Orthogonal Polynomials, 6J-Symbols, and Statistical Weights of SOS Models


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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.

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P. Valinevich

St. Petersburg Department of Steklov Institute of Mathematics

Autor responsável pela correspondência
Email: valinevich@pdmi.ras.ru
Rússia, St.Petersburg

S. Derkachov

St. Petersburg Department of Steklov Institute of Mathematics

Email: valinevich@pdmi.ras.ru
Rússia, St.Petersburg

A. Isaev

Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research

Email: valinevich@pdmi.ras.ru
Rússia, Dubna

A. Komisarchuk

St. Petersburg Department of Steklov Institute of Mathematics

Email: valinevich@pdmi.ras.ru
Rússia, St.Petersburg

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