Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

Electrons on a square lattice with half a flux quantum per plaquette are considered. An effective description for the current loops is given by a two-dimensional Dirac theory with random mass. It is shown that the conductivity and the localization length can be calculated from a product of Dirac Green's functions with the {\it same} frequency. This implies that the delocalization of electrons in a magnetic field is due to a critical point in a phase with a spontaneously broken discrete symmetry. The estimation of the localization length is performed for a generalized model with $N$ fermion levels using a $1/N$--expansion and the Schwarz inequality. An argument for the existence of two Hall transition points is given in terms of percolation theory.Comment: 10 pages, RevTeX, no figure

Quantum Monte Carlo study of a nonmagnetic impurity in the two-dimensional Hubbard model

In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, Quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li and Zn substituted layered cuprates.Comment: 10 pages, 7 figure

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14

Friedel oscillations induced by non-magnetic impurities in the two-dimensional Hubbard model

We study the interplay of correlations and disorder using an unrestricted Slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.Comment: 9 pages, RevTeX, includes 8 figure

Crystallographically oriented Co and Ni nanocrystals inside ZnO formed by ion implantation and postannealing

In the last decade, transition-metal-doped ZnO has been intensively investigated as a route to room-temperature diluted magnetic semiconductors (DMSs). However, the origin for the reported ferromagnetism in ZnO-based DMS remains questionable. Possible options are diluted magnetic semiconductors, spinodal decomposition, or secondary phases. In order to clarify this question, we have performed a thorough characterization of the structural and magnetic properties of Co- and Ni-implanted ZnO single crystals. Our measurements reveal that Co or Ni nanocrystals (NCs) are the major contribution of the measured ferromagnetism. Already in the as-implanted samples, Co or Ni NCs have formed and they exhibit superparamagnetic properties. The Co or Ni NCs are crystallographically oriented with respect to the ZnO matrix. Their magnetic properties, e.g., the anisotropy and the superparamagnetic blocking temperature, can be tuned by annealing. We discuss the magnetic anisotropy of Ni NCs embedded in ZnO concerning the strain anisotropy.Comment: 13 pages, 14 figure

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Ultracold atoms in optical lattices

Bosonic atoms trapped in an optical lattice at very low temperatures, can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.Comment: 29 pages, 10 figure

3D-MHD simulations of an accretion disk with star-disk boundary layer

We present global 3D MHD simulations of geometrically thin but unstratified accretion disks in which a near Keplerian disk rotates between two bounding regions with initial rotation profiles that are stable to the MRI. The inner region models the boundary layer between the disk and an assumed more slowly rotating central, non magnetic star. We investigate the dynamical evolution of this system in response to initial vertical and toroidal fields imposed in a variety of domains contained within the near Keplerian disk. Cases with both non zero and zero net magnetic flux are considered and sustained dynamo activity found in runs for up to fifty orbital periods at the outer boundary of the near Keplerian disk. Simulations starting from fields with small radial scale and with zero net flux lead to the lowest levels of turbulence and smoothest variation of disk mean state variables. For our computational set up, average values of the Shakura & Sunyaev (1973) $\alpha$ parameter in the Keplerian disk are typically $0.004\pm 0.002.$ Magnetic field eventually always diffuses into the boundary layer resulting in the build up of toroidal field inward angular momentum transport and the accretion of disk material. The mean radial velocity, while exhibiting large temporal fluctuations is always subsonic. Simulations starting with net toroidal flux may yield an average $\alpha \sim 0.04.$ While being characterized by one order of magnitude larger average $\alpha$, simulations starting from vertical fields with large radial scale and net flux may lead to the formation of persistent non-homogeneous, non-axisymmetric magnetically dominated regions of very low density.Comment: Accepted for publication in Ap

Scaling Relations for Logarithmic Corrections

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature.Comment: 4 page