Abstract
A ZN-symmetric theory with four-spin interactions on a three-dimensional FCC lattice is analysed. The model possesses an unusual semi-local symmetry and is self-dual. For N or=Nc it exhibits two continuous transitions which may or may not be infinite order. The intermediate phase appearing between the ferromagnetic ordered and disordered phases for N>or=Nc is a massless phase with no long-range order. The behaviour of the theory is strongly reminiscent of that of the two-dimensional ZN spin models and the four-dimensional ZN gauge theories and, quite naturally, constitutes a three-dimensional interpolating model. The possible relevance of this and related models to the Lifshitz point problem in certain helical magnetic and liquid crystal systems is briefly discussed.
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