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


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2019 Springer Science+Business Media, LLC, part of Springer Nature