PARAMETRIZED EIGHT-VERTEX MODEL AND KNOT INVARIANT 10136
Kassenova T.K.
June 2022E.A. Buketov Karaganda University Publish house
Eurasian Physical Technical Journal
2022#19Issue 1119 - 126 pp.
The article discusses and expands the known elements of the eight-vertex model, paying special attention to the parameterization of the matrix. The matrix values are interconnected with the knot through the braids and this model is valid on finite square lattices in two-dimensional space. A new solution of the parametrized eight-vertex model of free fermions with a complex version of elliptic functions, which is valid on a finite lattice, will be constructed. The range of applicability of the eight-vertex model with elements of the Jacobi elliptic function and the construction of a knot invariant on its basis is discussed by comparing the results obtained analytically for the model. The construction of the knot invariant using the Clebsch-Gordan coefficients and the main tool of statistical mechanics of the Yang-Baxter equation will be studied in detail.
10136knot , Clebsch-Gordan coefficients , elliptic function
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L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
M.Kh.Dulaty Taraz Regional University, Taraz, Kazakhstan
L.N. Gumilyov Eurasian National University
M.Kh.Dulaty Taraz Regional University
10 лет помогаем публиковать статьи Международный издатель
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