SO(3) vortices and disorder in the 2d SU(2) chiral model

Details SO(3) vortices and disorder in the 2d SU(2) chiral model SO(3) vortices and disorder in the 2d SU(2) chiral model

1995-08-07

arxiv.org/abs/hep-lat/9508010v1

Phys.Lett. B367 (1996) 254-258

Physics

High Energy Physics

High Energy Physics - Lattice

13 pages LaTeX

Scientific paper

10.1016/0370-2693(95)01428-4

We study the correlation function of the 2d SU(2) principal chiral model on the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a crucial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain inequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We also present some Monte Carlo evidence that these correlation inequalities are indeed satisfied. Our method can be easily translated to the language of 4d SU(2) gauge theory to establish the role of corresponding SO(3) monopoles in maintaining confinement at small couplings.

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