5,168 research outputs found
Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model
Generalized universality, as recently proposed, postulates a universal
non-Gaussian form of the probability density function (PDF) of certain global
observables for a wide class of highly correlated systems of finite volume N.
Studying the 2D XY -model, we link its validity to renormalization group
properties. It would be valid if there were a single dimension 0 operator, but
the actual existence of several such operators leads to T-dependent
corrections. The PDF is the Fourier transform of the partition function Z(q) of
an auxiliary theory which differs by a dimension 0 perturbation with a very
small imaginary coefficient iq/N from a theory which is asymptotically free in
the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).Comment: To be published in Phys. Rev.
Vortices and confinement at weak coupling
We discuss the physical picture of thick vortices as the mechanism
responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory.
By introducing appropriate variables on the lattice we distinguish between
thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop
boundaries. We present numerical lattice simulation results that demonstrate
that the full SU(2) string tension at weak coupling arises from the presence of
vortices linked to the Wilson loop. Conversely, excluding linked vortices
eliminates the confining potential. The numerical results are stable under
alternate choice of lattice action as well as a smoothing procedure which
removes short distance fluctuations while preserving long distance physics.Comment: 21 pages, LaTe
Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo
We analyze the kinematics of multigrid Monte Carlo algorithms by
investigating acceptance rates for nonlocal Metropolis updates. With the help
of a simple criterion we can decide whether or not a multigrid algorithm will
have a chance to overcome critial slowing down for a given model. Our method is
introduced in the context of spin models. A multigrid Monte Carlo procedure for
nonabelian lattice gauge theory is described, and its kinematics is analyzed in
detail.Comment: 7 pages, no figures, (talk at LATTICE 92 in Amsterdam
Effective Field Theories
Effective field theories encode the predictions of a quantum field theory at
low energy. The effective theory has a fairly low ultraviolet cutoff. As a
result, loop corrections are small, at least if the effective action contains a
term which is quadratic in the fields, and physical predictions can be read
straight from the effective Lagrangean.
Methods will be discussed how to compute an effective low energy action from
a given fundamental action, either analytically or numerically, or by a
combination of both methods. Basically,the idea is to integrate out the high
frequency components of fields. This requires the choice of a "blockspin",i.e.
the specification of a low frequency field as a function of the fundamental
fields. These blockspins will be the fields of the effective field theory. The
blockspin need not be a field of the same type as one of the fundamental
fields, and it may be composite. Special features of blockspins in nonabelian
gauge theories will be discussed in some detail.
In analytical work and in multigrid updating schemes one needs interpolation
kernels \A from coarse to fine grid in addition to the averaging kernels
which determines the blockspin. A neural net strategy for finding optimal
kernels is presented.
Numerical methods are applicable to obtain actions of effective theories on
lattices of finite volume. The constraint effective potential) is of particular
interest. In a Higgs model it yields the free energy, considered as a function
of a gauge covariant magnetization. Its shape determines the phase structure of
the theory. Its loop expansion with and without gauge fields can be used to
determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps
format
The giant radio galaxy 8C0821+695 and its environment
We present new VLA and Effelsberg observations of the radio galaxy
8C0821+695. We have obtained detailed images in total intensity and
polarization of this 2 Mpc sized giant. The magnetic field has a configuration
predominantly parallel to the source main axis. We observe Faraday rotation at
low frequencies, most probably produced by an ionized medium external to the
radio source. The spectral index distribution is that typical of FR II radio
galaxies, with spectral indices gradually steepening from the source extremes
towards the core. Modeling the spectrum in the lobes using standard synchrotron
loss models yields the spectral age of the source and the mean velocity of the
jet-head with respect to the lobe material. The existence of a possible
backflow in the lobe is considered to relate spectral with dynamical
determinations of the age and the velocity with respect to the external medium.
Through a very simple model, we obtain a physical characterization of the jets
and the external medium in which the radio galaxy expands. The results in
8C0821+695 are consistent with a relativistic jet nourishing the lobes which
expand in a hot, low density halo. We infer a deceleration of the source
expansion velocity which we explain through a progressive increase in the
hot-spot size.Comment: 11 pages; 8 figures; accepted in A&
Dual variables for the SU(2) lattice gauge theory at finite temperature
We study the three-dimensional SU(2) lattice gauge theory at finite
temperature using an observable which is dual to the Wilson line. This
observable displays a behaviour which is the reverse of that seen for the
Wilson line. It is non-zero in the confined phase and becomes zero in the
deconfined phase. At large distances, it's correlation function falls off
exponentially in the deconfined phase and remains non-zero in the confined
phase. The dual variable is non-local and has a string attached to it which
creates a Z(2) interface in the system. It's correlation function measures the
string tension between oppositely oriented Z(2) domains. The construction of
this variable can also be made in the four-dimensional theory where it measures
the surface tension between oppositely oriented Z(2) domains.Comment: 13 pages, LaTeX, 4 figures are included in the latex fil
Polarization Properties of Extragalactic Radio Sources and Their Contribution to Microwave Polarization Fluctuations
We investigate the statistical properties of the polarized emission of
extragalactic radio sources and estimate their contribution to the power
spectrum of polarization fluctuations in the microwave region. The basic
ingredients of our analysis are the NVSS polarization data, the multifrequency
study of polarization properties of the B3-VLA sample (Mack et al. 2002) which
has allowed us to quantify Faraday depolarization effects, and the 15 GHz
survey by Taylor et al. (2001), which has provided strong constraints on the
high-frequency spectral indices of sources. The polarization degree of both
steep- and flat-spectrum at 1.4 GHz is found to be anti-correlated with the
flux density. The median polarization degree at 1.4 GHz of both steep- and
flat-spectrum sources brighter than mJy is . The data by Mack et al. (2002) indicate a substantial mean Faraday
depolarization at 1.4 GHz for steep spectrum sources, while the depolarization
is undetermined for most flat/inverted-spectrum sources. Exploiting this
complex of information we have estimated the power spectrum of polarization
fluctuations due to extragalactic radio sources at microwave frequencies. We
confirm that extragalactic sources are expected to be the main contaminant of
Cosmic Microwave Background (CMB) polarization maps on small angular scales. At
frequencies GHz the amplitude of their power spectrum is expected to be
comparable to that of the -mode of the CMB. At higher frequencies, however,
the CMB dominates.Comment: 10 pages, A&A in pres
A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions
In d=3 SU(N) gauge theory, we study a scalar field theory model of center
vortices that furnishes an approach to the determination of so-called k-string
tensions. This model is constructed from string-like quantum solitons
introduced previously, and exploits the well-known relation between string
partition functions and scalar field theories in d=3. Center vortices
corresponding to magnetic flux J (in units of 2\pi /N) are composites of J
elementary J=1 constituent vortices that come in N-1 types, with repulsion
between like constituents and attraction between unlike constituents. The
scalar field theory involves N scalar fields \phi_i (one of which is
eliminated) that can merge, dissociate, and recombine while conserving flux mod
N. The properties of these fields are deduced directly from the corresponding
gauge-theory quantum solitons. Every vacuum Feynman graph of the theory
corresponds to a real-space configuration of center vortices. We study
qualitatively the problem of k-string tensions at large N, whose solution is
far from obvious in center-vortex language. We construct a simplified dynamical
picture of constituent-vortex merging, dissociation, and recombination, which
allows in principle for the determination of vortex areal densities and
k-string tensions. This picture involves point-like "molecules" (cross-sections
of center vortices) made of constituent "atoms" that combine and disassociate
dynamically in a d=2 test plane . The vortices evolve in a Euclidean "time"
which is the location of the test plane along an axis perpendicular to the
plane. A simple approximation to the molecular dynamics is compatible with
k-string tensions that are linear in k for k<< N, as naively expected.Comment: 21 pages; RevTeX4; 4 .eps figure
- âŠ