English

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

R2 v1 2026-06-22T12:23:09.111Z