Dynamic Duality and the Phase Structure of Some Non-Abelian Spin Systems.

Lattice systems with discrete Z(,N) (CRTIMES) S(,N) and S(,N) (CRTIMES) S(,N) global symmetry admit a complete set of locally commuting disorder variables. Any kink state can be created by finite products of these operators acting on the classical vacuum. Exact dual forms of the partition functions are constructed and dual order parameters are defined. The Z(,N) (CRTIMES) S(,N) spin systems in two dimensions with an appropriate choice of action are vulnerable to a variety of analytic methods and are exactly dual to a vortex-charge plasma. They are shown to have an intermediate spin wave dominated phase between the conventional ordered and disordered phases for N > 16. A renormalization group analysis of the plasma indicates that, unlike that of the Z(,N) models, the spin wave phase is massive, the mass being the reciprocal of a dual correlation length. This length becomes infinite in the limit of large N with (beta)/N fixed. In any number of dimensions the large N limit is infinitely stable against magnetization, though long range order can occur for dimensionality greater than two.