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

Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions

The spontaneous breaking of of translational invariance in non-commutative self-interacting scalar field theory in two dimensions is investigated by effective action techniques. The analysis confirms the existence of the stripe phase, already observed in lattice simulations, due to the non-local nature of the non-commutative dynamics.Comment: 7 pages, 2 figure

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

Bendings of radio jets in BL Lacertae objects I: EVN and MERLIN observations

Several blazars, and BL Lac objects in particular, show a misalignment between the jet orientation on parsec and kiloparsec scales. Some authors (i.e. Conway & Murphy, 1993) have attempted to explain this behaviour invoking helical jets for misalignment angles around 90\degr, showing how in this case there are interesting implications for the understanding of the medium into which the jet is expanding. By comparing sensitive VLA observations (Cassaro et al., 1999) with images available in the literature for the BL Lac objects from the 1-Jy Sample (Stickel et al., 1991), it is clear that there is a wide range of misalignments between the initial jet direction and the kpc-scale jet, when detected. We have carried out VLBI observations of these BL Lac objects, in order to investigate the spatial evolution of the radio jets from few tens to hundreds of mas, and to search for helical jets in this class of sources. We present here the first dataset obtained from EVN+MERLIN observations at 5 GHz for seven objects. From these observations we never have a clear detection of helical jets, we only have a possible signature of their presence in 2 objects. In only one of the sources with a misalignment angle around 90\degr the presence of helical jets can be ruled out. This implies that it is not possible to invoke helical jets to explain the morphology of all the sources showing a misalignment of about 90\degr between the parsec and the kiloparsec scale jets.Comment: 12 pages, 9 figures, latex, accepted by Astronomy & Astrophysic