Overcoming the slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles

We study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that flat-histogram Monte Carlo methods with single-spin flip updates such as the Wang-Landau algorithm or the multicanonical method perform suboptimally in comparison to an unbiased Markovian random walk in energy space. For the d=1, 2, 3 Ising model, the mean first-passage time τ scales with the number of spins N=Ld as τ∝N2Lz. The exponent z is found to decrease as the dimensionality d is increased. In the mean-field limit of infinite dimensions we find that z vanishes up to logarithmic corrections. We then demonstrate how the slowdown characterized by z\u3e0 for finite d can be overcome by two complementary approaches—cluster dynamics in connection with Wang-Landau sampling and the recently developed ensemble optimization technique. Both approaches are found to improve the random walk in energy space so that τ∝N2 up to logarithmic corrections for the d=1, 2 Ising model

Spectral fluctuation characterization of random matrix ensembles through wavelets

A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and supports the Fourier power spectral analysis. It also finds evidence for multi-fractal nature in the atomic spectra. The multi-resolution and localization nature of the discrete wavelets ideally characterizes the fluctuations in these time series, some of which are not stationary.Comment: 7 pages, 2 eps figure

Some constraints on neutral heavy leptons from flavor-conserving decays of the Z boson

Small neutrino masses can arise in some grand unified models or superstring theories. We consider a model with an enhanced fermion sector containing Dirac neutral heavy leptons. The dependence on the mass and mixing parameters of these new fermions is investigated for several measurable quantities. We study the flavor-conserving leptonic decays of the Z boson and universality breaking in these decays. We also consider the W boson mass dependence on neutral heavy lepton parameters.Comment: 20 pages, Revtex 3.0, 6 uuencoded and compressed postscript figures included. Compressed postscript file of paper, including figures, also available by anonymous ftp at ftp://ftp.physics.carleton.ca/pub/theory/gour/ocipc9411.ps.Z . Accepted for publication in Phys. Rev. D

Dynamics of relaxor ferroelectrics

We study a dynamic model of relaxor ferroelectrics based on the spherical random-bond---random-field model and the Langevin equations of motion. The solution to these equations is obtained in the long-time limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and third-order nonlinear susceptibilities $\chi_1(\omega)$ and $\chi_3(\omega)$, respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in $\chi_3(T,\omega)$, which mimics a transition into a glass-like state.Comment: 15 pages, Revtex plus 5 eps figure

Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in FCC Metals

We develop a finite element based dislocation dynamics model to simulate the structure and strength of dislocation junctions in FCC crystals. The model is based on anisotropic elasticity theory supplemented by the explicit inclusion of the separation of perfect dislocations into partial dislocations bounding a stacking fault. We demonstrate that the model reproduces in precise detail the structure of the Lomer-Cottrell lock already obtained from atomistic simulations. In light of this success, we also examine the strength of junctions culminating in a stress-strength diagram which is the locus of points in stress space corresponding to dissolution of the junction.Comment: 9 Pages + 4 Figure

Heavy quark supermultiplet excitations

Lorentz covariant wave functions for meson and baryon supermultiplets are simply derived by boosting $SU(2)_J$ representations corresponding to multiquark systems at rest.Comment: 12 pages (Revtex), UTAS-PHYS-93-4

Compton Scattering in Static and Moving Media. II. System-Frame Solutions for Spherically Symmetric Flows

I study the formation of Comptonization spectra in spherically symmetric, fast moving media in a flat spacetime. I analyze the mathematical character of the moments of the transfer equation in the system-frame and describe a numerical method that provides fast solutions of the time-independent radiative transfer problem that are accurate in both the diffusion and free-streaming regimes. I show that even if the flows are mildly relativistic (V~0.1, where V is the electron bulk velocity in units of the speed of light), terms that are second-order in V alter the emerging spectrum both quantitatively and qualitatively. In particular, terms that are second-order in V produce power-law spectral tails, which are the dominant feature at high energies, and therefore cannot be neglected. I further show that photons from a static source are upscattered by the bulk motion of the medium even if the velocity field does not converge. Finally, I discuss these results in the context of radial accretion onto and outflows from compact objects.Comment: 28 pages, 9 figures; minor changes, to appear in the Astrophysical Journa

Optimized Variables of the Study of Λb\Lambda_b Polarization

The value of the $b$-baryon polarization can be extracted from inclusive data at LEP with better than 10\% precision based on current statistics. We present a new variable by which to measure the polarization, which is the ratio of the average electron energy to the average neutrino energy. This variable is both sensitive to polarization and insensitive to fragmentation uncertainties.Comment: 10 pages (LaTeX), 2 figures, MIT-CTP-2270, CERN-PPE/94-0