652 research outputs found
From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
We propose a nonlinear integral equation (NLIE) with only one unknown
function, which gives the free energy of the integrable one dimensional
Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum
Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives
the solution of the T-system, plays an important role. In addition, we also
calculate the high temperature expansion of the specific heat and the magnetic
susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added;
typos corrected; to appear in J. Phys. A: Math. Ge
The XXZ model with anti-periodic twisted boundary conditions
We derive functional equations for the eigenvalues of the XXZ model subject
to anti-diagonal twisted boundary conditions by means of fusion of transfer
matrices and by Sklyanin's method of separation of variables. Our findings
coincide with those obtained using Baxter's method and are compared to the
recent solution of Galleas. As an application we study the finite size scaling
of the ground state energy of the model in the critical regime.Comment: 22 pages and 3 figure
Integrability of a t-J model with impurities
A t-J model for correlated electrons with impurities is proposed. The
impurities are introduced in such a way that integrability of the model in one
dimension is not violated. The algebraic Bethe ansatz solution of the model is
also given and it is shown that the Bethe states are highest weight states with
respect to the supersymmetry algebra gl(2/1)Comment: 14 page
Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity
Multidimensional model describing the cosmological evolution of n Einstein
spaces in the theory with l scalar fields and forms is considered. When
electro-magnetic composite p-brane ansatz is adopted, and certain restrictions
on the parameters of the model are imposed, the dynamics of the model near the
singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky
space, N = n+l. The geometrical criterion for the finiteness of the billiard
volume and its compactness is used. This criterion reduces the problem to the
problem of illumination of (N-2)-dimensional sphere by point-like sources. Some
examples with billiards of finite volume and hence oscillating behaviour near
the singularity are considered. Among them examples with square and triangle
2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional
billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons
term) are considered. It is shown that the inclusion of the Chern-Simons term
destroys the confining of a billiard.Comment: 27 pages Latex, 3 figs., submit. to Class. Quantum Gra
Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field
We show that in multidimensional gravity vector fields completely determine
the structure and properties of singularity. It turns out that in the presence
of a vector field the oscillatory regime exists in all spatial dimensions and
for all homogeneous models. By analyzing the Hamiltonian equations we derive
the Poincar\'e return map associated to the Kasner indexes and fix the rules
according to which the Kasner vectors rotate. In correspondence to a
4-dimensional space time, the oscillatory regime here constructed overlap the
usual Belinski-Khalatnikov-Liftshitz one.Comment: 9 pages, published on Classical and Quantum Gravit
Further solutions of critical ABF RSOS models
The restricted SOS model of Andrews, Baxter and Forrester has been studied.
The finite size corrections to the eigenvalue spectra of the transfer matrix of
the model with a more general crossing parameter have been calculated.
Therefore the conformal weights and the central charges of the non-unitary or
unitary minimal conformal field have been extracted from the finite size
corrections.Comment: Pages 11; revised versio
Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
There being no precise definition of the quantum integrability, the
separability of variables can serve as its practical substitute. For any
quantum integrable model generated by the Yangian Y[sl(3)] the canonical
coordinates and the conjugated operators are constructed which satisfy the
``quantum characteristic equation'' (quantum counterpart of the spectral
algebraic curve for the L operator). The coordinates constructed provide a
local separation of variables. The conditions are enlisted which are necessary
for the global separation of variables to take place.Comment: 15 page
Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
In proving the Fermionic formulae, combinatorial bijection called the
Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a
bijection between the set of highest paths and the set of rigged
configurations. In this paper, we give a proof of crystal theoretic
reformulation of the KKR bijection. It is the main claim of Part I
(math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the
author. The proof is given by introducing a structure of affine combinatorial
matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more
explanations added to the main tex
Crystal Graphs and -Analogues of Weight Multiplicities for the Root System
We give an expression of the -analogues of the multiplicities of weights
in irreducible \sl_{n+1}-modules in terms of the geometry of the crystal
graph attached to the corresponding U_q(\sl_{n+1})-modules. As an
application, we describe multivariate polynomial analogues of the
multiplicities of the zero weight, refining Kostant's generalized exponents.Comment: LaTeX file with epic, eepic pictures, 17 pages, November 1994, to
appear in Lett. Math. Phy
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