First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension d_0 of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with d_0=2 is not thermodynamically stable under graph noise.Comment: 12 pages, 12 figures, 1 tabl

Supersymmetric Construction of W-Algebras from Super Toda and Wznw Theories

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy-momentum tensor, is dicussed in general terms for all super Lie algebras whose simple roots are fermionic . A detailed discussion employing the Dirac bracket structure and an explicit construction of W-algebras for the cases of $OSP(1,2)$, $OSP(2,2)$ , $OSP(3,2)$ and $D(2,1 \mid \alpha )$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed in the pertinent cases.Comment: 24 page

Mean-field analysis of the majority-vote model broken-ergodicity steady state

We study analytically a variant of the one-dimensional majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. The individuals are fixed in the sites of a ring of size $L$ and can interact with their nearest neighbors only. The interesting feature of this model is that it exhibits an infinity of spatially heterogeneous absorbing configurations for $L \to \infty$ whose statistical properties we probe analytically using a mean-field framework based on the decomposition of the $L$-site joint probability distribution into the $n$-contiguous-site joint distributions, the so-called $n$-site approximation. To describe the broken-ergodicity steady state of the model we solve analytically the mean-field dynamic equations for arbitrary time $t$ in the cases n=3 and 4. The asymptotic limit $t \to \infty$ reveals the mapping between the statistical properties of the random initial configurations and those of the final absorbing configurations. For the pair approximation ($n=2$) we derive that mapping using a trick that avoids solving the full dynamics. Most remarkably, we find that the predictions of the 4-site approximation reduce to those of the 3-site in the case of expectations involving three contiguous sites. In addition, those expectations fit the Monte Carlo data perfectly and so we conjecture that they are in fact the exact expectations for the one-dimensional majority-vote model

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer--Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page

Critical behavior and correlations on scale-free small-world networks: Application to network design

We analyze critical phenomena on networks generated as the union of hidden variable models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small worlds similar to those a la Watts and Strogatz, but with a heterogeneous degree distribution. We prove that the critical behavior (thermal or percolative) remains completely unchanged by the presence of finite loops (or finite clustering). Then, we show that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature. Quite interestingly, if gamma is the exponent for the power-law distribution of the vertex degree, for gamma <= 3 and with or without short-range couplings, such strong correlations persist even in the thermodynamic limit, contradicting the common opinion that, in mean-field models, correlations always disappear in this limit. Finally, we provide the optimal choice of rewiring under which percolation phenomena in the rewired network are best performed, a natural criterion to reach best communication features, at least in noncongested regimes.PTDC/FIS/108476/2008,PTDC/MAT/114515/2009SOCIALNET

Carbon nanotube: a low-loss spin-current waveguide

We demonstrate with a quantum-mechanical approach that carbon nanotubes are excellent spin-current waveguides and are able to carry information stored in a precessing magnetic moment for long distances with very little dispersion and with tunable degrees of attenuation. Pulsed magnetic excitations are predicted to travel with the nanotube Fermi velocity and are able to induce similar excitations in remote locations. Such an efficient way of transporting magnetic information suggests that nanotubes are promising candidates for memory devices with fast magnetization switchings

Microcrystalline silicon thin films prepared by RF reactive magnetron sputter deposition

Hydrogenated microcrystalline silicon (microc-Si:H) thin films with Cu as a dopant material (about 2 wt.%) were deposited by RF planar magnetron sputtering in an argon/hydrogen plasma. The composition and microstructure of the films were analysed by SEM, ERD/RBS, X-ray diffraction and Raman spectroscopy. These techniques revealed a columnar film structure, each column consisting of several small (nano) crystals with a lateral dimension up to 10nm. The crystals are oriented, generally with the (111) plane parallel to the sample surface. The hydrogen content of the thin films is about 27-33 at.%. Low deposition rates and low sputter gas pressures favour crystallisation and grain growth. The behaviour can be understood in terms of the diffusion or relaxation length of the deposited Si-atoms

Simulation of VUV electroluminescence in micropattern gaseous detectors: the case of GEM and MHSP

Electroluminescence produced during avalanche development in gaseous avalanche detectors is an useful information for triggering, calorimetry and tracking in gaseous detectors. Noble gases present high electroluminescence yields, emitting mainly in the VUV region. The photons can provide signal readout if appropriate photosensors are used. Micropattern gaseous detectors are good candidates for signal amplification in high background and/or low rate experiments due to their high electroluminescence yields and radiopurity. In this work, the VUV light responses of the Gas Electron Multiplier and of the Micro-Hole Strip Plate, working with pure xenon, are simulated and studied in detail using a new and versatile C++ toolkit. It is shown that the solid angle subtended by a photosensor placed below the microstructures depends on the operating conditions. The obtained absolute EL yields, determined for different gas pressures and as functions of the applied voltage, are compared with those determined experimentally.Comment: Accepted for publication in Journal of Instrumentatio