9,745 research outputs found

### SU(N) Meander Determinants

We propose a generalization of meanders, i.e., configurations of
non-selfintersecting loops crossing a line through a given number of points, to
SU(N). This uses the reformulation of meanders as pairs of reduced elements of
the Temperley-Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with
a natural generalization to SU(N). We also derive explicit formulas for SU(N)
meander determinants, defined as the Gram determinants of the corresponding
bases of the Hecke algebra.Comment: TeX using harvmac.tex and epsf.tex, 60 pages (l-mode), 5 figure

### Combinatorial point for higher spin loop models

Integrable loop models associated with higher representations (spin k/2) of
U_q(sl(2)) are investigated at the point q=-e^{i\pi/(k+2)}. The ground state
eigenvalue and eigenvectors are described. Introducing inhomogeneities into the
models allows to derive a sum rule for the ground state entries.Comment: latest version adds some reference

### Fully Packed O(n=1) Model on Random Eulerian Triangulations

We introduce a matrix model describing the fully-packed O(n) model on random
Eulerian triangulations (i.e. triangulations with all vertices of even
valency). For n=1 the model is mapped onto a particular gravitational 6-vertex
model with central charge c=1, hence displaying the expected shift c -> c+1
when going from ordinary random triangulations to Eulerian ones. The case of
arbitrary n is also discussed.Comment: 12 pages, 3 figures, tex, harvmac, eps

### Folding Transitions of the Square-Diagonal Lattice

We address the problem of "phantom" folding of the tethered membrane modelled
by the two-dimensional square lattice, with bonds on the edges and diagonals of
each face. Introducing bending rigidities $K_1$ and $K_2$ for respectively long
and short bonds, we derive the complete phase diagram of the model, using
transfer matrix calculations. The latter displays two transition curves, one
corresponding to a first order (ferromagnetic) folding transition, and the
other to a continuous (anti-ferromagnetic) unfolding transition.Comment: TeX using harvmac.tex and epsf.tex, 22 pages (l mode), 17 figure

### Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation
with reflecting boundary conditions which is relevant to the Temperley--Lieb
model of loops on a strip. By use of integral formulae we prove conjectures
relating it to the weighted enumeration of Cyclically Symmetric Transpose
Complement Plane Partitions and related combinatorial objects

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