Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Influence of Constituents on Creep Properties of SiC/SiC Composites

SiC-SiC composites are being considered as potential candidate materials for next generation turbine components such as combustor liners, nozzle vanes and blades because of their low density, high temperature capability, and tailorable mechanical properties. These composites are essentially fabricated by infiltrating matrix into a stacked array of fibers or fiber preform by one or a combination of manufacturing methods such as, Melt Infiltration (MI) of molten silicon metal, Chemical Vapor Infiltration (CVI), Polymer Infiltration and Pyrolysis (PIP). To understand the influence of constituents, the SiC-SiC composites fabricated by MI, CVI, and PIP methods were creep tested in air between 12000 and 14500 degrees Centigrade for up to 500 hours. The failed specimens were analyzed under a scanning electron microscope to assess damage mechanisms. Also, knowing the creep deformation parameters of the fiber and the matrix under the testing conditions, the creep behavior of the composites was modeled and compared with the measured data. The implications of the results on the long term durability of these composites will be discussed

Bound Magnetic Polaron Interactions in Insulating Doped Diluted Magnetic Semiconductors

The magnetic behavior of insulating doped diluted magnetic semiconductors (DMS) is characterized by the interaction of large collective spins known as bound magnetic polarons. Experimental measurements of the susceptibility of these materials have suggested that the polaron-polaron interaction is ferromagnetic, in contrast to the antiferromagnetic carrier-carrier interactions that are characteristic of nonmagnetic semiconductors. To explain this behavior, a model has been developed in which polarons interact via both the standard direct carrier-carrier exchange interaction (due to virtual carrier hopping) and an indirect carrier-ion-carrier exchange interaction (due to the interactions of polarons with magnetic ions in an interstitial region). Using a variational procedure, the optimal values of the model parameters were determined as a function of temperature. At temperatures of interest, the parameters describing polaron-polaron interactions were found to be nearly temperature-independent. For reasonable values of these constant parameters, we find that indirect ferromagnetic interactions can dominate the direct antiferromagnetic interactions and cause the polarons to align. This result supports the experimental evidence for ferromagnetism in insulating doped DMS.Comment: 11 pages, 7 figure

Laparoscopic cholecystectomy at the Aga Khan Hospital, Nairobi

Objective: To evaluate our experience of laparoscopic cholecystectomies at the Aga Khan Hospital, Nairobi over a three-year period from the inception of the technique, and to assess its value and advantages to the patients. Design: A prospective case series study. Setting: The Aga Khan Hospital, Nairobi. Patients: One hundred and thirty five cases operated from February 1996 to April 1999. All patients were subjected to the American method of laparoscopic cholecystectomy, which is described in detail in this paper. Main outcome measures: Clinical presentation, age and sex demographics, average hospital stay, intraoperative and postoperative complications and outcome. Results: There was a female preponderance with a female to male ratio of 5:1. Mean age was forty nine years. Majority of patients suffered from chronic cholecystitis. The conversion rate to an open procedure was five per cent. There were two cases of significant bile leakage which required laparotomy. No mortality was reported in this series. Conclusion: This technique was found to have distinct advantages such as shorter hospital stay, lesser postoperative pain and very good cosmesis. It is a safe procedure if performed by a well trained surgeon

Renormalization group study of the two-dimensional random transverse-field Ising model

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\nu=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\psi=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases

The Lower Critical Dimension of the XY Spin Glass

We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be $d_{c}\approx 3$ rather than four as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition but they are also compatible with the system being at or slightly below its lower critical dimension.Comment: 4 pages, 3 ps figures. Typos have been corrected, one reference has been added and the concluding paragraph has been expanded. To appear in Phys. Rev. Let

Two-component approach for thermodynamic properties in diluted magnetic semiconductors

We examine the feasibility of a simple description of Mn ions in III-V diluted magnetic semiconductors (DMSs) in terms of two species (components), motivated by the expectation that the Mn-hole exchange couplings are widely distributed, expecially for low Mn concentrations. We find, using distributions indicated by recent numerical mean field studies, that the thermodynamic properties (magnetization, susceptibility, and specific heat) cannot be fit by a single coupling as in a homogeneous model, but can be fit well by a two-component model with a temperature dependent number of ``strongly'' and ``weakly'' coupled spins. This suggests that a two-component description may be a minimal model for the interpretation of experimental measurements of thermodynamic quantities in III-V DMS systems.Comment: 10 pages, 9 figures, 1 new figure, substantial revision

Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder

The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.Comment: 5 pp., REVTeX, epsf, 3 eps figs, final version as published, including erratu

Phase Transition in the Three-Dimensional ±J\pm J Ising Spin Glass

We have studied the three-dimensional Ising spin glass with a $\pm J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, $T_c$, with ordering below $T_c$. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, $\nu$, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that $T_c = 0$ or that $T_c$ is finite but with no order below $T_c$. However, from our data, these possibilities seem less likely.Comment: Postscript file compressed using uufiles. The postscript file is also available by anonymous ftp at ftp://chopin.ucsc.edu/pub/sg3d.p