9,818 research outputs found
Gaudin Hypothesis for the XYZ Spin Chain
The XYZ spin chain is considered in the framework of the generalized
algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of
the Bethe vectors is computed and expressed in the form of a Jacobian. This
result corresponds to the Gaudin hypothesis for the XYZ spin chain.Comment: 12 pages, LaTeX2e (+ amssymb, amsthm); to appear in J. Phys.
Buoyant Venus Station feasibility study. Volume III - Instrumentation study Final report
Scientific instrumentation for inflatable buoyant Venus statio
Entropy of Folding of the Triangular Lattice
The problem of counting the different ways of folding the planar triangular
lattice is shown to be equivalent to that of counting the possible 3-colorings
of its bonds, a dual version of the 3-coloring problem of the hexagonal lattice
solved by Baxter. The folding entropy Log q per triangle is thus given by
Baxter's formula q=sqrt(3)(Gamma[1/3])^(3/2)/2pi =1.2087...Comment: 9 pages, harvmac, epsf, uuencoded, 5 figures included, Saclay
preprint T/9401
Selfduality for coupled Potts models on the triangular lattice
We present selfdual manifolds for coupled Potts models on the triangular
lattice. We exploit two different techniques: duality followed by decimation,
and mapping to a related loop model. The latter technique is found to be
superior, and it allows to include three-spin couplings. Starting from three
coupled models, such couplings are necessary for generating selfdual solutions.
A numerical study of the case of two coupled models leads to the identification
of novel critical points
Baxter equations and Deformation of Abelian Differentials
In this paper the proofs are given of important properties of deformed
Abelian differentials introduced earlier in connection with quantum integrable
systems. The starting point of the construction is Baxter equation. In
particular, we prove Riemann bilinear relation. Duality plays important role in
our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur
Magnetic behavior of a spin-1 Blume-Emery-Griffiths model
I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear
and biquadratic exchange interactions and single-ion crystal field under an
applied magnetic field. This model can be exactly mapped into a tight-binding
Hubbard model - extended to include intersite interactions - provided one
renormalizes the chemical and the on-site potentials, which become temperature
dependent. After this transformation, I provide the exact solution of the
Blume-Emery-Griffiths model in one dimension by means of the Green's functions
and equations of motion formalism. I investigate the magnetic variations of
physical quantities - such as magnetization, quadrupolar moment, susceptibility
- for different values of the interaction parameters and of the applied field,
focusing on the role played by the biquadratic interaction in the breakdown of
the magnetization plateaus.Comment: 4 pages, 5 figures. ICM 2009 (Karlsruhe) Conference proceeding
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
On the Lagrangian structure of integrable hierarchies
We develop the concept of pluri-Lagrangian structures for integrable
hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or
Lagrangian multiform) theory of integrable lattice systems. We derive the
multi-time Euler Lagrange equations in their full generality for hierarchies of
two-dimensional systems, and construct a pluri-Lagrangian formulation of the
potential Korteweg-de Vries hierarchy.Comment: 29 page
New critical frontiers for the Potts and percolation models
We obtain the critical threshold for a host of Potts and percolation models
on lattices having a structure which permits a duality consideration. The
consideration generalizes the recently obtained thresholds of Scullard and Ziff
for bond and site percolation on the martini and related lattices to the Potts
model and to other lattices.Comment: 9 pages, 5 figure
Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
We consider the six-vertex model with anti-periodic boundary conditions
across a finite strip. The row-to-row transfer matrix is diagonalised by the
`commuting transfer matrices' method. {}From the exact solution we obtain an
independent derivation of the interfacial tension of the six-vertex model in
the anti-ferroelectric phase. The nature of the corresponding integrable
boundary condition on the spin chain is also discussed.Comment: 18 pages, LaTeX with 1 PostScript figur
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