Block Spin Effective Action for Polyakov Loops in 4D SU(2) LGT

Using a variant of the IMCRG method of Gupta and Cordery, we explicitly compute majority rule block spin effective actions for the signs of the Polyakov loops in 4D SU(2) finite temperature lattice gauge theories. To the best of our knowledge, this is the first attempt to compute numerically effective actions for the Polyakov loop degrees of freedom in 4D SU(2). The most important observations are: 1. The renormalization group flow at the deconfinement transition can be nicely matched with the flow of the 3D Ising model, thus confirming the Svetitsky-Yaffe conjecture. 2. The IMCRG simulations of the FT SU(2) model have strongly reduced critical slowing down.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3 figures, uses espcrc2.sty, epsfig.st

Non-perturbative determination of anisotropy coefficients in lattice gauge theories

We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients), which are required in an evaluation of thermodynamic quantities from numerical simulations on the lattice. Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We test the method for the cases of SU(2) and SU(3) gauge theories at the deconfining transition point on lattices with the lattice size in the time direction $N_t=4$ -- 6. In both cases, there is a clear discrepancy between our results and perturbative values. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved: we obtain $\Delta p/T^4 = 0.001(15)$ and $-0.003(17)$ on $N_t=4$ and 6 lattices, respectively.Comment: 24pages,7figures,5table

Non-perturbative determination of anisotropy coefficients and pressure gap at the deconfining transition of QCD

We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients). Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We determine the anisotropy coefficients for the cases of SU(2) and SU(3) gauge theories. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved.Comment: LATTICE98(hightemp

Book review: Handbook of the Media in Asia

Gunaratne, Shelton (ed) (2000) Handbook of the Media in Asia, Sage Publications, New Delhi, 722 pp. ISBN 0-7619-9427-0 Reviewed by Kevin Engels To describe this book as a ‘Handbook’ is an understatement. It is a comprehensive survey and outline of the media throughout 25 countries of Asia, from Pakistan in the West to Mongolia in the Northeast and the Philippines in the Southeast. Not only are the major nations and economies covered but countries such as Maldives and Macau are included

Scaling Properties of the Energy Density in SU(2) Lattice Gauge Theory

The lattice data for the energy density of $SU(2)$ gauge theory are calculated with \nop~derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the \nop~beta function in accord with the measured critical temperature and $\Delta\beta-$values and ii) a \nop~calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near $T_c$. It is shown that at the critical temperature the energy density is scaling as a function of $VT^3$ with the corresponding $3d$ Ising model critical exponents. The value of $\epsilon(T_c)/T^4_c$ in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at $T/T_c \approx 2$ it has reached only about $70\%$ of the limit.Comment: 15 pages + 9 figures, BI-TP 94/3

On a possibility of adjoint colored states condensation at finite temperatures in lattice gauge model

Cooled down and diluted quark-gluon matter is considered. A possibility of condensation of multiquark clusters with zero N-alities is discussed.Comment: Lattice99:Finite Temperature and Density sessio

Finite temperature QCD

Engels J. Finite temperature QCD. In: Bleuler K, ed. Quarks and Nuclear Structure: Proceedings of the 3rd Klaus Erkelenz Symposium held at Bad Honnef, June 13–16,1983. Lecture Notes in Physics, 197. Berlin [u.a.]: Springer; 1984: 39-56.A review of finite temperature lattice calculations for quantum chromodynamics is given. We show how the thermodynamic quantities can be evaluated by Monte Carlo methods, once finite temperature field theory has been formulated on a lattice. The existing results for chemical potential zero and in quenched approximation are discussed. They exhibit a clear first order transition for SU(3) lattice QCD and probably a second order transition for SU(2) lattice QCD. The chiral and deconfinement transitions are coinciding in the quenched approximation

Critical behaviour and scaling functions of the three-dimensional O(6) model

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices within the critical region at zero magnetic field, as well as at finite magnetic field on the critical isotherm and for several fixed couplings in the broken and the symmetric phase. We obtain from the Binder cumulant at vanishing magnetic field the critical coupling J_c=1.42865(3). The universal value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and \nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore, we verify predicted effects induced by massless Goldstone modes in the broken phase. The results are well described by the perturbative form of the model's equation of state. Our O(6)-result is compared to the corresponding Ising, O(2) and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour of the magnetisation on the pseudocritical line.Comment: 13 pages, 20 figures, REVTEX, fixed an error in the determination of R_\chi and changed the corresponding line in figure 13

Critical behavior of 3D SU(2) gauge theory at finite temperature: exact results from universality

We show that universality arguments, namely the Svetitsky-Yaffe conjecture, allow one to obtain exact results on the critical behavior of 3D SU(2) gauge theory at the finite temperature deconfinement transition,through a mapping into the 2D Ising model. In particular, we consider the finite-size scaling behavior of the plaquette operator, which can be mapped into the energy operator of the 2D Ising model. We obtain exact predictions for the dependence of the plaquette expectation value on the size and shape of the lattice and we compare them to Monte Carlo results, finding complete agreement. We discuss the application of this method to the computation of more general correlators of the plaquette operator at criticality, and its relevance to the study of the color flux tube structure.Comment: 10 pages, LaTeX file + 3 eps figure