Orbital order in classical models of transition-metal compounds

We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these models exhibit a long-range order which arises via an "order by disorder" mechanism. This strongly indicates that there is orbital ordering in the quantum version of these models, notwithstanding recent rigorous results on the absence of spin order in these systems.Comment: 7 pages, 1 eps fi

Dilution Effects in Two-dimensional Quantum Orbital System

We study dilution effects in a Mott insulating state with quantum orbital degree of freedom, termed the two-dimensional orbital compass model. This is a quantum and two-dimensional version of the orbital model where the interactions along different bond directions cause frustration between different orbital configurations. A long-range correlation of a kind of orbital at each row or column, termed the directional order, is studied by means of the quantum Monte-Carlo method. It is shown that decrease of the ordering temperature due to dilution is much stronger than that in spin models. Quantum effect enhances the effective dimensionality in the system and makes the directional order robust against dilution. We discuss an essential mechanism of the dilute orbital systems.Comment: 5pages, 4 figure

Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Let

Pulsed laser deposition growth of heteroepitaxial YBa2Cu3O7/La0.67Ca0.33MnO3 superlattices on NdGaO3 and Sr0.7La0.3Al0.65Ta0.35O3 substrates

Heteroepitaxial superlattices of [YBa2Cu3O7(n)/ La0.67Ca0.33MnO3(m)]x, where n and m are the number of YBCO and LCMO monolayers and x the number of bilayer repetitions, have been grown with pulsed laser deposition on NdGaO3 (110) and Sr0.7La0.3Al0.65Ta0.35O3 (LSAT) (001). These substrates are well lattice matched with YBCO and LCMO and, unlike the commonly used SrTiO3, they do not give rise to complex and uncontrolled strain effects due to structural transitions at low temperature. The growth dynamics and the structure have been studied in-situ with reflection high energy electron diffraction (RHEED) and ex-situ with scanning transmission electron microscopy (STEM), x-ray diffraction, and neutron reflectometry. The individual layers are found to be flat and continuous over long lateral distances with sharp and coherent interfaces and with a well-defined thickness of the individual layer. The only visible defects are antiphase boundaries in the YBCO layers that originate from perovskite unit cell height steps at the interfaces with the LCMO layers. We also find that the first YBCO monolayer at the interface with LCMO has an unusual growth dynamics and is lacking the CuO chain layer while the subsequent YBCO layers have the regular Y-123 structure. Accordingly, the CuO2 bilayers at both the LCMO/YBCO and the YBCO/LCMO interfaces are lacking one of their neighboring CuO chain layers and thus half of their hole doping reservoir. Nevertheless, from electric transport measurements on asuperlattice with n=2 we obtain evidence that the interfacial CuO2 bilayers remain conducting and even exhibit the onset of a superconducting transition at very low temperature. Finally, we show from dc magnetization and neutron reflectometry measurements that the LCMO layers are strongly ferromagnetic

Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.Comment: Latex 2e; 25 pages (a4wide); small editorial corrections; one reference adde

Differences in zinc status and the leptin axis in anorexic and recovered adolescents and young adults: a pilot study

Evidence from animal studies suggests that leptin metabolism is associated with zinc (Zn) status. However, research investigating this relationship in adolescents and young adults with anorexia nervosa (AN) is scarce; the present study aims to fill that gap.Serum concentrations of leptin, the soluble leptin receptor (sOB-R) and the free leptin index (FLI) were obtained in healthy control subjects (n=19), acutely ill individuals (n=14) and recovered patients with AN (n=15). Serum Zn concentrations noted in previous research data were also incorporated for all groups.Leptin, FLI and Zn concentrations were higher in recovered subjects with AN when compared with acutely ill AN patients. Remitted patients showed higher sOB-R concentrations but no difference in FLI compared with the control group. Leptin and FLI were lower in the acutely ill patients compared with the control subjects, who showed no differences in Zn concentrations. Zn concentrations were not correlated with leptin, sOB-R or FLI concentrations in any of the three investigated subgroups.The present investigation does not entirely support an association between Zn, Leptin and FLI concentrations in subjects with AN, possibly due to limited statistical power. Further research and replication of the present findings related to the interaction between leptin and Zn is warranted. However, with respect to serum leptin levels the data of the present investigation indicate that acutely ill and remitted patients with AN differ as regards serum leptin concentrations and FLI, which is in line with previous research