Abstract
A model in statistical physics is presented based on assigning non-Abelian phase factors to the turning points of polygons in three dimensions. This model allows for an exact solution and exhibits an unexpectedly rich phase structure. The model as well as the solution are obtained by a generalization of the methods of Kac and Ward and by mapping the problem to a Markov process as was done by Feynman for the two-dimensional Ising model
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