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V. V. Mangazeev

Publications and source records attributed to V. V. Mangazeev.

10 recordsLinked to original sources
arXiv2001

Separation of variables for the A_3 elliptic Calogero-Moser system

We consider the classical elliptic Calogero-Moser model. A set of canonical separated variables for this model has been constructed in Kuznetsov et al. However, the generating function of the separating canonical transform is known only for two- and three-particle cases . We construct this generating function for the next A_3 case as the limit of the conjectured form of the quantum separating operator. We show explicitly that this generating function gives a canonical transform from the set of original variables to the separated ones.

nlin.SI↗
arXiv1999

Bethe ansatz for the three-layer Zamolodchikov model

This paper is a continuation of our previous work (solv-int/9903001). We obtain two more functional relations for the eigenvalues of the transfer matrices for the $sl(3)$ chiral Potts model at $q^2=-1$. This model, up to a modification of boundary conditions, is equivalent to the three-layer three-dimensional Zamolodchikov model. From these relations we derive the Bethe ansatz equations.

solv-int↗
arXiv1999

Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q^2=-1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.

solv-int↗
arXiv1995

A_2 Macdonald polynomials: a separation of variables

In this paper we construct a discrete linear operator $K$ which transforms $A_2$ Macdonald polynomials into the product of two basic $3ϕ_2$ hypergeometric series with known arguments. The action of the operator $K$ on power sums in two variables can be reduced to a generalization of one particular case of the Bailey's summation formula for a very-well-poised $6ψ_6$ series. We also propose the conjecture for a transformation of $6ψ_6$ series with different arguments.

q-alg↗
arXiv1995

The vertex formulation of the Bazhanov-Baxter Model

In this paper we formulate an integrable model on the simple cubic lattice. The $N$ -- valued spin variables of the model belong to edges of the lattice. The Boltzmann weights of the model obey the vertex type Tetrahedron Equation. In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter Model. In the case when $N=2$ we reproduce the Korepanov's and Hietarinta's solutions of the Tetrahedron equation as some special cases.

hep-th↗
arXiv1994

New solution of vertex type tetrahedron equations

In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of the model satisfy tetrahedron equations.

hep-th↗
arXiv1994

Modified Tetrahedron Equations and Related 3D Integrable Models

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 parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus.

hep-th↗
arXiv1993

New series of 3D lattice integrable models

In this paper we present a new series of 3-dimensional integrable lattice models with $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. 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 parameterized 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.

hep-th↗
arXiv1993

Elliptic solution for modified tetrahedron equations

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.

hep-th↗