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Graph invariants related to statistical mechanical models: Examples and problems. (English) Zbl 0729.57003

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. In case a graph X represents a knot or a link L in \({\mathbb{R}}^ 3\), 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.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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