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

  • P. A. ValinevichEmail author
  • S. E. Derkachov
  • A. P. Isaev
  • A. V. Komisarchuk

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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Authors and Affiliations

  • P. A. Valinevich
    • 1
    Email author
  • S. E. Derkachov
    • 1
  • A. P. Isaev
    • 2
  • A. V. Komisarchuk
    • 1
  1. 1.St. Petersburg Department of Steklov Institute of MathematicsSt.PetersburgRussia
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute of Nuclear ResearchDubnaRussia

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