205 research outputs found
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 chiral Potts model at . 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.Comment: 22 pages, LaTeX, 5 figure
The Integrals of Motion for the Deformed W-Algebra II: Proof of the commutation relations
We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra , and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th
birthda
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.Comment: 20 pages, 6 figures, to appear in J. Phys. A: Math. and Ge
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
Three-Dimensional Integrable Models and Associated Tangle Invariants
In this paper we show that the Boltzmann weights of the three-dimensional
Baxter-Bazhanov model give representations of the braid group, if some suitable
spectral limits are taken. In the trigonometric case we classify all possible
spectral limits which produce braid group representations. Furthermore we prove
that for some of them we get cyclotomic invariants of links and for others we
obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil
Exact and simple results for the XYZ and strongly interacting fermion chains
We conjecture exact and simple formulas for physical quantities in two
quantum chains. A classic result of this type is Onsager, Kaufman and Yang's
formula for the spontaneous magnetization in the Ising model, subsequently
generalized to the chiral Potts models. We conjecture that analogous results
occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and
in a related fermion chain with strong interactions and supersymmetry. We find
exact formulas for the magnetization and gap in the former, and the staggered
density in the latter, by exploiting the fact that certain quantities are
independent of finite-size effects
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Scaling functions from q-deformed Virasoro characters
We propose a renormalization group scaling function which is constructed from
q-deformed fermionic versions of Virasoro characters. By comparison with
alternative methods, which take their starting point in the massive theories,
we demonstrate that these new functions contain qualitatively the same
information. We show that these functions allow for RG-flows not only amongst
members of a particular series of conformal field theories, but also between
different series such as N=0,1,2 supersymmetric conformal field theories. We
provide a detailed analysis of how Weyl characters may be utilized in order to
solve various recurrence relations emerging at the fixed points of these flows.
The q-deformed Virasoro characters allow furthermore for the construction of
particle spectra, which involve unstable pseudo-particles.Comment: 31 pages of Latex, 5 figure
From the braided to the usual Yang-Baxter relation
Quantum monodromy matrices coming from a theory of two coupled (m)KdV
equations are modified in order to satisfy the usual Yang-Baxter relation. As a
consequence, a general connection between braided and {\it unbraided} (usual)
Yang-Baxter algebras is derived and also analysed.Comment: 13 Latex page
Integrable Circular Brane Model and Coulomb Charging at Large Conduction
We study a model of 2D QFT with boundary interaction, in which two-component
massless Bose field is constrained to a circle at the boundary. We argue that
this model is integrable at two values of the topological angle,
and . For we propose exact partition function in terms
of solutions of ordinary linear differential equation. The circular brane model
is equivalent to the model of quantum Brownian dynamics commonly used in
describing the Coulomb charging in quantum dots, in the limit of small
dimensionless resistance of the tunneling contact. Our proposal
translates to partition function of this model at integer charge.Comment: 20 pages, minor change
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