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A cyclic graph is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model (P. de la Harpe, V.F.R. Jones (1993) [4]). They are characterized by ‘weak reflection positivity’, which amounts to the positive semidefiniteness of matrices based on...
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