MASS GAP, ABELIAN DOMINANCE AND VORTEX DYNAMICS IN SU(2) SPIN MODEL

We discuss a new approach to the investigation of the nature of the ma ss gap in spin systems with continuous global symmetries which is much analogous to the method of abelian projection in the gauge theories. We suggest that the abelian degrees of freedom, in particular, abelian vortices are responsible for the mass gap generation phenomena in the non-abelian spin systems. To check our hypothesis we study numericall y the three-dimensional SU(2) spill model in the Maximal Abelian proje ction. We find that the abelian mass gap in the projected theory coinc ides with the full non-abelian mass gap within numerical errors. The s tudy of the percolation properties of the abelian vortex trajectories shows that the phase transition and the mass gap generation in the 3D SU(2) spin model are driven by the abelian vortex condensation. (C) 19 98 Published by Elsevier Science B.V.