SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2) principal chiral model

Details SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2) principal chiral model SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2) principal chiral model

1996-03-25

arxiv.org/abs/hep-lat/9603022v1

Nucl.Phys. B482 (1996) 613-638

Physics

High Energy Physics

High Energy Physics - Lattice

33 pages, LaTeX2e, all figures included in LaTeX format

Scientific paper

10.1016/S0550-3213(96)00561-5

We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external Z(2) flux introduced by twisted boundary conditions. This condition in turn is transformed into an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a nonzero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a nonzero effective magnetic field. Finally we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.

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