(Lattice) Propagators and Extraction of Spectral Densities

In this proceeding, we explain a few steps for an alternative extraction of the spectral density of a two-point function (propagator) based on a discrete set of data points. We present a so-called Tikhonov regularization of this particular inverse problem. We test it on 2 cases: lattice 0++} glueball data and mock gluon data.Comment: 8 pages, 4 figures. Proceedings of Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching, Munich, German

The lattice gluon propagator in renormalizable ξ\xi gauges

We study the SU(3) gluon propagator in renormalizable $R_\xi$ gauges implemented on a symmetric lattice with a total volume of (3.25 fm)$^4$ for values of the guage fixing parameter up to $\xi=0.5$. As expected, the longitudinal gluon dressing function stays constant at its tree-level value $\xi$. Similar to the Landau gauge, the transverse $R_\xi$ gauge gluon propagator saturates at a non-vanishing value in the deep infrared for all values of $\xi$ studied. We compare with very recent continuum studies and perform a simple analysis of the found saturation with a dynamically generated effective gluon mass.Comment: 6 pages, 4 figure

From propagators to glueballs in the Gribov-Zwanziger framework

Over the last years, lattice calculations in pure Yang-Mills gauge theory seem to have come more or less to a consensus. The ghost propagator is not enhanced and the gluon propagator is positivity violating, infrared suppressed and non-vanishing at zero momentum. From an analytical point of view, several groups are agreeing with these results. Among them, the refined Gribov-Zwanziger (RGZ) framework also accommodates for these results. The question which rises next is, if our models hold the right form for the propagators, how to extract information on the real physical observables, i.e. the glueballs? How do the operators which represent glueballs look like? We review the current status of this matter within the RGZ framework.Comment: 3 pages, Conference contribution for Confinement IX, Madrid 2010 (30/08-03/09), to appear in American Institute of Physics (AIP

Corrections to Finite Size Scaling in Percolation

A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r=1/2 is estimated as C = 0.876657(45)

Scaling behavior of explosive percolation on the square lattice

Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold with unrestricted bond placement (allowing loops) is found precisely using several different criteria based upon both moments and wrapping probabilities, yielding p_c = 0.526565 +/- 0.000005, consistent with the recent result of Radicchi and Fortunato. The correlation-length exponent nu is found to be close to 1. The qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability P_(infinity) (size of largest cluster), the susceptibility, and of the second moment of finite clusters, where discontinuities appears at the threshold. The critical cluster-size distribution does not follow a consistent power-law for the range of system sizes we study L 2 for larger L.Comment: v2: Updated results in original version with new data; expanded discussion. v3: Resubmitted version. New figures, reference

Gluon and Ghost Dynamics from Lattice QCD

The two point gluon and ghost correlation functions and the three gluon vertex are investigated, in the Landau gauge, using lattice simulations. For the two point functions, we discuss the approach to the continuum limit looking at the dependence on the lattice spacing and volume. The analytical structure of the propagators is also investigated by computing the corresponding spectral functions using an implementation of the Tikhonov regularisation to solve the integral equation. For the three point function we report results when the momentum of one of the gluon lines is set to zero and discuss its implications.Comment: Proceedings of Light Cone 2016, held in Lisbon, September 2016. Minor changes in text. To appear in Few B Sy

Self-Similar Collapse of Scalar Field in Higher Dimensions

This paper constructs continuously self-similar solution of a spherically symmetric gravitational collapse of a scalar field in n dimensions. The qualitative behavior of these solutions is explained, and closed-form answers are provided where possible. Equivalence of scalar field couplings is used to show a way to generalize minimally coupled scalar field solutions to the model with general coupling.Comment: RevTex 3.1, 15 pages, 3 figures; references adde