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The 't Hooft disorder parameters are constructed within the framework of SU(N) lattice gauge theories in three or four dimensions. It is found that these operators arise naturally from a duality transformation which is simllar to the standard transformation for Z(N) gauge theories. To illustrate the behavior of dual variables in a simpler context, we study the Villain form of the Z(N) gauge system in three and four dimensions. The techniques include duality, strong-coupling expansions, and the electrodynamic representation. In four dimensions it is found that for N > N, -4, the system possesses at least three phases: a strong-coupling phase with electric confinement, a weak-coupling phase with magnetic confinement, and an intermediate phase which resembles QED, with a massless photon and no confinement. We also study an SU(N)-Hlggs system, which interpolates between the Z(N) and SU(N) systems.

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A simple model showing a 1/f behavior is proposed. It is argued, on the basis of a scaling argument, that is has