10,687 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.
Ex-nihilo: Obstacles Surrounding Teaching the Standard Model
The model of the Big Bang is an integral part of the national curriculum for
England. Previous work (e.g. Baxter 1989) has shown that pupils often come into
education with many and varied prior misconceptions emanating from both
internal and external sources. Whilst virtually all of these misconceptions can
be remedied, there will remain (by its very nature) the obstacle of ex-nihilo,
as characterised by the question `how do you get something from nothing?' There
are two origins of this obstacle: conceptual (i.e. knowledge-based) and
cultural (e.g. deeply held religious viewpoints). The article shows how the
citizenship section of the national curriculum, coming `online' in England from
September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E
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
Buoyant Venus Station feasibility study. Volume III - Instrumentation study Final report
Scientific instrumentation for inflatable buoyant Venus statio
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
Entropy of polydisperse chains: solution on the Bethe lattice
We consider the entropy of polydisperse chains placed on a lattice. In
particular, we study a model for equilibrium polymerization, where the
polydispersivity is determined by two activities, for internal and endpoint
monomers of a chain. We solve the problem exactly on a Bethe lattice with
arbitrary coordination number, obtaining an expression for the entropy as a
function of the density of monomers and mean molecular weight of the chains. We
compare this entropy with the one for the monodisperse case, and find that the
excess of entropy due to polydispersivity is identical to the one obtained for
the one-dimensional case. Finally, we obtain an exponential distribution of
molecular weights.Comment: 5 pages, 2 figures. Reference place
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
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
Buoyant Venus station feasibility study. Volume IV - Communications and power Final report
Telecommunication and power supply requirements for inflatable buoyant Venus statio
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