258 research outputs found
Generalized Yang-Baxter Equation
A generalization of the Yang-Baxter equation is proposed. It enables 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 Botzmann weights of the chiral Potts model.Comment: 13 pages, TeX file. IHEP-93-?
New series of 3D lattice integrable models
In this paper we present a new series of 3-dimensional integrable lattice
models with colors. The case generalizes the elliptic model of our
previous paper. The weight functions of the models satisfy modified tetrahedron
equations with 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 . Also we briefly
discuss symmetry properties of weight functions of the models.Comment: 17 pages, IHEP-93-126, Late
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.Comment: 12 pages, LaTeX, IHEP-94-10
- Vectors for Three Dimensional Models
In this paper we apply the method of psi-vectors to three dimensional
statistical models. This method gives the correspondence between the Bazhanov
-- Baxter model and its vertex formulation. Considering psi-vectors for the
Planar model, we obtain its self-duality.Comment: 11 pages, LaTeX, no figure
Three-coloring statistical model with domain wall boundary conditions. I. Functional equations
In 1970 Baxter considered the statistical three-coloring lattice model for
the case of toroidal boundary conditions. He used the Bethe ansatz and found
the partition function of the model in the thermodynamic limit. We consider the
same model but use other boundary conditions for which one can prove that the
partition function satisfies some functional equations similar to the
functional equations satisfied by the partition function of the six-vertex
model for a special value of the crossing parameter.Comment: 16 pages, notations changed for consistency with the next part,
appendix adde
The Wave Functions for the Free-Fermion Part of the Spectrum of the Quantum Spin Models
We conjecture that the free-fermion part of the eigenspectrum observed
recently for the Perk-Schultz spin chain Hamiltonian in a finite
lattice with is a consequence of the existence of a
special simple eigenvalue for the transfer matrix of the auxiliary
inhomogeneous vertex model which appears in the nested Bethe ansatz
approach. We prove that this conjecture is valid for the case of the SU(3) spin
chain with periodic boundary condition. In this case we obtain a formula for
the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model
(), which permit us to find one by one all components of
this eigenvector and consequently to find the eigenvectors of the free-fermion
part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known
case of the case at our numerical and analytical
studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure
A possible combinatorial point for XYZ-spin chain
We formulate and discuss a number of conjectures on the ground state vectors
of the XYZ-spin chains of odd length with periodic boundary conditions and a
special choice of the Hamiltonian parameters. In particular, arguments for the
validity of a sum rule for the components, which describes in a sense the
degree of antiferromagneticity of the chain, are given.Comment: AMSLaTeX, 15 page
Spin chains and combinatorics: twisted boundary conditions
The finite XXZ Heisenberg spin chain with twisted boundary conditions was
considered. For the case of even number of sites , anisotropy parameter -1/2
and twisting angle the Hamiltonian of the system possesses an
eigenvalue . The explicit form of the corresponding eigenvector was
found for . Conjecturing that this vector is the ground state of the
system we made and verified several conjectures related to the norm of the
ground state vector, its component with maximal absolute value and some
correlation functions, which have combinatorial nature. In particular, the
squared norm of the ground state vector is probably coincides with the number
of half-turn symmetric alternating sign matrices.Comment: LaTeX file, 7 page
Bethe roots and refined enumeration of alternating-sign matrices
The properties of the most probable ground state candidate for the XXZ spin
chain with the anisotropy parameter equal to -1/2 and an odd number of sites is
considered. Some linear combinations of the components of the considered state,
divided by the maximal component, coincide with the elementary symmetric
polynomials in the corresponding Bethe roots. It is proved that those
polynomials are equal to the numbers providing the refined enumeration of the
alternating-sign matrices of order M+1 divided by the total number of the
alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde
Test of Guttmann and Enting's conjecture in the eight-vertex model
We investigate the analyticity property of the partially resummed series
expansion(PRSE) of the partition function for the eight-vertex model.
Developing a graphical technique, we have obtained a first few terms of the
PRSE and found that these terms have a pole only at one point in the complex
plane of the coupling constant. This result supports the conjecture proposed by
Guttmann and Enting concerning the ``solvability'' in statistical mechanical
lattice models.Comment: 15 pages, 3 figures, RevTe
- âŠ