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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 465, Pages 105–134 (Mi znsl6533)  
This article is cited in 1 scientific paper (total in 1 paper)

Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models

P. A. Valinevicha, S. E. Derkachova, A. P. Isaevb, A. V. Komisarchuka

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia
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Abstract: A simple diagrammatic method which allows to connect Boltzmann weights of the vertex models of statistical mechanics with those of SOS models is described. The analogy with the computation of the $6j-$symbols is pointed out. The construction of statistical weights heavily relies on the realization of the $SU(2)$ group on the space of functions of one variable. The closed-form answer for some particular cases is obtained. It is shown, that in the general case the statistical weight of SOS model, as well as $6j-$symbol, can be presented as the scalar product of two polynomials of certain type.
Key words and phrases: Yang–Baxter equation, $6j-$symbols, exactly solvable statistical models.
Funding agency Grant number
Russian Science Foundation 14-11-00598
Russian Foundation for Basic Research 17-01-00283_А
Received: 06.12.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 238, Issue 6, Pages 834–853
DOI: https://doi.org/10.1007/s10958-019-04279-w
Document Type: Article
UDC: 517.9
Language: Russian
Citation: P. A. Valinevich, S. E. Derkachov, A. P. Isaev, A. V. Komisarchuk, “Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 105–134; J. Math. Sci. (N. Y.), 238:6 (2019), 834–853
Citation in format AMSBIB
\Bibitem{ValDerIsa17}
\by P.~A.~Valinevich, S.~E.~Derkachov, A.~P.~Isaev, A.~V.~Komisarchuk
\paper Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models
\inbook Questions of quantum field theory and statistical physics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 465
\pages 105--134
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6533}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 6
\pages 834--853
\crossref{https://doi.org/10.1007/s10958-019-04279-w}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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