A Study on the Connection Between the Potts Model and the Dichromatic Polynomial by Means of Some Special Knots

This study examines the relationship between the Potts model in statistical mechanics and mathematical knots. This is done by transforming the Potts model into knot polynomials. The knot polynomial in the Kauffman square brackets is used. Temperley–Lieb algebra is used to obtain the dichromatic polynomial of a graph. A special family of knots called Zengi knots (links) is considered, consisting of four different models. We reveal the partition functions of these knots (links) by using a strain factor corresponding to the particles in the Potts model. One of the deep connections between physics and mathematics is the existence of the relationship between the Potts model and similar models developed for some algebras and knot and link invariants. This is clearly stated here by the given applications.