The modified tetrahedron equation and its solutions
Abstract
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.
Keywords
Cite
@article{arxiv.nlin/0303043,
title = {The modified tetrahedron equation and its solutions},
author = {G. von Gehlen and S. Pakuliak and S. Sergeev},
journal= {arXiv preprint arXiv:nlin/0303043},
year = {2009}
}
Comments
24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Spetember 2002, reference added