Knot theory and statistical mechanics

Abstract

This is a tutorial review on knot invariants and their construction using the method of statistical mechanics. We begin with brief reviews of the elements of knot theory and relevant results in statistical mechanics. We then show how knot invariants, including those discovered recently, can be obtained by applying techniques used in solving lattice models in lattice statistics. Our approach is based on the consideration of solvable models with strictly local Boltzmann weights. The presentation, which is self-contained and elementary, is intended for a general readership. A table of polynomial invariants for knot and links containing up to six crossings is included in the Appendix.