arXiv:hep-th/9311020 · International Journal of Modern Physics A

NEW SERIES OF 3D LATTICE INTEGRABLE MODELS

Vladimir V. Mangazeev, S.M. SERGEEV, YU. G. STROGANOV

Published Dec 20, 1994• 15 citations

Abstract

In this paper we present a new series of three-dimensional integrable lattice models with N colors. The case N=2 generalizes the elliptic model of Ref. 8. The weight functions of the models satisfy modified tetrahedron equations with N states and give a commuting family of two-layer transfer matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations, and weights are parametrized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter η. Also, we briefly discuss symmetry properties of weight functions of the models.

DOI: 10.1142/s0217751x94002247

Related papers

New series of 3D lattice integrable models

Mangazeev, V V, Sergeev, S M, Stroganov, Yu G

Oct 28, 199317 citations

MODIFIED TETRAHEDRON EQUATIONS AND RELATED 3D INTEGRABLE MODELS, I

Herman E. Boos, Vladimir V. Mangazeev, С. М. Сергеев

Using a modified version of the tetrahedron equations we construct a new family of N- state three-dimensional integrable models with commuting two-layer transfer matrices. We investigate a particular class of solutions to these equations and parametrize them in terms of elliptic functions. The corresponding models contain one free parameter, k—an elliptic modulus.

arXiv:hep-th/9407146International Journal of Modern Physics ANov 10, 199518 citations

ELLIPTIC SOLUTION FOR MODIFIED TETRAHEDRON EQUATIONS

Vladimir V. Mangazeev, Yu. G. Stroganov

As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of the 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.

arXiv:hep-th/9305145Modern Physics Letters ANov 30, 199319 citations

Quantum Dilogarithms and New Integrable Lattice Models in Three Dimensions

Vladimir V. Bazhanov, Rinat Kashaev, Vladimir V. Mangazeev +1 more

In this paper we introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local Boltzmann weights in terms of quantum dilogarithms satisfying the inversion and pentagon identities. We give three examples of such quantum dilogarithms, leading to integrable 3D lattice models. The partition function per site in these models can be exactly calculated in the limit of an infinite lattice by using the functional relations, symmetry and factorization properties of the transfer matrix. The results of such calculations for 3D models associated with the Faddeev modular quantum dilogarithm are briefly presented.

arXiv:2512.23338Dec 29, 20250 citations

An integrable 3D lattice model with positive Boltzmann weights

Vladimir V. Mangazeev, Vladimir V. Bazhanov, С. М. Сергеев

In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. The weights depend on a free parameter 0

arXiv:1308.4773Journal of Physics A Mathematical and TheoreticalNov 6, 201321 citations

Quantized six-vertex model on a torus

Rei Inoue, Atsuo Kuniba, Yuji Terashima +1 more

We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain.

arXiv:2505.08924May 13, 20250 citations