17 research outputs found
Exact Solution of a Three-Dimensional Dimer System
We consider a three-dimensional lattice model consisting of layers of vertex
models coupled with interlayer interactions. For a particular non-trivial
interlayer interaction between charge-conserving vertex models and using a
transfer matrix approach, we show that the eigenvalues and eigenvectors of the
transfer matrix are related to those of the two-dimensional vertex model. The
result is applied to analyze the phase transitions in a realistic
three-dimensional dimer system.Comment: 11 pages in REVTex with 2 PS figure
Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model
We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov
model is dependent on four spin variables which are the linear combinations of
the spins on the corner sites of the cube and the Wu-Kadanoff duality between
the cube and vertex type tetrahedron equations is obtained explicitly for the
Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by
considering the symmetry property of the weight function, which is
corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type
weight function is parametrized as the dihedral angles between the rapidity
planes connected with the cube. And we write down the symmetry relations of the
weight functions under the actions of the symmetry group of the cube. The
six angles with a constrained condition, appeared in the tetrahedron equation,
can be regarded as the six spectrums connected with the six spaces in which the
vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29
The Quantum Super Yangian and Casimir Operators of
The quantum super Yangian associated with the Perk - Schultz
solution of the Yang - Baxter equation is introduced. Its structural properties
are investigated, in particular, an extensive study of its central algebra is
carried out. A graded associative algebra epimorphism is established and constructed explicitly. Images of the central
elements of the quantum super Yangian under this epimorphism yield the Casimir
operators of the quantum supergroup constructed in an earlier
publication.Comment: 10 pages in plain LaTe
Exact solution of the simplest super-orthosymplectic invariant magnet
We present the exact solution of the invariant magnet by the Bethe
ansatz approach. The associated Bethe ansatz equation exhibit a new feature by
presenting an explicit and distinct phase behaviour in even and odd sectors of
the theory. The ground state, the low-lying excitations and the critical
properties are discussed by exploiting the Bethe ansatz solution.Comment: 8 pages, UFSCARF-TH-1
Integrable Hamiltonians with symmetry from the Fateev-Zamolodchikov model
A special case of the Fateev-Zamolodchikov model is studied resulting in a
solution of the Yang-Baxter equation with two spectral parameters. Integrable
models from this solution are shown to have the symmetry of the Drinfeld double
of a dihedral group. Viewing this solution as a descendant of the zero-field
six-vertex model allows for the construction of functional relations and Bethe
ansatz equations
sl(N) Onsager's Algebra and Integrability
We define an analog of Onsager's Algebra through a finite set of
relations that generalize the Dolan Grady defining relations for the original
Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be
isomorphic to a fixed point subalgebra of Loop Algebra with respect
to a certain involution. As the consequence of the generalized Dolan Grady
relations a Hamiltonian linear in the generators of Onsager's Algebra
is shown to posses an infinite number of mutually commuting integrals of
motion
Finite dimensional representations of at arbitrary
A method is developed to construct irreducible representations(irreps) of the
quantum supergroup in a systematic fashion. It is shown that
every finite dimensional irrep of this quantum supergroup at generic is a
deformation of a finite dimensional irrep of its underlying Lie superalgebra
, and is essentially uniquely characterized by a highest weight. The
character of the irrep is given. When is a root of unity, all irreps of
are finite dimensional; multiply atypical highest weight irreps
and (semi)cyclic irreps also exist. As examples, all the highest weight and
(semi)cyclic irreps of are thoroughly studied.Comment: 21 page
The Chiral Potts Models Revisited
In honor of Onsager's ninetieth birthday, we like to review some exact
results obtained so far in the chiral Potts models and to translate these
results into language more transparent to physicists, so that experts in Monte
Carlo calculations, high and low temperature expansions, and various other
methods, can use them. We shall pay special attention to the interfacial
tension between the state and the state. By examining
the ground states, it is seen that the integrable line ends at a superwetting
point, on which the relation is satisfied, so that it
is energetically neutral to have one interface or more. We present also some
partial results on the meaning of the integrable line for low temperatures
where it lives in the non-wet regime. We make Baxter's exact results more
explicit for the symmetric case. By performing a Bethe Ansatz calculation with
open boundary conditions we confirm a dilogarithm identity for the
low-temperature expansion which may be new. We propose a new model for
numerical studies. This model has only two variables and exhibits commensurate
and incommensurate phase transitions and wetting transitions near zero
temperature. It appears to be not integrable, except at one point, and at each
temperature there is a point, where it is almost identical with the integrable
chiral Potts model.Comment: J. Stat. Phys., LaTeX using psbox.tex and AMS fonts, 69 pages, 30
figure
Nonlinear Integral Equations for Thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz Model
We propose a system of nonlinear integral equations (NLIE) which describes
the thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz model. These NLIE
correspond to a trigonometric analogue of our previous result
(cond-mat/0212280), and contain only r unknown functions. In particular, they
reduce to Takahashi's NLIE for the XXZ spin chain (cond-mat/0010486) if r=1. We
also calculate the high temperature expansion of the free energy. In particular
for r=1 case, we have succeeded to derive the coefficients of order
O((\frac{J}{T})^{99}).Comment: 19 pages, 4 figures, only the Mathematica file for the high
temperature expansion is replaced, to appear in J.Phys.Soc.Jpn.Vol.74 No.3
(2005
The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
The most general cyclic representations of the quantum integrable tau_2-model
are analyzed. The complete characterization of the tau_2-spectrum (eigenvalues
and eigenstates) is achieved in the framework of Sklyanin's Separation of
Variables (SOV) method by extending and adapting the ideas first introduced in
[1, 2]: i) The determination of the tau_2-spectrum is reduced to the
classification of the solutions of a given functional equation in a class of
polynomials. ii) The determination of the tau_2-eigenstates is reduced to the
classification of the solutions of an associated Baxter equation. These last
solutions are proven to be polynomials for a quite general class of
tau_2-self-adjoint representations and the completeness of the associated Bethe
ansatz type equations is derived. Finally, the following results are derived
for the inhomogeneous chiral Potts model: i) Simplicity of the spectrum, for
general representations. ii) Complete characterization of the chiral Potts
spectrum (eigenvalues and eigenstates) and completeness of Bethe ansatz type
equations, for the self-adjoint representations of tau_2-model on the chiral
Potts algebraic curves.Comment: 40 pages. Minor modifications in the text and some notation