Abstract
Recent development in the mathematical theory of knots using the method of statistical mechanics is examined. We show that knot invariants can be obtained by considering statistical‐mechanical models on a lattice. Particularly, we establish that the Kauffman’s bracket polynomial is the partition function of a q‐state vertex model previously considered by Perk and Wu, and that the Jones polynomial is generated by a q2‐state Potts model partition function. The generation of further new knot and link invariants many very well rely on computed‐aided studies of solutions of certain Yang‐Baxter equations.
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