SO(3) VORTICES AND DISORDER IN THE 2D SU(2) PRINCIPAL CHIRAL MODEL

We study the correlation function of the 2d SU(2) principal chiral mod el on the lattice. By rewriting the model in terms of 2(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a cru cial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain i nequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We also pres ent 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.