Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for $\varphi ^4$-theory and scalar electrodynamics. The Ba{\l}aban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here.Comment: path to figures (in added uu-file) revised, no other changes 33 pages, 3 figures, late

Large-Scale Radio Structure in the Universe: Giant Radio Galaxies

Giant radio galaxies (GRGs), with linear sizes larger than 1 Mpc (H0=50 km/s/Mpc), represent the biggest single objects in the Universe. GRGs are rare among the entire population of radio galaxies (RGs) and their physical evolution is not well understood though for many years they have been of special interest for several reasons. The lobes of radio sources can compress cold gas clumps and trigger star or even dwarf galaxy formation, they can also transport gas from a host galaxy to large distances and seed the IGM with magnetic fields. Since GRGs have about 10 to 100 times larger sizes than normal RGs, their influence on the ambient medium is correspondingly wider and is pronounced on scales comparable to those of clusters of galaxies or larger. Therefore `giants' could play an important role in the process of large-scale structure formation in the Universe. Recently, thanks to the new all sky radio surveys, significant progress in searching for new GRGs has been made.Comment: To appear in Multiwavelength AGN Surveys, ed. R. Maiolino and R. Mujica, Singapore: World Scientific, 2004, 2 page

Multi-Frequency Study of the B3-VLA Sample II. The Database

We present total flux densities of 1049 radio sources in the frequency range from 151 MHz to 10.6 GHz. These sources belong to the B3-VLA sample, which is complete down to 100 mJy at 408 MHz. The data constitute a homogeneous spectral database for a large sample of radio sources, 50 times fainter than the 3C catalogue, and will be used to perform a spectral ageing analysis, which is one of the critical points in understanding the physics and evolution of extragalactic radio sources.Comment: 14 pages, 3 figures, accepted for publication in Astronomy & Astrophysics Supplement Series, gzipped postscript file also available at http://multivac.jb.man.ac.uk:8000/ceres/papers/papers.html or http://gladia.astro.rug.nl:8000/ceres/papers/papers.htm

A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. % This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations.Comment: 3 pages, LaTeX file, contribution to Lattice 9

The spectral-curvature parameter: an alternative tool for the analysis of synchrotron spectra

The so-called Spectral Curvature Parameter(SCP), when plotted versus the high-frequency spectral index ($alpha_{high}$) of synchrotron sources, provides crucial parameters on the continuum spectrum of synchrotron radiation without the more complex modeling of spectral ageing scenarios. An important merit of the SCP-$alpha$ diagram is the enhanced reliability of extracting multiple injection spectra, $alpha_{inj}$. Different from the colour-colour diagram, tracks of different $alpha_{inj}$s, especially when the synchrotron particles are young, exhibit less overlap and less smearing in the SCP-$alpha$ diagram. Three giant radio galaxies(GRGs) and a sample of Compact steep spectrum(CSS) souces are presented. GRGs exhibit asymmetries of their injection spectral indices $alpha_{inj}$ in the SCP-$alpha_{high}$ diagram. The obtained $alpha_{inj}$s and the trends in the sources are cross-checked with the literature and show remarkable confidence. Besides the spectral steepening, spectral flattening is prominent in the radio lobes. The spectral flattening is a clue to efficient re-acceleration processes in the lobes. It implies interaction with the surrounding intergalactic or intra-cluster medium is an important characteristic of GRGs. In the SW lobe of DA240, there is a clear sign of CI and KP/JP bifurcation at the source extremity. This indicates a highly relativistic energy transportation from the core or in situ acceleration in this typical FR I lobe. Our analysis proves, if exists, KP spectra imply the existence of strong $B_{sync}$ field with $B_{sync} > B_{CMB}$. In the CSS sources, our result confirms the CI model and $B_{sync} >> B_{CMB}$. The synchrotron self-absorption is significant in the CSS sample.Comment: to be published in A&

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

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 $S(1.4 \hbox{GHz})=80$mJy is $\simeq 2.2$. 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 $< 30$GHz the amplitude of their power spectrum is expected to be comparable to that of the $E$-mode of the CMB. At higher frequencies, however, the CMB dominates.Comment: 10 pages, A&A in pres

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&