Deformation analysis of matrix models

The Tracy-Widom equations associated with level spacing distributions are realized as a special case of monodromy preserving deformations.Comment: 23 page

New Integrable Lattice Models From Fuss-Catalan Algebras

We construct new trigonometric solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops.Comment: 30 pages, 23 eps figures, uses harvmac.tex, epsf.te

Boundary ABF Models

We diagonalise the transfer matrix of boundary ABF models using bosonized vertex operators. We compute the boundary S-matrix and check the scaling limit against known results for perturbed boundary conformal field theories.Comment: 26 pages, Latex, uses amssymbols.sty and pb-diagram.sty, 3 ps figure

Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra ${\cal U}_q (\hat{sl}_2)$ together with the corner transfer matrix approach (massive regime).Comment: Latex2e, 26 page

Central elements of the elliptic ZnZ_n monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the $\mathbb{Z}_n$ R-matrix are studied. When the crossing parameter $w$ takes a special rational value $w=\frac{n}{N}$, where $N$ and $n$ are positive coprime integers, the center is substantially larger than that in the generic case for which the "quantum determinant" provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.Comment: Latex file, 18 pages; V2: minor typos corrected and a reference update

Correlation functions of the XYZ model with a boundary

Integral formulae for the correlation functions of the XYZ model with a boundary are calculated by mapping the model to the bosonized boundary SOS model. The boundary K-matrix considered here coincides with the known general solution of the boundary Yang-Baxter equation. For the case of diagonal K-matrix, our formulae reproduce the one-point function previously obtained by solving boundary version of quantum Knizhnik-Zamolodchikov equation.Comment: 35 pages, 12 figure

Fermionic screening operators in the sine-Gordon model

Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.Comment: 18 pages, 1 figur

The 19-Vertex Model at critical regime ∣q∣=1|q|=1

We study the 19-vertex model associated with the quantum group $U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the type-I vertex operators in terms of free bosons and free fermions. Using these free field realizations, we give the integral representations for the correlation functions.Comment: LaTEX2e, 19page