1,614 research outputs found
Spins coupled to a -Regge lattice in 4d
We study an Ising spin system coupled to a fluctuating four-dimensional
-Regge lattice and compare with the results of the four-dimensional Ising
model on a regular lattice. Particular emphasis is placed on the phase
transition of the spin system and the associated critical exponents. We present
results from finite-size scaling analyses of extensive Monte Carlo simulations
which are consistent with mean-field predictions.Comment: Lattice2001(surfaces), 3 pages, 2 figure
Parallel-tempering cluster algorithm for computer simulations of critical phenomena
In finite-size scaling analyses of Monte Carlo simulations of second-order
phase transitions one often needs an extended temperature range around the
critical point. By combining the parallel tempering algorithm with cluster
updates and an adaptive routine to find the temperature window of interest, we
introduce a flexible and powerful method for systematic investigations of
critical phenomena. As a result, we gain one to two orders of magnitude in the
performance for 2D and 3D Ising models in comparison with the recently proposed
Wang-Landau recursion for cluster algorithms based on the multibondic
algorithm, which is already a great improvement over the standard
multicanonical variant.Comment: pages, 5 figures, and 2 table
Ising spins coupled to a four-dimensional discrete Regge skeleton
Regge calculus is a powerful method to approximate a continuous manifold by a
simplicial lattice, keeping the connectivities of the underlying lattice fixed
and taking the edge lengths as degrees of freedom. The discrete Regge model
employed in this work limits the choice of the link lengths to a finite number.
To get more precise insight into the behavior of the four-dimensional discrete
Regge model, we coupled spins to the fluctuating manifolds. We examined the
phase transition of the spin system and the associated critical exponents. The
results are obtained from finite-size scaling analyses of Monte Carlo
simulations. We find consistency with the mean-field theory of the Ising model
on a static four-dimensional lattice.Comment: 19 pages, 7 figure
Lattice Models of Quantum Gravity
Standard Regge Calculus provides an interesting method to explore quantum
gravity in a non-perturbative fashion but turns out to be a CPU-time demanding
enterprise. One therefore seeks for suitable approximations which retain most
of its universal features. The -Regge model could be such a desired
simplification. Here the quadratic edge lengths of the simplicial complexes
are restricted to only two possible values , with
, in close analogy to the ancestor of all lattice theories, the
Ising model. To test whether this simpler model still contains the essential
qualities of the standard Regge Calculus, we study both models in two
dimensions and determine several observables on the same lattice size. In order
to compare expectation values, e.g. of the average curvature or the Liouville
field susceptibility, we employ in both models the same functional integration
measure. The phase structure is under current investigation using mean field
theory and numerical simulation.Comment: 4 pages, 1 figure
Make life simple: unleash the full power of the parallel tempering algorithm
We introduce a new update scheme to systematically improve the efficiency of
parallel tempering simulations. We show that by adapting the number of sweeps
between replica exchanges to the canonical autocorrelation time, the average
round-trip time of a replica in temperature space can be significantly
decreased. The temperatures are not dynamically adjusted as in previous
attempts but chosen to yield a 50% exchange rate of adjacent replicas. We
illustrate the new algorithm with results for the Ising model in two and the
Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure
Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach
Quantum wires and electromagnetic waveguides possess common features since
their physics is described by the same wave equation. We exploit this analogy
to investigate experimentally with microwave waveguides and theoretically with
the help of an effective potential approach the occurrence of bound states in
sharply bent quantum wires. In particular, we compute the bound states, study
the features of the transition from a bound to an unbound state caused by the
variation of the bending angle and determine the critical bending angles at
which such a transition takes place. The predictions are confirmed by
calculations based on a conventional numerical method as well as experimental
measurements of the spectra and electric field intensity distributions of
electromagnetic waveguides
Football fever: goal distributions and non-Gaussian statistics
Analyzing football score data with statistical techniques, we investigate how the
not purely random, but highly co-operative nature of the game is reflected in
averaged properties such as the probability distributions of scored goals for the
home and away teams. As it turns out, especially the tails of the distributions are
not well described by the Poissonian or binomial model resulting from the
assumption of uncorrelated random events. Instead, a good effective description of
the data is provided by less basic distributions such as the negative binomial one
or the probability densities of extreme value statistics. To understand this
behavior from a microscopical point of view, however, no waiting time problem or
extremal process need be invoked. Instead, modifying the Bernoulli random process
underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to
understand the observed deviation from Gaussian statistics. The phenomenological
distributions used before can be understood as special cases within this framework.
We analyzed historical football score data from many leagues in Europe as well as
from international tournaments, including data from all past tournaments of the “FIFA World
Cup” series, and found the proposed models to be applicable rather universally. In
particular, here we analyze the results of the German women's premier football league
and consider the two separate German men's premier leagues in the East
and West during the cold war times as well as the unified league after 1990 to see how
scoring in football and the component of self-affirmation depend on cultural and
political circumstances
Matrix models and QCD with chemical potential
The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed
Electrically pumped semiconductor laser with low spatial coherence and directional emission
We design and fabricate an on-chip laser source that produces a directional
beam with low spatial coherence. The lasing modes are based on the axial orbit
in a stable cavity and have good directionality. To reduce the spatial
coherence of emission, the number of transverse lasing modes is maximized by
fine-tuning the cavity geometry. Decoherence is reached in a few nanoseconds.
Such rapid decoherence will facilitate applications in ultrafast speckle-free
full-field imaging
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl
- …