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

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.

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

Buoyant Venus Station feasibility study. Volume III - Instrumentation study Final report

Scientific instrumentation for inflatable buoyant Venus statio

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

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

Grain boundary partitioning of Ar and He

An experimental procedure has been developed that permits measurement of the partitioning of Ar and He between crystal interiors and the intergranular medium (ITM) that surrounds them in synthetic melt-free polycrystalline diopside aggregates. ^(37)Ar and ^(4)He are introduced into the samples via neutron irradiation. As samples are crystallized under sub-solidus conditions from a pure diopside glass in a piston cylinder apparatus, noble gases diffusively equilibrate between the evolving crystal and intergranular reservoirs. After equilibration, ITM Ar and He is distinguished from that incorporated within the crystals by means of step heating analysis. An apparent equilibrium state (i.e., constant partitioning) is reached after about 20 h in the 1450 °C experiments. Data for longer durations show a systematic trend of decreasing ITM Ar (and He) with decreasing grain boundary (GB) interfacial area as would be predicted for partitioning controlled by the network of planar grain boundaries (as opposed to ITM gases distributed in discrete micro-bubbles or melt). These data yield values of GB-area-normalized partitioning, K¯^(Ar)_(ITM), with units of (Ar/m^3 of solid)/(Ar/m^2 of GB) of 6.8 x 10^3 – 2.4 x 104 m^(-1). Combined petrographic microscope, SEM, and limited TEM observation showed no evidence that a residual glass phase or grain boundary micro-bubbles dominated the ITM, though they may represent minor components. If a nominal GB thickness (δ) is assumed, and if the density of crystals and the grain boundaries are assumed equal, then a true grain boundary partition coefficient (K^(Ar)_(GB) = X^(Ar)_(crystals)/X^(Ar)_(GB) may be determined. For reasonable values of δ, K^(Ar)_(GB) is at least an order of magnitude lower than the Ar partition coefficient between diopside and melt. Helium partitioning data provide a less robust constraint with K¯^(He)_(ITM) between 4 x 10^3 and 4 x 10^4 cm^(-1), similar to the Ar partitioning data. These data suggest that an ITM consisting of nominally melt free, bubble free, tight grain boundaries can constitute a significant but not infinite reservoir, and therefore bulk transport pathway, for noble gases in fine grained portions of the crust and mantle where aqueous or melt fluids are non-wetting and of very low abundance (i.e., <0.1% fluid). Heterogeneities in grain size within dry equilibrated systems will correspond to significant differences in bulk rock noble gas content

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

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