Mass Gap, Abelian Dominance and Vortex Dynamics in SU(2) Spin Model

Details Mass Gap, Abelian Dominance and Vortex Dynamics in SU(2) Spin Model Mass Gap, Abelian Dominance and Vortex Dynamics in SU(2) Spin Model

1997-05-07

arxiv.org/abs/hep-lat/9705010v2

Phys.Lett. B423 (1998) 130-136

Physics

High Energy Physics

High Energy Physics - Lattice

12 pages, LaTeX, 4 figures, uses epsf.sty; Fig.3 is replaced and a few comments are added

Scientific paper

10.1016/S0370-2693(98)00102-6

We discuss a new approach to the investigation of the nature of the mass 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 numerically the three-dimensional SU(2) spin model in the Maximal Abelian projection. We find that the abelian mass gap in the projected theory coincides with the full non-abelian mass gap within numerical errors. The study 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.

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