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Integrable 3D Statistical Models on Six-Valent Graphs

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Abstract

The paper is devoted to the study of a special statistical model on graphs with vertices of degrees 6 and 1. We show that this model is invariant with respect to certain Roseman moves if one regards the graph as the singular point set of the diagram of a 2-knot. Our approach is based on the properties of the tetrahedron cohomology complex.

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993, Russia

    I. G. Korepanov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    D. V. Talalaev & G. I. Sharygin

  3. Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute,”, Bol’shaya Cheremushkinskaya ul. 25, Moscow, 117218, Russia

    D. V. Talalaev & G. I. Sharygin

Authors
  1. I. G. Korepanov
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  2. D. V. Talalaev
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  3. G. I. Sharygin
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Corresponding author

Correspondence to I. G. Korepanov.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 302, pp. 214–233.

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Korepanov, I.G., Talalaev, D.V. & Sharygin, G.I. Integrable 3D Statistical Models on Six-Valent Graphs. Proc. Steklov Inst. Math. 302, 198–216 (2018). https://doi.org/10.1134/S008154381806010X

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  • DOI: https://doi.org/10.1134/S008154381806010X

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