Some Constant Solutions to Zamolodchikov's Tetrahedron Equations

Abstract

In this letter we present constant solutions to the tetrahedron equations proposed by Zamolodchikov. In general, from a given solution of the Yang-Baxter equation there are two ways to construct solutions to the tetrahedron equation. There are also other kinds of solutions. We present some two-dimensional solutions that were obtained by directly solving the equations using either an upper triangular or Zamolodchikov's ansatz.

7 pages, AMSTEX, TURKU-FL-P1

References in corpus (1)

• The complete solution to the constant quantum Yang-Baxter equation in two dimensions

Cited by in corpus (6)

• Permutation-type solutions to the Yang-Baxter and other n-simplex equations
• Labeling Schemes for Tetrahedron Equations and Dualities between Them
• Let's Baxterise
• A comment on free-fermion conditions for lattice models in two and more dimensions
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation