Email this article Orthogonal Polynomials, 6J-Symbols, and Statistical Weights of SOS Models
- Authors: Valinevich P.A.1, Derkachov S.E.1, Isaev A.P.2, Komisarchuk A.V.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research
- Issue: Vol 238, No 6 (2019)
- Pages: 834-853
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/242609
- DOI: https://doi.org/10.1007/s10958-019-04279-w
- ID: 242609
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Abstract
We describe a simple diagrammatic method that allows one to connect the Boltzmann weights of vertex models of statistical mechanics with those of SOS models. An analogy with the computation of 6j-symbols is pointed out. The construction of statistical weights heavily relies on the realization of the group SU(2) on the space of functions of one variable. A closed-form answer for some particular cases is obtained. It is shown that in the general case, the statistical weight of a SOS model, as well as the 6j-symbol, can be presented as the scalar product of two polynomials of a certain type. Bibliography: 16 titles.
About the authors
P. A. Valinevich
St. Petersburg Department of Steklov Institute of Mathematics
Author for correspondence.
Email: valinevich@pdmi.ras.ru
Russian Federation, St.Petersburg
S. E. Derkachov
St. Petersburg Department of Steklov Institute of Mathematics
Email: valinevich@pdmi.ras.ru
Russian Federation, St.Petersburg
A. P. Isaev
Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research
Email: valinevich@pdmi.ras.ru
Russian Federation, Dubna
A. V. Komisarchuk
St. Petersburg Department of Steklov Institute of Mathematics
Email: valinevich@pdmi.ras.ru
Russian Federation, St.Petersburg
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