The modified tetrahedron equation amd its solutions

Gunter Von Gehlen, Stanislav Pakuliak, Sergey Sergeev

Research output: Contribution to journalArticlepeer-review


A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator R1,2,3 in the space of a triple Weyl algebra. R1,2,3 is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for R1,2,3 follows without further calculation. If the Weyl parameter is taken to be a root of unity, R1,2,3 decomposes into a matrix conjugation operator R 1,2,3 and a c-number functional mapping R1,2,3(f). The operator R1,2,3 satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equations. R1,2,3 can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject
Original languageEnglish
Pages (from-to)179-204
Number of pages26
JournalInternational Journal of Modern Physics A
Publication statusPublished - 2004
Externally publishedYes


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