Effective average action in statistical physics and quantum field theory

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.Comment: 34 pages,5 figures,LaTe

A New Gauge for Computing Effective Potentials in Spontaneously Broken Gauge Theories

A new class of renormalizable gauges is introduced that is particularly well suited to compute effective potentials in spontaneously broken gauge theories. It allows one to keep free gauge parameters when computing the effective potential from vacuum graphs or tadpoles without encountering mixed propagators of would-be-Goldstone bosons and longitudinal modes of the gauge field. As an illustrative example several quantities are computed within the Abelian Higgs model, which is renormalized at the two-loop level. The zero temperature effective potential in the new gauge is compared to that in $R_\xi$ gauge at the one-loop level and found to be not only easier to compute but also to have a more convenient analytical structure. To demonstrate renormalizability of the gauge for the non-Abelian case, the renormalization of an SU(2)-Higgs model with completely broken gauge group and of an SO(3)-Higgs model with an unbroken SO(2) subgroup is outlined and renormalization constants are given at the one-loop level.Comment: 24 pages, figures produced by LaTeX, plain LaTeX, THU-93/16. (Completely revised. Essential changes. New stuff added. To appear in Phys.Rev.D.

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small correction

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

CHERCAM: A Cherenkov imager for the CREAM experiment

International audienceThe CREAM experiment (Cosmic Ray Energetics and Mass) is dedicated to the measurement of the energy spectrum of nuclear elements in cosmic rays, over the range 10$^{12}$ to 10$^{15}$ eV. The individual elements separation, which is a key feature of CREAM, requires instruments with strong identification capabilities. A proximity focused type of Cherenkov imager, CHERCAM (CHERenkov CAMera), providing both a good signature of downgoing Z=1 particles and good single element separation through the whole range of nuclear charges [Buénerd et al. 28th ICRC, Tsukuba, OG 1.5, 2003, p. 2157], is under development. After a brief introduction, the main features and the construction status of the CHERCAM are being summarized

Performance of the CREAM calorimeter in accelerator beam test

The CREAM calorimeter, designed to measure the spectra of cosmic-ray nuclei from under 1 TeV to 1000 TeV, is a 20 radiation length (X0) deep sampling calorimeter. The calorimeter is comprised of 20 layers of tungsten interleaved with 20 layers of scintillating fiber ribbons, and is preceded by a pair of graphite interaction targets providing about 0.42 proton interaction lengths (\lambda int). The calorimeter was placed in one of CERN's SPS accelerator beams for calibration and testing. Beams of 150 GeV electrons were used for calibration, and a variety of electron, proton, and nuclear fragment beams were used to test the simulation model of the detector. In this paper we discuss the performance of the calorimeter in the electron beam and compare electron beam data with simulation results.The CREAM calorimeter, designed to measure the spectra of cosmic-ray nuclei from under 1 TeV to 1000 TeV, is a 20 radiation length (X0) deep sampling calorimeter. The calorimeter is comprised of 20 layers of tungsten interleaved with 20 layers of scintillating fiber ribbons, and is preceded by a pair of graphite interaction targets providing about 0.42 proton interaction lengths (\lambda int). The calorimeter was placed in one of CERN's SPS accelerator beams for calibration and testing. Beams of 150 GeV electrons were used for calibration, and a variety of electron, proton, and nuclear fragment beams were used to test the simulation model of the detector. In this paper we discuss the performance of the calorimeter in the electron beam and compare electron beam data with simulation results

A Cherenkov imager for charge measurements of Nuclear Cosmic Rays in the CREAM II instrument

A proximity focusing Cherenkov imager for the charge measurement of nuclear cosmic rays in the CREAM II instrument, called CHERCAM, is under construction. This imager consists of a silica aerogel radiator plane facing a detector plane equipped with standard photomultipliers. The two planes are separated by a minimal ring expansion gap. The Cherenkov light yield is proportional to the squared charge of the detected particle. The expected relative light collection accuracy is in the few percents range. It should lead to single element separation over the range of nuclear charge Z of main interest 1 $leq$ Z $<$\approx$ 26

CHERCAM: the Cherenkov imager of the CREAM experiment, results in Z=1 test beams

International audienceThe CREAM experiment investigates the high energy spectrum of nuclear elements from H to Fe in the cosmic ray flux up to $10^{15}$ eV, with an instrument designed to achieve individual elements separation over the whole mass range. A proximity focused Cherenkov imager, CHERCAM (CHERenkov CAMera), will provide both a good topological signature (Cherenkov ring) for downgoing Z=1 particles, and a charge independent individual element separation through the considered range of nuclear charges. It will be implemented in the forthcoming CREAM flight 3. The contribution reports on the CHERCAM main features and on the preliminary results from in-beam tests at CERN

Expanding non homogeneous configurations of the λϕ4\lambda \phi^4 model

A time dependent variational approach is considered to derive the equations of movement for the $\lambda \phi^4$ model. The temporal evolution of the model is performed numerically in the frame of the Gaussian approximation in a lattice of 1+1 dimensions given non homogeneous initial conditions (like bubbles) for the classical and quantum parts of the field which expands. A schematic model for the initial conditions is presented considering the model at finite fermionic density. The non zero fermionic density may lead either to the restoration of the symmetry or to an even more asymmetric phase. Both kinds of situations are considered as initial conditions and the eventual differences in early time dynamics are discussed. In the early time evolution there is strong energy exchange between the classical and quantum parts of the field as the initial configuration expands. The contribution of the quantum fluctuations is discussed especially in the strong coupling constant limit. The continuum limit is analyzed.Comment: 23 pages (latex) plus thirteen figures in eps file