1,034 research outputs found
Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
The Hamiltonian approach to the theory of dual isomonodromic deformations is
developed within the framework of rational classical R-matrix structures on
loop algebras. Particular solutions to the isomonodromic deformation equations
appearing in the computation of correlation functions in integrable quantum
field theory models are constructed through the Riemann-Hilbert problem method.
The corresponding -functions are shown to be given by the Fredholm
determinant of a special class of integral operators.Comment: LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop:
Supersymmetric and Integrable Systems, University of Illinois, Chicago
Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physic
Free field constructions for the elliptic algebra and Baxter's eight-vertex model
Three examples of free field constructions for the vertex operators of the
elliptic quantum group are obtained. Two of these
(for ) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
-algebra of Lepowsky and Wilson. The third one () is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at , however, is not related to the deformed
Virasoro algebra. Using these free field constructions, an integral formula for
the correlation functions of Baxter's eight-vertex model is obtained. This
formula shows different structure compared with the one obtained by Lashkevich
and Pugai.Comment: 23 pages. Based on talks given at "MATHPHYS ODYSSEY 2001-Integrable
Models and Beyond" at Okayama and Kyoto, February 19-23, 2001, et
Random Words, Toeplitz Determinants and Integrable Systems. I
It is proved that the limiting distribution of the length of the longest
weakly increasing subsequence in an inhomogeneous random word is related to the
distribution function for the eigenvalues of a certain direct sum of Gaussian
unitary ensembles subject to an overall constraint that the eigenvalues lie in
a hyperplane.Comment: 15 pages, no figure
Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of
-symmetric model and tail operators are expressed in
terms of bosonized vertex operators in the model. Correlation
functions of -symmetric model can be obtained by
using these objects, in principle. In particular, we calculate spontaneous
polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available
at http://stacks.iop.org/1751-8121/42/16521
Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
We discuss an algebraic method for constructing eigenvectors of the transfer
matrix of the eight vertex model at the discrete coupling parameters. We
consider the algebraic Bethe ansatz of the elliptic quantum group for the case where the parameter satisfies for arbitrary integers , and . When or
is odd, the eigenvectors thus obtained have not been discussed previously.
Furthermore, we construct a family of degenerate eigenvectors of the XYZ spin
chain, some of which are shown to be related to the loop algebra
symmetry of the XXZ spin chain. We show that the dimension of some degenerate
eigenspace of the XYZ spin chain on sites is given by , if
is an even integer. The construction of eigenvectors of the transfer matrices
of some related IRF models is also discussed.Comment: 19 pages, no figure (revisd version with three appendices
Elliptic Deformed Superalgebra
We introduce the elliptic superalgebra as one
parameter deformation of the quantum superalgebra . For an
arbitrary level we give the bosonization of the elliptic
superalgebra and the screening currents that commute
with modulo total difference.Comment: LaTEX, 25 page
Form factor expansion of the row and diagonal correlation functions of the two dimensional Ising model
We derive and prove exponential and form factor expansions of the row
correlation function and the diagonal correlation function of the two
dimensional Ising model
Notes on highest weight modules of the elliptic algebra
We discuss a construction of highest weight modules for the recently defined
elliptic algebra , and make several conjectures
concerning them. The modules are generated by the action of the components of
the operator on the highest weight vectors. We introduce the vertex
operators and through their commutation relations with the
-operator. We present ordering rules for the - and -operators and
find an upper bound for the number of linearly independent vectors generated by
them, which agrees with the known characters of -modules.Comment: Nonstandard macro package eliminate
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