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
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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.
@article{ZNSL_2017_465_a6,
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},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {105--134},
publisher = {mathdoc},
volume = {465},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a6/}
}
TY - JOUR AU - P. A. Valinevich AU - S. E. Derkachov AU - A. P. Isaev AU - A. V. Komisarchuk TI - Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models JO - Zapiski Nauchnykh Seminarov POMI PY - 2017 SP - 105 EP - 134 VL - 465 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a6/ LA - ru ID - ZNSL_2017_465_a6 ER -
%0 Journal Article %A P. A. Valinevich %A S. E. Derkachov %A A. P. Isaev %A A. V. Komisarchuk %T Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models %J Zapiski Nauchnykh Seminarov POMI %D 2017 %P 105-134 %V 465 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a6/ %G ru %F ZNSL_2017_465_a6
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/