Unquenched Numerical Stochastic Perturbation Theory

The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice SU(3), we report on the performance of the current implementation of the algorithm and the status of first computations undertaken.Comment: 3 pages, 3 figures, Lattice2002(algor

Two and three loops computations of renormalization constants for lattice QCD

Renormalization constants can be computed by means of Numerical Stochastic Perturbation Theory to two/three loops in lattice perturbation theory, both in the quenched approximation and in the full (unquenched) theory. As a case of study we report on the computation of renormalization constants of the propagator for Wilson fermions. We present our unquenched (N_f=2) computations and compare the results with non perturbative determinations.Comment: Lattice2004(improv), 3 pages, 4 figure

Numerical Stochastic Perturbation Theory. Convergence and features of the stochastic process. Computations at fixed (Landau) Gauge

Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected fluctuations in the observables and give some idea to reduce them. In the end we show that also computation of quantities at fixed (Landau) Gauge is now possible.Comment: 3 pages. Contributed to 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199

3-d lattice SU(3) free energy to four loops

We report on the perturbative computation of the 3d lattice Yang-Mills free energy to four loops by means of Numerical Stochastic Perturbation Theory. The known first and second orders have been correctly reproduced; the third and fourth order coefficients are new results and the known logarithmic IR divergence in the fourth order has been correctly identified. Progress is being made in switching to the gluon mass IR regularization and the related inclusion of the Faddeev-Popov determinant.Comment: Lattice2004(non-zero), 3 pages, 2 figure

Beta-function, Renormalons and the Mass Term from Perturbative Wilson Loops

Several Wilson loops on several lattice sizes are computed in Perturbation Theory via a stochastic method. Applications include: Renormalons, the Mass Term in Heavy Quark Effective Theory and (possibly) the beta-function.Comment: 3 pages, 1 eps figure. Contributed to 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199

Stochastic Geometry Modeling and Performance Evaluation of mmWave Cellular Communications

In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from experimental data recently reported in the literature. The path-loss model accounts for different distributions for line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying upon a noise-limited approximation for typical millimeter wave network deployments, exact integral expressions for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. Furthermore, it is shown that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.Comment: Presented at 2015 IEEE International Conference on Communications (ICC), London, UK (June 2015). arXiv admin note: substantial text overlap with arXiv:1410.357

Simulating lattice field theories on multiple thimbles

Simulating thimble regularization of lattice field theory can be tricky when more than one thimble is to be taken into account. A couple of years ago we proposed a solution for this problem. More recently this solution proved to be effective in the case of 0+1 dimensional QCD. A few lessons we can learnt, including the role of symmetries and general hints on algorithmic solutions.Comment: 8 pages, 2 figures; Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spai

Renormalization constants for Lattice QCD: new results from Numerical Stochastic Perturbation Theory

By making use of Numerical Stochastic Perturbation Theory (NSPT) we can compute renormalization constants for Lattice QCD to high orders, e.g. three or four loops for quark bilinears. We report on the status of our computations, which provide several results for Wilson quarks and in particular (values and/or ratios of) Z_V, Z_A, Z_S, Z_P. Results are given for various number of flavors (n_f = 0, 2, 3, 4). While we recall the care which is due for the computation of quantities for which an anomalous dimension is in place, we point out that our computational framework is well suited to a variety of other calculations and we briefly discuss the application of NSPT to other regularizations (in particular the Clover action).Comment: 7 pages, talk given at Lattice 2006 (Quark Masses, Gauge Couplings, and Renormalization

Effects of large field cutoffs in scalar and gauge models

We discuss the notion of a large field cutoff for lattice gauge models with compact groups. We propose and compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and ``small-field'' configurations. We show that the correlations between volume average of field size indicators and the behavior of the tail of the distribution are very different in the gauge and scalar cases. We show that the effect of discarding the large field configurations on the plaquette average is very different above, below and near beta=5.6 for a pure SU(3) LGT.Comment: Lattice2004(theory