Three-dimensionalizing the eight-vertex model
Mathematical Physics
2016-01-07 v2 math.MP
Abstract
A simple ansatz is proposed for two-color R-matrix satisfying the tetrahedron equation. It generalizes, on one hand, a particular case of the eight-vertex model to three dimensions, and on another hand - Hietarinta's permutation-type operators to their linear combinations. Each separate R-matrix depends on one parameter, and the tetrahedron equation holds provided the quadruple of parameters belongs to an algebraic set containing five irreducible two-dimensional components.
Keywords
Cite
@article{arxiv.1601.00794,
title = {Three-dimensionalizing the eight-vertex model},
author = {I. G. Korepanov},
journal= {arXiv preprint arXiv:1601.00794},
year = {2016}
}
Comments
7 pages, 3 figures. v2: Fig. 3 corrected