Statistical mechanics of non-intersecting line systems

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Abstract
Statistical assemblies of non-intersecting closed lines (loops) with a variable loop multiplicity are considered which may have relevance for defect models of certain phase transitions. A loop gas model on a lattice is formulated and shown to be formally equivalent to an m-anisotropic n-vector model in the limit n=0. In two dimensions, the equivalence with the eight-vertex model in a field is discussed. In a few special cases the novel model is equivalent to known ones.