Generalised Shastry-Sutherland Models in three and higher dimensions

We construct Heisenberg anti-ferromagnetic models in arbitrary dimensions that have isotropic valence bond crystals (VBC) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the 3-d case we show that it is possible to have a lattice structure, analogous to that of SrCu_2(BO_3)_2, where the stronger bonds are associated with shorter bond lengths. A dimer mean field theory becomes exact at d -> infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.Comment: Published version; slightly expande

Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time and the inverse occupation time, and show that in many cases disorder modifies the behavior drastically.Comment: Revtex two column 27 pages, 10 figures, 3 table

Black hole mass and variability in quasars

We report on a study that finds a positive correlation between black hole mass and variability amplitude in quasars. Roughly 100 quasars at z<0.75 were selected by matching objects from the QUEST1 Variability Survey with broad-lined objects from the Sloan Digital Sky Survey. Black hole masses were estimated with the virial method using the broad Hbeta line, and variability was characterized from the QUEST1 light curves. The correlation between black hole mass and variability amplitude is significant at the 99% level or better and does not appear to be caused by obvious selection effects inherent to flux-limited samples. It is most evident for rest frame time lags of the order a few months up to the QUEST1 maximum temporal resolution of about 2 years. The correlation between black hole mass and variability amplitude means that the more massive black holes have larger percentage flux variations. Over 2-3 orders of magnitude in black hole mass, the amplitude increases by approximately 0.2 mag. A likely explanation for the correlation is that the more massive black holes are starving and produce larger flux variations because they do not have a steady inflow of gaseous fuel. Assuming that the variability arises from changes in the accretion rate Li & Cao [8] show that flux variations similar to those observed are expected as a consequence of the more massive black holes having cooler accretion disks.Comment: 4 pages, to be published in the proceedings of the "2nd Kolkata conference on observational evidence for black holes in the Universe", Feb 10-15, 2008, Kolkata, Indi

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes

We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n, where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D, is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta T) and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and the one-dimensional random acceleration problem. We also consider `alternating persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure

Phase diagram and hidden order for generalized spin ladders

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the $S=1/2$ chain with competing nn and nnn interactions, the $S=1/2$ chain with alternating exchange and the antiferromagnetic $S=1$ chain. The Majumdar-Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the af $S=1$ chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar-Ghosh points are in the same phase as the af $S=1$ chain.Comment: 23 pages, REVTEX, 7 figure

Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics

We study relaxation processes in spin systems near criticality after a quench from a high-temperature initial state. Special attention is paid to the stage where universal behavior, with increasing order parameter emerges from an early non-universal period. We compare various algorithms, lattice types, and updating schemes and find in each case the same universal behavior at macroscopic times, despite of surprising differences during the early non-universal stages.Comment: 9 pages, 3 figures, RevTeX, submitted to Phys. Rev. Let

Non Markovian persistence in the diluted Ising model at criticality

We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability $\bar{{P}_c}(t)$ of the global magnetization is found to decay algebraically with an exponent $\theta_c$ that we compute analytically in a dimensional expansion in $d=4-\epsilon$. Corrections to Markov process are found to occur already at one loop order and $\theta_c$ is thus a novel exponent characterizing this disordered critical point. Our result is thoroughly compared with Monte Carlo simulations in $d=3$, which also include a measurement of the initial slip exponent. Taking carefully into account corrections to scaling, $\theta_c$ is found to be a universal exponent, independent of the dilution factor $p$ along the critical line at $T_c(p)$, and in good agreement with our one loop calculation.Comment: 7 pages, 4 figure

Surface and interface study of pulsed-laser-deposited off-stoichiometric NiMnSb thin films on Si(100) substrate

We report a detailed study of surface and interface properties of pulsed-laser deposited NiMnSb films on Si (100) substrate as a function of film thickness. As the thickness of films is reduced below 35 nm formation of a porous layer is observed. Porosity in this layer increases with decrease in NiMnSb film thickness. These morphological changes of the ultra thin films are reflected in the interesting transport and magnetic properties of these films. On the other hand, there are no influences of compositional in-homogeneity and surface/interface roughness on the magnetic and transport properties of the films.Comment: 13 pages, 7 figures, Submitted to Phys. Rev.

Interparticle Potential up to Next-to-leading Order for Gravitational, Electrical, and Dilatonic Forces

Long-range forces up to next-to-leading order are computed in the framework of the Einstein-Maxwell-dilaton system by means of a semiclassical approach to gravity. As has been recently shown, this approach is effective if one of the masses under consideration is significantly greater than all the energies involved in the system. Further, we obtain the condition for the equilibrium of charged masses in the system.Comment: 19 pages, 19 figures, RevTeX4.1. Revised version, Title change

Entangled random pure states with orthogonal symmetry: exact results

We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices of entangled random pure states with orthogonal symmetry $(\beta=1)$. The results are valid for arbitrary dimensions $N=2k,M$ of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.Comment: 15 pages, 5 figure