The SU(2) $\times$ SU(2) chiral spin model in terms of SO(3) and Z${}_2$ variables: vortices and disorder

Abstract

We rewrite the two-dimensional SU(2)$\times$ SU(2) chiral spin model in terms of SO(3) and {\bf Z}${}_2$ degrees of freedom. The transformation, which is motivated by a similar representation of the corresponding lattice gauge theory in higher dimensions, exhibits the presence of dynamical SO(3) vortices and associated strings. We present arguments that (pairs of) SO(3) vortices with long strings play a crucial role in disordering the spin system at arbitrarily low temperatures.

13 pages, UCLA/93/TEP/39

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• Generalizing the Tomboulis-Yaffe Inequality to SU(N) Lattice Gauge Theories and General Classical Spin Systems
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