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Tetrahedron equation and spin integrable models on a cubic lattice

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Abstract

This paper is a survey of results on the three-dimensional generalization of the Yang-Baxter equation obtained since the pioneer works by Zamolodchikov (1979) up to our articles in 1995. The integrability condition for statistical spin models on a simple cubic lattice (tetrahedron equation) is discussed and different versions of this equation are considered together with their symmetrical properties. The solution of the tetrahedron equation corresponding to the Bazhanov-Baxter model is considered in detail. The review contains an updated list of solutions for this equation. Generalization to inhomogeneous spin models with two types of Boltzmann weights forming a chessboard-type lattice is considered.

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Authors and Affiliations

  1. Institute of High Energy Physics, Protvino

    Yu. G. Stroganov

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  1. Yu. G. Stroganov
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The paper was written at the request of the Editorial Board.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 179–213, February, 1997.

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Stroganov, Y.G. Tetrahedron equation and spin integrable models on a cubic lattice. Theor Math Phys 110, 141–167 (1997). https://doi.org/10.1007/BF02630441

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