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

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 $\text{leftangle}\mu \text{rightangle}$ is defined dual to the magnetization $\text{leftangle}\vec{n}\text{rightangle}$, 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.

Comments: LateX, 15 pages, 3 figures