Skip to main content
Log in

Auxiliary transfer matrices for three-dimensional integrable models

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We formulate the local combinatorial method for constructing the complete set of operators that commute with the transfer matrix of the Zamolodchikov-Bazhanov-Baxter model in the vertex formulation. We find the compact functional equation satisfied by the generating functional of this complete set of operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. B. Zamolodchikov,Commun. Math. Phys.,79, 489–505 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  2. V. V. Bazhanov and R. J. Baxter,J. Stat. Phys.,69, 453–485 (1992).

    Article  MathSciNet  Google Scholar 

  3. V. V. Bazhanov and R. J. Baxter,J. Stat. Phys.,71, 839–864 (1992).

    Article  MathSciNet  Google Scholar 

  4. R. J. Baxter,Physica D,18, 321–347 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  5. V. V. Mangazeev, S. M. Sergeev, and Yu. G. Stroganov,J. Stat. Phys.,82, No. 1/2 (1996).

    Google Scholar 

  6. S. M. Sergeev, “On a two-dimensional system associated with the complex of the solutions of the tetrahedron equation,” Prepint solv-int/9709013 (1997);Phys. Lett. A,253, No. 3-4, 145–150 (1999);J. Phys. A,32, 5693–5714 (1999); “Solitons in a 3d integrable model,” Preprint solv-int/9904013 (1999);J. Nonlinear Math. Phys.,7, 1–17 (2000);Theor. Math. Phys.,118, 378–384 (1999).

  7. V. V. Bazhanov and Yu. G. Stroganov,Theor. Math. Phys.,52, 685–691 (1982).

    Article  MathSciNet  Google Scholar 

  8. V. V. Bazhanov, R. M. Kashaev, V. V. Mangazeev, and Yu. G. Stroganov,Commun. Math. Phys.,138, 393–408 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  9. V. V. Mangazeev, S. M., Sergeev, and Yu. G. Stroganov,Int. J. Mod. Phys. A,9, 5517–5530 (1994).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 391–409, September, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sergeev, S.M. Auxiliary transfer matrices for three-dimensional integrable models. Theor Math Phys 124, 1187–1201 (2000). https://doi.org/10.1007/BF02550997

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02550997

Keywords

Navigation