Geodesic
Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 105-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {P. A. Valinevich and S. E. Derkachov and A. P. Isaev and A. V. Komisarchuk},
     title = {Orthogonal polynomials, $6j$-symbols and statistical weights of {SOS} models},
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P. A. Valinevich; S. E. Derkachov; A. P. Isaev; A. V. Komisarchuk. Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 105-134. http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a6/

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