scholarly journals ELLIPTIC SOLUTION FOR MODIFIED TETRAHEDRON EQUATIONS

1993 ◽  
Vol 08 (36) ◽  
pp. 3475-3482 ◽  
Author(s):  
V. V. MANGAZEEV ◽  
YU. G. STROGANOV
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Elliptic Functions ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Elliptic Solution ◽  
Static Limit ◽  
Dimensional Lattice

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.

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

scholarly journals MODIFIED TETRAHEDRON EQUATIONS AND RELATED 3D INTEGRABLE MODELS, I

1995 ◽  
Vol 10 (28) ◽  
pp. 4041-4063 ◽  
Author(s):  
H.E. BOOS ◽  
V.V. MANGAZEEV ◽  
S.M. SERGEEV
Keyword(s):  
Free Parameter ◽  
Three Dimensional ◽  
Elliptic Functions ◽  
Integrable Models ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
New Family

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.

Solvable Three-Dimensional Lattice Models

1963 ◽  
Vol 132 (3) ◽  
pp. 1085-1092 ◽  
Author(s):  
Bruce W. Knight ◽  
Gerald A. Peterson
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice

scholarly journals NEW SERIES OF 3D LATTICE INTEGRABLE MODELS

1994 ◽  
Vol 09 (31) ◽  
pp. 5517-5530 ◽  
Author(s):  
V.V. MANGAZEEV ◽  
S.M. SERGEEV ◽  
YU. G. STROGANOV
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Elliptic Functions ◽  
Weight Functions ◽  
Additional Parameter ◽  
Spectral Parameters ◽  
Integrable Lattice ◽  
Symmetry Properties ◽  
Elliptic Model ◽  
Integrable Lattice Models

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.

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