The modified tetrahedron equation and its solutions

Details The modified tetrahedron equation and its solutions The modified tetrahedron equation and its solutions

2003-03-21

arxiv.org/abs/nlin/0303043v3

Int.J.Mod.Phys. A19S2 (2004) 179-204

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and

Scientific paper

10.1142/S0217751X04020403

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for this operator follows without further calculations. If the Weyl parameter is taken to be a root of unity, the mapping operator decomposes into a matrix conjugation and a C-number functional mapping. The operator of the matrix conjugation satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equation. The matrix elements of this operator 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.

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