On Solutions of Tetrahedron Equations based on Korepanov Mechanism

TL;DR

This paper explores solutions to tetrahedron equations using Korepanov's mechanism, introduces a new integrable 2D lattice model, and investigates the relationship between tetrahedral Zamolodchikov algebras and tetrahedron equations.

Contribution

It presents a novel approach to solving tetrahedron equations via Korepanov mechanism and introduces a new integrable lattice model.

Findings

Found solutions of tetrahedron equations from elliptic free fermion model

Discovered a new integrable 2D lattice model

Analyzed the relation between tetrahedral Zamolodchikov algebras and tetrahedron equations

Abstract

We have examined solutions of tetrahedron equations from the elliptic free fermion model by using Korepanov mechanism based on tetrahedral Zamolodchikov algebras. As a byproduct, we have found a new integrable 2-dim. lattice model. We have also studied the relation between tetrahedral Zamolodchikov algebras and tetrahedron equations.