Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density matrix, conceived as a map which associates with every local operator its thermal expectation value, can be written as the trace of the exponential of an operator constructed from weighted traces of the elements of certain monodromy matrices related to $U_q (\hat{\mathfrak{sl}}_2)$ and only two transcendental functions pertaining to the one-point function and the neighbour correlators, respectively. Our conjecture implies that all static correlation functions of the XXZ chain are polynomials in these two functions and their derivatives with coefficients of purely algebraic origin.Comment: 35 page

On the Three-dimensional Lattice Model

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.Comment: 8 pages, latex, 4 figure

Short-distance thermal correlations in the XXZ chain

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < \Delta < 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure

Is there the radion in the RS2 model ?

We analyse the physical boundary conditions at infinity for metric fluctuations and gauge functions in the RS2 model with matter on the brane. We argue that due to these boundary conditions the radion field cannot be gauged out in this case. Thus, it represents a physical degree of freedom of the model.Comment: 9 page

Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length $m$. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.Comment: 35 page

Caractérisation physico-chimique du gypse de Tahoua

Le Gypse rencontr&#233; dans la r&#233;gion de Tahoua se pr&#233;sente sous trois formes : fibreux, nodulaire et en plaquette. Les gypses nodulaire et fibreux font l&#8217;objet de ce travail. La diffraction des rayons X (DRX) montre que l&#8217;&#233;chantillon fibreux est du gypse presque pur mais que le nodulaire contient une proportion importante d&#8217;impuret&#233;s. L&#8217;analyse chimique par ICP-AES a permis de d&#233;terminer le pourcentage de gypse (CaSO4, 2H2O) dans chaque &#233;chantillon: soit 98,44% dans le fibreux et 68,40% dans le nodulaire. L&#8217;analyse par ICP-MS avec une sensibilit&#233; de l&#8217;appareil de l&#8217;ordre du ppb, a montr&#233; que les &#233;l&#233;ments chimiques suivants: B, Sc, V, Cr, Mn, Co, Ni, Cu, Ga, As, Se, Br, Rb, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, In, Sb, Te, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Th et U sont &#224; des concentrations inf&#233;rieures &#224; 1&#956;g/Kg dans chaque &#233;chantillon. Les isothermes d&#8217;adsorption et de d&#233;sorption de l&#8217;azote par le gypse fibreux montrent que la surface sp&#233;cifique et le volume poreux de l'&#233;chantillon sont respectivement de 21 m&#178;/g et de 0,03 cm3/g. Les analyses ATG-ATD des gypses fibreux et nodulaire r&#233;v&#232;lent une perte en masse respectivement de 20% et 17% &#224; 138 &#176;C.Mots cl&#233;s: Gypse, analyse, min&#233;ralogie, ea

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}<H<H_{c2}$. The critical behaviour in the vicinity of the critical points is of the Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.Comment: 90 pages, 33 figures, extensive revisio

Universal integrability objects

We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional relations correcting inexactitudes of the previous considerations. A special attention is given to the connection of the representations used to construct the universal transfer operators and $Q$-operators.Comment: 21 pages, submitted to the Proceedings of the International Workshop "CQIS-2012" (Dubna, January 23-27, 2012

The process gg -> WW as a background to the Higgs signal at the LHC

The production of W pairs from the one-loop gluon fusion process is studied. Formulas are presented for the helicity amplitudes keeping the top mass finite, but all other quark masses zero. The correlations among the leptons coming from the W bosons are kept. The contribution of this background to the Higgs boson search in the WW decay mode at the LHC is estimated by applying the cuts foreseen in experimental searches using the PYTHIA Monte Carlo program. Kinematic distributions for the final state leptons are compared to those of the Higgs boson signal and of the q qbar -> WW background. After applying final cuts, the gg background is found to be large, at the level of 35% of the q qbar background.The characteristics of the gg background are very similar to those of the signal. Therefore, an experimental normalization of this background component appears to be very difficult and the uncertainty must largely be determined by theory. As a result, the significance of a Higgs signal in the gg -> H -> WW mode at the LHC is reduced.Comment: 24 pages, 4 figure

Why do we need higher order fully exclusive Monte Carlo generator for Higgs boson production from heavy quark fusion at LHC?

In this paper we argue that having available higher order fully exclusive Monte Carlo generator for Higgs boson production from heavy quark fusion will be mandatory for data analysis at LHC. The H to tau tau channel, a key for early discovery of the Higgs boson in the MSSM scenario, is discussed. With simplified example and for mH = 120 GeV we show, that depending on choice among presently available approaches, used for simulation of Higgs boson production from b bbar H Yukawa coupling, final acceptance for the signal events being reconstructed inside mass window may differ by a factor of 3. The spread is even larger (up to a factor of 10) for other production mechanisms (promising for some regions of the MSSM parameter space). The complete analysis, which necessarily will add stringent requirements for background rejection (such as identification of b-jet or veto on b-jet) and which will require statistical combination of samples selected with different selection criteria may only enhance the uncertainty.Comment: 14 pages, 22 figure