Magnetism and Phase Separation in the Ground State of the Hubbard Model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilise a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed.Comment: 9 pages, 11 figure

Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Phase diagram of the frustrated Hubbard model

The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the one-band Hubbard model has long been used to describe similar features in real materials like V$_2$O$_3$. Here we show that this transition is hidden inside a rather robust antiferromagnetic insulator even in the presence of comparatively strong magnetic frustration. This result raises the question of the relevance of the Mott-Hubbard metal-insulator transition for the generic phase diagram of the one-band Hubbard model.Comment: 4 pages, 6 figure

Tracing the development of dust around evolved stars: The case of 47 Tuc

We observed mid-infrared (7.5-22 mum) spectra of AGB stars in the globular cluster 47 Tuc with the Spitzer telescope and find significant dust features of various types. Comparison of the characteristics of the dust spectra with the location of the stars in a logP-K-diagram shows that dust mineralogy and position on the AGB are related. A 13 mum feature is seen in spectra of low luminosity AGB stars. More luminous AGB stars show a broad feature at 11.5 mum. The spectra of the most luminous stars are dominated by the amorphous silicate bending vibration centered at 9.7 mum. For 47 Tuc AGB stars, we conclude that early on the AGB dust consisting primarily of Mg-, Al- and Fe oxides is formed. With further AGB evolution amorphous silicates become the dominant species.Comment: 2 figures, accepted for publication in ApJ Letter

XMM-Newton study of the ULIRG NGC 6240

A recently performed XMM-Newton observation of the ULIRG NGC 6240 clearly indicates the presence of an AGN contribution to its X-ray spectrum. In the 5.0 - 7.0 keV energy range there is a clear signature of the fluorescent Fe K lines at 6.4, 6.7 and 6.9 keV, respectively. The line strength of the 6.4 keV line cannot be produced by a thermal component. The 0.3 - 10.0 keV spectral energy distribution is characterized by the following components: (I) two hot thermal components (the starburst), (II) one direct component (heavily absorbed; AGN is hidden), (III) one reflection component (the AGN), (IV) three narrow Fe lines. The model parameters for the broad-band spectral energy distribution are consistent with the results of previously works.Comment: 2 pages incl. 2 figures, to appear in the proceedings of the "New Century of X-ray Astronomy" symposium held in Yokohama, Japan (March 6-8, 2001), eds. H. Kunieda and H. Inoue, ASP pres

Quantum spherical spin models

A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without momenta in the Hamiltonian can be described, which may lead to different symmetry classes. Two models that show this difference are analyzed. Both models are exactly solvable and their phase diagram is analyzed. A transversal external field leads to a phase transition line that ends in a quantum critical point. The two considered symmetries of the Hamiltonian considered give different critical phenomena in the quantum critical region. The model with momenta is argued to be analog to the large-N limit of an SU(N) Heisenberg ferromagnet, and the model without momenta shares the critical phenomena of an SU(N) Heisenberg antiferromagnet.Comment: 22 page