Knots,links, braids and exactly solvable models in statistical mechanics |
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Authors: | Yasuhiro Akutsu Miki Wadati |
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Affiliation: | (1) Institute of Physics, Kanagawa University, Rokkakubashi, Kanagawa-ku, 221 Yokohama, Japan;(2) Institute of Physics, College of Arts and Sciences, University of Tokyo, Komaba, Meguro-ku, 153 Tokyo, Japan |
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Abstract: | We present a general method to construct the sequence of new link polynomials and its two variable extension from exactly solvable models in statistical mechanics. First, we find representations of the braid group from the Boltzmann weights of the exactly solvable models. Second, we give the Markov traces associated with new braid group representations and using them construct new link polynomials. Third, we extend the theory into a two-variable version of the new link polynomials. Throughout the paper, we emphasize the essential roles played by the exactly solvable models and the underlying Yang-Baxter relation. |
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