Three-dimensionalizing the eight-vertex model

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.

7 pages, 3 figures. v2: Fig. 3 corrected

References in corpus (2)

• Permutation-type solutions to the Yang-Baxter and other n-simplex equations
• Particles and strings in a (2+1)-D integrable quantum model