Knot theory and statistical mechanics

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 q 2‐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.