lat/9905007

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

A. Di Giacomo·D. Martelli·G. Paffuti
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Abstract

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 $\leftangleμ\rightangle$ 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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A. Di Giacomo, D. Martelli, G. Paffuti. 1999-05-06. A dual view of the 3d Heisenberg model and the abelian projection. https://doi.org/10.1103/physrevd.60.094511

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