Magnetic component of Yang-Mills plasma

Confinement in non-Abelian gauge theories is commonly ascribed to percolation of magnetic monopoles, or strings in the vacuum. At the deconfinement phase transition the condensed magnetic degrees of freedom are released into gluon plasma as thermal magnetic monopoles. We point out that within the percolation picture lattice simulations can be used to estimate the monopole content of the gluon plasma. We show that right above the critical temperature the monopole density remains a constant function of temperature, as for a liquid, and then grows, like for a gas.Comment: 4 pages, no figures; replaced to match published versio

High energy parton-parton amplitudes from lattice QCD and the stochastic vacuum model

Making use of the gluon gauge-invariant two-point correlation function, recently determined by numerical simulation on the lattice in the quenched approximation and the stochastic vacuum model, we calculate the elementary (parton-parton) amplitudes in both impact-parameter and momentum transfer spaces. The results are compared with those obtained from the Kr\"{a}mer and Dosch ansatz for the correlators. Our main conclusion is that the divergences in the correlations functions suggested by the lattice calculations do not affect substantially the elementary amplitudes. Phenomenological and semiempirical information presently available on elementary amplitudes is also referred to and is critically discussed in connection with some theoretical issues.Comment: Text with 11 pages in LaTeX (twocolumn form), 10 figures in PostScript (psfig.tex used). Replaced with changes, Fig.1 modified, two references added, some points clarified, various typos corrected. Version to appear in Phys. Rev.

Planar Drawings of Fixed-Mobile Bigraphs

A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of "layered" 1-bend drawings

The 2-dimensional non-linear sigma-model on a random latice

The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations, we calculate the mass gap for $n=3, 4$ and 8, analysing the asymptotic scaling of the data and computing the ratio of Lambda parameters $\Lambda_{\rm random}/\Lambda_{\rm regular}$. These ratios are in agreement with previous semi-analytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.Comment: REVTeX file, 23 pages. 13 postscript figures in a separate compressed tar fil

Non-Perturbative Scales in Soft Hadronic Collisions at High Energies

We investigate the role of nonperturbative quark-gluon dynamics in soft high energy processes. In order to reproduce differential and total cross sections for elastic proton-proton and proton-antiproton-scattering at high energy and small momentum transfer it turns out that we need two scales, the gluonic correlation length and a confinement scale. We find a small gluonic correlation length, a = 0.2 fm, in accordance with recent lattice QCD results.Comment: 8 pages,latex, 2 figures uuencode

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Asymptotic Energy Dependence of Hadronic Total Cross Sections from Lattice QCD

The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, allows to investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD. In this paper we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind B log^2 s for hadronic total cross sections.Comment: Revised and extended version; 29 pages, 4 figure