Alex A. Schmidt

Spin-glass freezing in Kondo-lattice compounds

A theory is presented that describes a spin-glass phase at finite temperatures in Kondo-lattice systems with an additional Ruderman‐Kittel‐Kasuya‐Yosida interaction represented by long range, random couplings among localized spins as in the Sherrington‐Kirkpatrick ~SK! spin-glass model. The problem is studied within the functional integral formalism where the spin operators are represented by bilinear combinations of fermionic ~anticommuting! Grassmann variables. The Kondo and spin-glass transitions are both described with the mean-field‐like static ansatz that reproduces good results in the two well-known limits. At high temperatures and low values of the Kondo coupling there is a paramagnetic ~disordered! phase with vanishing Kondo and spin-glass order parameters. By lowering the temperature, a second order transition line is found at TSG to a spin-glass phase. For larger values of the Kondo coupling there is a second order transition line at roughly Tk to a Kondo ordered state. For T,TSG the transition between the Kondo and spin-glass phases becomes first order.

The Ising spin glass in a transverse field revisited. Results of two fermionic models

We analyze the infinite range Ising spin glass in a transverse field Γ by using Grassmann variables in a field theory where the spin operators are represented by bilinear combinations of fermionic fields. We compare the results of two fermionic models. In the four state (4S)-model the diagonal Siz operator has two vanishing eigenvalues, that are suppressed by a restraint in the two states (2S)-model. Within a replica symmetric theory and in the static approximation we obtain qualitatively similar results for both models. They both exhibit a critical temperature Tc(Γ) that decreases when Γ increases, until it reaches a quantum critical point at the same value of Γc and they are both unstable under replica symmetry breaking in the whole spin glass phase. Our results are in agreement with recent renormalization group calculations in three-dimensional systems.

Structures in surface-brightness profiles of LMC and SMC star clusters: evidence of mergers?

Context. The LMC and SMC are rich in binary star clusters, and some mergers are expected. It is thus important to characterise single clusters, binary clusters and candidates for mergers. Aims. We selected a sample of star clusters in each Cloud with this aim. Surface photometry of 25 SMC and 22 LMC star clusters was carried with the ESO Danish 1.54 m telescope. 23 clusters were observed for the first time for these purposes. Methods. We fitted Elson, Fall and Freeman (EFF) profiles to the data, deriving structural parameters, luminosities and masses. We also use isophotal maps to constrain candidates for cluster interactions. Results. The structural parameters, luminosities and masses presented good agreement with those in the literature. Three binary clusters in the sample have a double profile. Four clusters (NGC 376, K 50, K 54 and NGC 1810) do not have companions and present important deviations from EFF profiles. Conclusions. The present sample contains blue and red Magellanic clusters. Profiles with excess with respect to EFF were detected in some blue clusters. We find evidence that important deviations from the body of EFF profiles might be used as a tool to detect cluster mergers.

Spin glass and antiferromagnetism in Kondo-lattice disordered system

Abstract.The competition between spin glass (SG), antiferromagnetism (AF) and Kondo effect is studied here in a model which consists of two Kondo sublattices with a Gaussian random interaction between spins in different sublattices with an antiferromagnetic mean J0 and standard deviation J. In the present approach there is no hopping of the conduction electrons between the sublattices and only spins in different sublattices can interact. The problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields which can be solved at mean field level within the static approximation and the replica symmetry ansatz. The obtained phase diagram shows the sequence of phases SG, AF and Kondo state for increasing Kondo coupling. This sequence agrees qualitatively with experimental data of the Ce2Au1-xCoxSi3 compound.

Fermionic Heisenberg model for spin glasses with BCS pairing interaction

In the present paper we have analysed a fermionic infinite-ranged quantum Heisenberg spin glass (s=1/2) with a BCS coupling in real space in the presence of an applied magnetic field. This model has been obtained by tracing out the conducting fermions in a superconducting alloy. The magnetic field is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spin variables are defined as bilinear combinations of the Grassmann fields. The static approximation is used to treat both the pairing and the spin terms together with the replica symmetry ansatz. Henceforth, the problem can be reduced to a one site problem. The field in the z direction, Hz, separates the order parameters in two groups: parallel and transverse to it. We have obtained a phase diagram in T-g space with zero transverse spin-glass ordering, g being the strength of the pairing interaction. It has been possible to locate the transition temperature between the normal paramagnetic phase (NP) and the phase where there is a long range order corresponding to formation of pairs (PAIR). The transition ends at the temperature Tf, the transition temperature between the NP phase and the spin glass (SG) phase. Tf decreases for stronger fields allowing us to calculate the NP-PAIR line transition even at low temperatures. The NP-PAIR transition line has a complex dependence with g and Hz, having a tricritical point depending on Hz from where second order transitions occur for higher values of g and first order transitions occur for lower values of g.

BS 196 : an old star cluster far from the Small Magellanic Cloud main body

We present B and V photometry of the outlying Small Magellanic Cloud (SMC) star cluster BS 196 with the 4.1-m SOAR telescope. The photometry is deep (to V≈25), showing ≈3 mag below the cluster turnoff point at M V = 2.5 (1.03 M ⊙ ). The cluster is located at the SMC distance. The colour-magnitude diagram and isochrone fittings provide a cluster age of 5.0 ± 0.5 Gyr, indicating that this is one of the 12 oldest clusters so far detected in the SMC. The estimated metallicity is [Fe/H] = - 1.68 ± 0.10. The structural analysis gives by means of the King profile fittings a core radius R c = 8.7 ± 1.1 arcsec (2.66 ± 0.14pc) and a tidal radius R t = 69.4 ± 1.7 arcsec (21.2 ± 1.2pc). BS 196 is rather loose with a concentration parameter c = 0.90. With M V = -1.89 ± 0.39, BS 196 belongs to the class of intrinsically fainter SMC clusters, which have started to be explored as compared to the well-known populous ones.

Splitting Wavelet Method for Solving 2D Conservation Laws

for which the grid adaptivity is controlled by the application of a wavelet transform to the numerical solution at each time step combined with a splitting method. Wavelet based adaptive schemes for uni-dimensional problems go back to Harten [4], who was one of the precursors in applying interpolating wavelet transforms to obtain a multiscale decomposition of the numerical solution. This multiresolution decomposition was used to decide whether the numerical flux function should be evaluated by an expensive high resolution scheme or it could be computed from a polynomial interpolation process in a multilevel fashion. For two-dimensional problems, the ideas proposed in [4] were extended in [6] where a two-dimensional wavelet transform is applied to the numerical divergence of (1). Again the multiresolution transform is used to analyze the smoothness of the numerical solution to decide where the numerical quantities can be obtained by interpolation or if they must be evaluated exactly by the numerical scheme. In reality, Martens approach provides a sensor to manage the flux (or divergence) computation but is far from being an adaptive mesh refinement technique since the numerical values on the highest resolution level (the finest dyadic grid of all multiresolution set) must be always available. An interesting alternative has been proposed by Holmstrom [2] in order to indeed produce an adaptive mesh refinement procedure based on a wavelet transform. Holmstrom introduced the concept of sparse point representation (SPR), which is a set of points obtained from the thresholded wavelet transform. The differential operator is then solved by a finite difference scheme over the sparse grid associated to the sparse point representation of the solution. For the SPR of uni-dimensional data the interpolating wavelet transform is considered and for the two-dimensional problems the basis for the bi-dimensional transform is obtained by the tensor product of one-dimensional wavelet and scaling function spaces [2]. The main idea proposed in this work is to avoid the application of a two-dimensional wavelet transform in order to construct an adaptive scheme for solving systems of type given by (1), keeping however the SPR approach. One possibihty for reducing the multidimensional problem to a sequence of one-dimensional problems is to consider a sphtting method (for example, here we have considered a time split MacCormack scheme [8]). Once the multidimensional problem is sphtted in many uni-dimensional sub-problems, each one, associated to a spatial direction, can be solved with an adaptive scheme in each slice of the spatial domain. The following section is reserved for presenting the wavelet time sphtting scheme, whose formulation is inspired by the standard MacCormack method [8]. The discretization is given with respect to a sparse grid per direction. In this sense, the adaptivity is performed for each spatial direction separately, meaning that no tensor product will be necessary to construct the wavelet transform. Each component of the sphtting method is solved by a Lax-Friedrichs scheme, in which numerical flux function is computed by an essentially non-oscillatory (ENO) reconstruction, as done for one-dimensional problems in [1]. The time evolution is done according to the time splitting formulation. Finally, in the last section some numerical simulations are presented.

A parallel wavelet adaptive WENO scheme for 2D conservation laws

Purpose The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method. Findings The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach. Research limitations/implications The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value. Practical implications So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used. Social implications This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators. Originality/value The proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.

A parallel splitting wavelet method for 2D conservation laws

The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.

A MINIMIZATION PROCEDURE APPLIED TO POPULATION SYNTHESIS IN GALAXY NUCLEI USING A STAR CLUSTER LIBRARY: M31, M32

We apply the MINOS optimization system to the population synthesis of galactic nuclei, using a grid of star cluster equivalent widths as a function of age and metallicity. For some classes of red galaxy nuclei, this observational approach to population synthesis produces results similar to those predicted by the theoretical approach of Arimoto and Yoshii (1987). The synthesis results for blue nuclei tend to scatter more in the age vs metallicity plane, probably because we use only visible and near-infrared spectral data. Additional information at shorter wavelengths will possibly produce better-focused solutions in the plane. However, strong bursts of star formation can easily be identified. We provide in this contribution population synthesis for the central regions of M31 and M32. The bulge and the semi-stellar nucleus of M31 are dominated by the old metal-rich population: the semi-stellar nucleus has reached up [Z/Z⊙]≃0.6 and the bulge [Z/Z⊙]≃0.3. In the central region of M32, a metallicity up to the solar value has been reached and the synthesis indicates that the intermediate age component is not dominant.