Towards an accurate determination of the critical exponents with the Renormalization Group flow equations

The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion generates a model dependence in the determination of the universal quantities. We derive new nonperturbative flow equations for the one-component, $Z_2$ symmetric scalar field to the next-to-leading order of the derivative expansion by means of a class of proper time regulators. The critical exponents $\eta$, $\nu$ and $\omega$ for the Wilson-Fisher fixed point are computed by numerical integration of the flow equations, without resorting to polynomial truncations. We show that by reducing the width of the cut-off employed, the critical exponents become rapidly insensitive to the cut-off width and their values are in good agreement with the results of entirely different approaches.Comment: minor changes, added referencecs, to appear on Phys. Lett.

Ising exponents from the functional renormalisation group

We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross-correlations of scaling exponents, and their dependence on dimensionality. We find a very good numerical convergence of the derivative expansion, also in comparison with earlier findings. Evaluating the data from all functional renormalisation group studies to date, we estimate the systematic error which is found to be small and in good agreement with findings from Monte Carlo simulations, \epsilon-expansion techniques, and resummed perturbation theory.Comment: 24 pages, 3 figures, 7 table

Scaling of variables and the relation between noncommutative parameters in Noncommutative Quantum Mechanics

We consider Noncommutative Quantum Mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.Comment: Revtex4, 4 pages; version to match the published on

Renormalization-Group flow for the field strength in scalar self-interacting theories

We consider the Renormalization-Group coupled equations for the effective potential V(\phi) and the field strength Z(\phi) in the spontaneously broken phase as a function of the infrared cutoff momentum k. In the k \to 0 limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(\phi), indicates a sharp peaking of Z(\phi) close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.Comment: 10 pages, 3 Figures, version accepted for publication in Phys. Lett.

Comment on "Feynman Effective Classical Potential in the Schrodinger Formulation"

We comment on the paper "Feynman Effective Classical Potential in the Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the results in this paper about the time evolution of a wave packet in a double well potential can be properly explained by resorting to a variational principle for the effective action. A way to improve on these results is also discussed.Comment: 1 page, 2eps figures, Revte

On the Vacuum Cherenkov Radiation in Noncommutative Electrodynamics and the Elusive Effects of Lorentz Violation

We show that in the framework of noncommutative classical electrodynamics Cherenkov radiation is permitted in vacuum and we explicitly compute its spectrum at first order in the noncommutative parameter. We discuss the phenomenological impact of the merge of this new analysis with the old results of the substantial modification to the spectrum of the synchrotron radiation obtained in P.Castorina, A.Iorio and D.Zappala, Phys. Rev. D 69 (2004)065008. We propose to consider the pulsars' radiation spectrum - due to its very strong magnetic field - to investigate these Lorentz violating effects in astrophysical phenomena.Comment: 6 pgs, latex file; published versio

Measurements of the First RF Prototype of the SPIRAL2 Single Bunch Selector

WEPD062International audienceThe single bunch selector of the Spiral2 driver uses 100 ­ travelling wave electrodes driven by fast pulse generators. A 2.5 kV, 1 kW feed-through and a vacuum chamber housing the water cooled electrodes have been designed and built. The paper reviews the whole design and reports the results of first RF and power measurements