Polymeric Phase of Simplicial Quantum Gravity

We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true in 3-dimensions.Comment: 6 pages, revte

Point processes and stochastic displacement fields

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. A particular attention is devoted to the kind of large scale correlations that can be introduced by the displacement field, and to the realizability of arbitrary ``superhomogeneous'' point processes.Comment: 17 pages, 7 figure

Scale invariant forces in 1d shuffled lattices

In this paper we present a detailed and exact study of the probability density function $P(F)$ of the total force $F$ acting on a point particle belonging to a perturbed lattice of identical point sources of a power law pair interaction. The main results concern the large $F$ tail of $P(F)$ for which two cases are mainly distinguished: (i) Gaussian-like fast decreasing $P(F)$ for lattice with perturbations forbidding any pair of particles to be found arbitrarily close to one each other; (ii) L\'evy-like power law decreasing $P(F)$ when this possibility is instead permitted. It is important to note that in the second case the exponent of the power law tail of $P(F)$ is the same for all perturbation (apart from very singular cases), and is in an one to one correspondence with the exponent characterizing the behavior of the pair interaction with the distance between the two particles.Comment: 10 pages, revtex4 forma

Chemical etching of a disordered solid: from experiments to field theory

We present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explain different experimental results showing that the corrosion stops spontaneously in a situation in which the concentration of the etchant is still finite while the corrosion surface develops clear fractal features. We show that these properties are strictly related to the percolation theory, and in particular to its behavior around the critical point. This task is accomplished both by a direct analysis in terms of a self-organized version of the Gradient Percolation model and by field theoretical arguments.Comment: 7 pages, 3 figure

A radiatively improved fermiophobic Higgs boson scenario

The naive fermiophobic scenario is unstable under radiative corrections, due to the chiral-symmetry breaking induced by fermion mass terms. In a recent study, the problem of including the radiative corrections has been tackled via an effective field theory approach. The renormalized Yukawa couplings are assumed to vanish at a high energy scale $\Lambda$, and their values at the electroweak scale are computed via modified Renormalization Group Equations. We show that, in case a fermiophobic Higgs scenario shows up at the LHC, a linear collider program will be needed to accurately measure the radiative Yukawa structure, and consequently constrain the $\Lambda$ scale.Comment: 7 pages, 3 figures, Proceedings of the 2011 International Workshop on Future Linear Colliders (LCWS11), Granada (Spain), 26-30 September 201

Voronoi and Voids Statistics for Super-homogeneous Point Processes

We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and in jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluctuations and correlations of the associated Voronoi cells. We derive exact results for the complete joint statistics of the size of two Voronoi cells. We also provide a sum rule that the correlation matrix for the Voronoi cells must obey in any space dimension. In contrast to the conventional picture of super-homogeneous systems, we show that infinitely large Voronoi cells or voids can exist in super-homogeneous point processes in any dimension. We also present two heuristic conditions to identify and classify any super-homogeneous point process in terms of the asymptotic behavior of the void size distribution.Comment: 27 pages, and 4 figure

Clustering and coalescence from multiplicative noise: the Kraichnan ensemble

We study the dynamics of the two-point statistics of the Kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions. The fundamental equation of this problem consists in the Fokker-Planck equation for the two-point correlation function of the density of particles performing spatially correlated Brownian motions with scale invariant correlations. This problem is equivalent to the stochastic motion of an effective particle driven by a generic multiplicative noise. In this paper we propose an alternative and more intuitive approach to the problem than the original one leading to the same conclusions. The general features of this new approach make possible to fit it to other more complex contexts.Comment: IOP-LaTeX, 17 pages J. Phys. A: Theor. Mat. 2008 in pres