Critical properties of the XXZ model with long-range interactions on the double chain

The $XXZ$ model $(s = 1/2)$ in a transverse field on a double chain with a uniform long-range interaction among the $z$ components of the spins is considered. The nearest-neighbour interactions are restricted to the components in the $xy$ plane and to the spins within the same chain leg, such that the Hamiltonian is given by $H = -\sum_{m=1}^{2} J_{m} \sum_{j=1}^{N}(S_{m,j}^{x}S_{m, j+1}^{x} + S_{m,j}^{y}S_{m,j+1}^{y}) - \frac{I}{N}\sum_{m,n=1}^{2} \sum_{j,k=1}^{N}S_{m,j}^{z}S_{n,k}^{z}-h\sum_{m=1}^{2} \sum_{j=1}^{N}S_{m,j}^{z}$, where $N$ is the number of sites of the lattice and $m,n$ $(m,n = 1, 2)$ label the chain legs. The model is solved exactly by introducing the Jordan-Wigner and integral Gaussian transformations, which map the Hamiltonian in a non-interacting fermion system and corresponds to an extension of the model recently studied by the authors for a single chain. The equation of state is obtained in closed form, and the critical classical (at $T > 0$) and quantum (at $T = 0$) behaviours can be determined exactly. The quantum critical surface is determined in the space generated by the transverse field and interaction parameters, and the crossover lines separating the different critical regimes are also obtained. It is also shown that, differently from the results obtained for the single chain, the system can present multiple quantum transitions.Comment: 02 pages, 02 figures, to appear in JMMM (Proceedings of ICM2006

The XY model on the one-dimensional superlattice: static properties

The XY model (s=1/2) on the one-dimensional alternating superlattice (closed chain) is solved exactly by using a generalized Jordan-Wigner transformation and the Green function method. Closed expressions are obtained for the excitation spectrum, the internal energy, the specific heat, the average magnetization per site, the static transverse susceptibility and the two-spin correlation function in the field direction at arbitrary temperature. At T=0 it is shown that the system presents multiple second order phase transitions induced by the transverse field, which are associated to the zero energy mode with wave number equal to 0 or $\pi$. It is also shown that the average magnetization as a function of the field presents, alternately, regions of plateaux (disordered phases) and regions of variable magnetization (ordered phases). The static correlation function presents an oscillating behaviour in the ordered phase and its period goes to infinity at the critical point.Comment: 16 pages, 16 figure

Effect of particle size distribution and dynamics on the performance of two-dimensional packing

AbstractExtensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L2. In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ⊖(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics

Unraveling the simultaneous shock magnetization and demagnetization of rocks

International audienceIn the natural case of an hypervelocity impact on a planetary or asteroidal surface, two competing phenomena occur: partial or complete shock demagnetization of pre-existing remanence and acquisition of shock remanent magnetization (SRM). In this paper, to better understand the effects of shock on the magnetic history of rocks, we simulate this natural case through laser shock experiments in controlled magnetic field. As previously shown, SRM is strictly proportional to the ambient field at the time of impact and parallel to the ambient field. Moreover, there is no directional or intensity heterogeneity of the SRM down to the scale of ∼0.2mm. We also show that the intensity of SRM is independent of the initial remanence state of the rock. Shock demagnetization and magnetization appear to be distinct phenomena that do not necessarily affect identical populations of grains. As such, shock demagnetization is not a limiting case of shock magnetization in zero field

M-Theory Moduli Space and Cosmology

We conduct a systematic search for a viable string/M-theory cosmology, focusing on cosmologies that include an era of slow-roll inflation, after which the moduli are stabilized and the Universe is in a state with an acceptably small cosmological constant. We observe that the duality relations between different cosmological backgrounds of string/M-theory moduli space are greatly simplified, and that this simplification leads to a truncated moduli space within which possible cosmological solutions lie. We review some known challenges to four dimensional models in the "outer", perturbative, region of moduli space, and use duality relations to extend them to models of all of the (compactified) perturbative string theories and 11D supergravity, including brane world models. We conclude that cosmologies restricted to the outer region are not viable, and that the most likely region of moduli space in which to find realistic cosmology is the "central", non-perturbative region, with coupling and compact volume both of order unity, in string units.Comment: 42 pages, 3 figure

Unified dark energy models : a phenomenological approach

A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth transition among the three main phases of the universe evolution (radiation era, matter domination, asymptotical de Sitter state) is naturally achieved. We use the estimated age of the universe, the Hubble diagram of Type Ia Supernovae and the angular size - redshift relation for compact and ultracompact radio structures to test whether the model is in agreement with astrophysical observation and to constrain its main parameters. Although phenomenologically motivated, the model may be straightforwardly interpreted as a two fluids scenario in which the quintessence is generated by a suitably chosen scalar field potential. On the other hand, the same model may also be read in the context of unified dark energy models or in the framework of modified Friedmann equation theories.Comment: 12 pages, 10 figures, accepted for publication on Physical Review

On exact solutions for quintessential (inflationary) cosmological models with exponential potentials

We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar fields can be connected to the inflationary phase, building up, for this class of potentials, a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have also been done by including radiation into the model.Comment: Revtex4, 10 figure

Agricultura orgânica: características básicas do seu produtor.

A agricultura orgânica é ainda pouco expressiva no Brasil. Sua relevância é, no entanto, crescente, seguindo tendência observada em outros países, em especial na Europa. Este estudo analisa as características básicas do produtor de produtos orgânicos, contribuindo para preencher uma lacuna existente na literatura de economia rural. Utilizando informações primárias sobre agricultores orgânicos da região próxima à cidade de Curitiba, Paraná, identificamos as suas características pessoais e econômicas, por meio de estatística descritiva, análise de correlação e regressão linear múltipla. Os produtores foram divididos em dois grupos: o primeiro com aqueles que ainda estão em conversão para a agricultura orgânica e o segundo grupo composto por produtores orgânicos que já obtiveram a certificação de seus produtos. Os resultados obtidos indicam que alta participação de capital próprio no financiamento da produção e elevado nível de escolaridade são duas das características mais marcantes dos produtores rurais orgânicos paranaenses. Outras características que influenciam o resultado líquido da atividade são a disponibilidade de mão de obra e a integração de atividades agrícolas, pecuárias e florestais

Integrated reduction/oxidation reactions and sorption processes for Cr(VI) removal from aqueous solutions using Laminaria digitata macro-algae

The main goal of this work was the valorization of seaweed Laminaria digitata, after acid pre-treatment, for the remediation of hexavalent chromium solutions. The Cr(VI) removal efficiency by the protonated biomass was studied as a function of different parameters, such as contact time, pH, biomass and Cr(VI) concentration, and temperature. Cr(VI) removal is based on a complex mechanism that includes a reduction of Cr(VI) to Cr(III), through the oxidation of biomass at acidic medium, and further chemical binding of Cr(III) to the negatively charged binding groups, mainly carboxylic groups. The optimum pH for chromium removal, using protonated L. digitata algae, was 2.5. The maximum amount of Cr(VI) reduction by the algae was around 2.1 mmol/g. The uptake capacity of Cr(III) by the oxidized biomass, after Cr(VI) reduction, was higher than by the algae in its original form (protonated algae). Results suggest that the oxidation of the biomass during Cr(VI) reduction, turns other active sites available for Cr(III) binding. Also, the Cr(III) binding from a solution of reduced Cr(VI) was much lower than from a pure Cr(III) solution. The result suggests the presence in solution of Cr(III) complexes with the organic matter released from the algae surface during Cr(VI) reduction. The activation energy obtained for the Cr(VI) reduction by L. digitata was 45 ± 20 kJ mol 1. A kinetic model based on the redox reaction between Cr(VI) species and organic compounds from the biosorbent surface was able to fit well the hexavalent chromium concentration. Trivalent chromium equilibrium biosorption was well described at different chromium concentrations, considering the interaction between carboxylic groups present in the surface of the biomass and Cr(III) in solution