Elliptic solution for modified tetrahedron equations

TL;DR

This paper introduces a modified version of tetrahedron equations that generate commuting two-layer transfer-matrices, with solutions expressed via elliptic functions in the static limit, advancing the understanding of 3D lattice model integrability.

Contribution

It presents a novel modification of tetrahedron equations and constructs elliptic function solutions, extending integrability concepts in three-dimensional lattice models.

Findings

Constructed solutions in terms of elliptic functions.

Established commuting properties of two-layer transfer-matrices.

Extended the framework of integrability in 3D lattice models.

Abstract

As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the commuting family of more complicated two-layer transfer-matrices. In the static limit we have succeeded in constructing the solution of these equations in terms of elliptic functions.