Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table

The phase transitions in 2D Z(N) vector models for N>4

We investigate both analytically and numerically the renormalization group equations in 2D Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index \nu\ is computed. For N=7, 17 the critical points are located by Monte Carlo simulations and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.Comment: 19 pages, 8 figures, 10 tables; version to appear on Phys. Rev.

Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our determination of the infinite volume critical point on the lattice with N_t=8 differs substantially from the pseudo-critical coupling at L=32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index $\nu$ computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large deviation from the expected universal value. The possible reasons of such behavior are discussed in details.Comment: 15 pages, 7 figures; version accepted for publication on J. Stat. Mech

Phase transitions in strongly coupled 3d Z(N) lattice gauge theories at finite temperature

We perform an analytical and numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4 exploiting equivalence of these models with a generalized version of the two-dimensional vector Potts models in the limit of vanishing spatial coupling. In this limit the Polyakov loops play the role of Z(N) spins. The effective couplings of these two-dimensional spin models are calculated explicitly. It is argued that the effective spin models have two phase transitions of BKT type. This is confirmed by large-scale Monte Carlo simulations. Using a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the helicity modulus, the average action and the specific heat. A scaling formula for the critical points with N is proposed.Comment: 28 pages, 12 figures, 12 tables; version to appear on Phys. Rev.

Assessment of the impact of chemical pollution of ferrous metallurgy enterprises on forests using satellite photographs

The considered operating ferrous metallurgy enterprise uses three different technological modes of steel smelting, each of which is characterized by an individual composition of the ingredients of chemical pollutant emissions into the atmosphere affecting the state of the forest areas around this enterprise. Based on the decoding of satellite pixel photographs of forest areas, the technological mode with the least impact on forest areas was determined. It corresponds to the condition of the minimum area of ecological zones around the ferrous metallurgy enterprise. The authors propose an assessment of the impact of chemical pollution of ferrous metallurgy enterprises on forests in the form of areas of ecological zones of the state of forest vegetation and the volume of biomass in its various parts. The mosaic of ecological zones of forest areas is determined from their satellite pixel photographs using an original algorithm of "controlled cluster analysis". The main recommendation for ferrous metallurgy enterprises to choose one of several alternative technological modes is as follows: the choice of technological mode should be based on a comparison of sizes of the areas of ecological zones. In this case, the technological mode with the smallest dimensions of the area is selected. Assessment of the damage caused by the chemical pollution of the plant to forest areas was determined by the area of ecological zones and the volume of biomass loss in forest areas in comparison with the background areas. The boundaries of ecological zones can be determined according to the "dose-effect" dependencies typical for the considered region

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87