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.

Chiral symmetry breaking in the Wegner-Houghton approach

The Wegner-Houghton formulation of the exact renormalization group evolution equation is used in order to study the chiral symmetry breaking of the linear sigma model coupled to an isospin doublet of quarks. A numerical investigation for a particular truncation of the equation which includes the scalar field renormalization function is presented.Comment: 4 pages,4 eps figures. Contribution to CRIS2000, Catania, May 200

Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity

We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of power-law evolution of the scale factor is followed by an accelerated expansion era at late times.Comment: 26 pages, 4 figures. To appear in New Journal of Physic

Quantum Gravity effects near the null black hole singularity

The structure of the Cauchy Horizon singularity of a black hole formed in a generic collapse is studied by means of a renormalization group equation for quantum gravity. It is shown that during the early evolution of the Cauchy Horizon the increase of the mass function is damped when quantum fluctuations of the metric are taken into account.Comment: 15 Pages, one figure. Minor changes in the presentation, to appear on Phys.Rev.

Role of Noise in a Market Model with Stochastic Volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.Comment: 13 pages, 6 figures, Eur. Phys. J. B, in pres

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.

Cosmological Perturbations in Renormalization Group Derived Cosmologies

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $\Lambda$ is presented. A gauge-invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, $G$, and $\Lambda$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $\Lambda$ vary according to renormalization group equations in the vicinity of a fixed point.Comment: 22 pages, revtex, subeqn.sty, to appear on IJMP

Prosperare al di là del merito: il senso della nemesis in Aristotele tra giustizia distributiva e giustizia correttiva

L’articolo prende in esame quella particolare forma di indignazione che Aristotele indica, nel secondo libro della Retorica, con l’infinito sostantivato to nemesan, derivato dal termine nemesis. Si tratta della reazione che si genera in un animo nobile contro chi prospera al di là del merito. Il sostantivo e i suoi derivati risultano poco usati in età classica e ricorre più frequentemente nell’epica omerica e in Esiodo. Aristotele sembra recuperarlo proprio dalla tradizione poetica arcaica, assegnandogli un ruolo nella sua riflessione sulla giustizia e in particolare nella differenza tra la forma distributiva e quella correttiva. Egli individua così in questa forma di indignazione, un’emozione da coltivare e sollecitare in quei giudici che, come accadeva nell’Atene classica, erano chiamati a formulare una sentenza, non solo sulla base della legge ma anche secondo un principio di equità.The article examines a particular form of indignation indicated by Aristotle, in the second book of the Rhetoric, with the infinitive to nemesan, derived from the noun nemesis. It describes the reaction of a noble mind towards people who prosper beyond merit. The noun and its derivatives are scarcely used in the classical age, but occur more frequently in the Homeric epics and in Hesiod. Aristotle retrieves them from the archaic poetic tradition and uses them in his general reflection about justice. He identifies nemesis as a useful emotion to be cultivated in the judges acting in contexts where they were called upon to formulate a judgement, not only according to the law but also following a principle of equity