Graph Invariants Related to Statistical Mechanical Models: Examples and Problems

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 R3, we describe models M for which the value ZMX at X of the graph function defined by M depends only on L and not on X.