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 condense in the disordered (demagnetized) phase. A disorder parameter [mu] is defined, dual to the magnetization [(n) over right arrow], which signals the condensation of vortices, i.e., spontaneous breaking of dual U(1) symmetry. This study sheds light on the procedure known as Abelian projection in non-Abelian gauge theories. [S0556-2821(99)03221-X].