Investigation of Partition Function Transformation for the Potts Model into a Dichromatic Knot Polynomial 74

Author:

Kassenova Tolkyn1ORCID,Tsyba Pyotr2ORCID,Razina Olga2ORCID

Affiliation:

1. Department of Applied Mathematics and Physics, M.Kh. Dulaty Taraz Regional University, Taraz 080000, Kazakhstan

2. Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan

Abstract

This article examines quantum group symmetry using the Potts model. The transformation of the Potts model into a polynomial knot state on Kaufman square brackets is analyzed. It is shown how a dichromatic polynomial for a planar graph can be obtained using Temperley–Lieb operator algebra. The proposed work provides insight into the 74 knot-partition function of Takara Musubi using a strain factor that represents the particles in the lattice knots of the above-mentioned model. As far as theoretical physics is concerned, this statement provides a correct explanation of the connection between the Potts model and the similar square lattice of knot and link invariants.

Funder

Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan

Publisher

MDPI AG

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