We characterize the rank of edge connection matrices of partition functions of real vertex models, as the dimension of the homogeneous components of the algebra of @math -invariant tensors. Here @math is the sub- group of the real orthogonal group that stabilizes the vertex model. This answers a question of Bal 'azs Szegedy from 2007.
Let @math be strictly positive and let @math be symmetric. Following de la Harpe and Jones @cite_6 we call the pair @math a . Let @math be the collection of all graphs, allowing multiple edges but no loops or circles. The of @math is the graph parameter @math defined by for @math .
@cite_6
2013439277
Abstract Spin models and vertex models on graphs are defined as appropriate generalizations of the Ising-Potts model of statistical mechanics. We review some of these state models and the graph functions defined by them. If a graph X represents a knot or a link L in R 3 , we describe models M for which the value Z M X at X of the graph function defined by M depends only on L and not on X .