Jürgen Engels

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N-tau = 4, 6 and 8 and spatial extent N-sigma = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T-c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N, = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32(4) lattices to fix the temperature scale. An extrapolation to the continuum limit yields T-c/root sigma = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension, These observables suggest that the temperature dependent running coupling remains large even at T similar or equal to 5T(c). For the spatial string tension we find root sigma(s)/T = 0.566(13)g(2)(T) with g(2)(5T(c)) similar or equal to 1.5.

Gauge field thermodynamics for the SU(2) Yang-Mills system

After reviewing the euclidean formulation of the thermodynamics for quantum spin systems, we develop the corresponding formalism for SU(N) gauge fields on the lattice. The results are then evaluated for the SU(2) system, using Monte Carlo simulation on lattices of (space × temperature) size 103 × 2,3,4,5. At high temperature, the system exhibits Stefan-Boltzmann behaviour, with three gluonic colour degrees of freedom. At Tc ≈ 43ΛL (215 MeV), the transition to “hadronic” behaviour occurs, signalled by a sharp peak in the specific heat. From the behaviour below the deconfinement transition (T<Tc), we obtain mG ≈ 200ΛL (1000 MeV) for the mass of the lowest gluonium state (glueball).

High temperature SU(2) gluon matter of the lattice

We calculate by Monte Carlo simulation on the lattice the energy density [epsilon] of an SU(2) Yang-Mills system at finite physical temperature. First, we study the high temperature form of [epsilon], showing that the conventional euclidean lattice formulation converges to the parameter-free Stefan-Boltzmann limit of a free gluon gas in the continuum. Secondly, we show that the specific heat of gluon matter exhibits a sharp peak at the transition point from the confined phase to the color-screened gluon gas. The resulting transition temperature is found to be 210 ± 10 MeV.

Non-perturbative thermodynamics of SU (N) gauge theories

Abstract The pressure near the deconfinement transition as determined up to now in lattice gauge theories shows unphysical behaviour: it can become negative and may in SU (3) even have a gap at the transition. This has been attributed to the use of only perturbatively known derivatives of coupling constants. We propose a method to evaluate the pressure, which works without these derivatives, and is valid on large lattices. In SU (2) we study the finite-volume effects and show that for lattices with spatial extent N σ ⪆15 these effects are negligible. In SU (3) we then obtain a positive and continuous pressure. The influence of non-perturbative corrections to the β-function on the energy density are investigated and found to be important, in particular for the latent heat.

EQUATION OF STATE FOR THE SU(3) GAUGE-THEORY

By investigating the SU(3) gauge theory thermodynamics on lattices of various sizes we can control finite lattice cutoff effects. We calculate the pressure and energy density on lattices with temporal extent {ital N}{sub {tau}}=4, 6, and 8 and spatial extent {ital N}{sub {sigma}}=16 and 32, and extrapolate to the continuum limit. We find a deviation from ideal gas behavior of (15--20)%, even at temperatures as high as {ital T}{similar_to}3{ital T}{sub {ital c}}. A calculation of the critical temperature for {ital N}{sub {tau}}=8 and 12 and the string tension for {ital N}{sub {tau}}=32 is performed to fix the temperature scale, yielding {ital T}{sub {ital c}}/{radical}{sigma}=0.629(3) in the continuum limit. {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}.

Finite size effects in euclidean lattice thermodynamics for non-interacting Bose and Fermi systems

In the Monte Carlo simulation of QCD, the euclidean form of the partition function is evaluated on a finite lattice. We use this method to calculate the partition function for non-interacting Bose and Fermi fields. Here the expressions on the lattice can be evaluated in closed form and the continuum limit is well-known; this provides us with a measure for finite lattice size effects in such approaches.

THE ORDER OF THE DECONFINEMENT TRANSITION IN SU(3) YANG-MILLS THEORY

We study the finite temperature deconfinement transition in SU(3) Yang-Mills theory, using a high statistics Monte Carlo evaluation on a 83 × 3 lattice. It is shown to be of first order: at the critical temperature, there is a clear two-state signal; above and below, we have hysteresis behaviour.

The latent heat of deconfinement in SU(3) Yang-Mills theory

Abstract We calculate the latent heat of deconfinement in SU(3) Yang-Mills theory from the difference in energy density between the deconfined and the confined phases at the critical temperature Tc. The calculation is based on a high statistics Monte Carlo evaluation using lattices with 83 and 103 spatial sites and 2, 3 and 4 temperature sites. Both Tc and the latent heat Δϵ are shown to satisfy scaling. We find Tc = 208 ± 20 MeV, Δϵ/Tc4 = 3.75 ± 0.25; the latter is in ac cord with bag model arguments.

Scaling properties of the energy density in SU(2) lattice gauge theory

Abstract The lattice data for the energy density of SU(2) gauge theory are calculated with non-perturbative derivatives of the coupling constants. These derivatives are obtained from two sources: (i) a parametrization of the non-perturbative beta function in accord with the measured critical temperature and Δβ-values and (ii) a non-perturbative calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near Tc. It is shown that at the critical temperature the energy density is scaling as a function of VT3 with the corresponding 3D Ising model critical exponents. The value of ϵ(T c ) T c 4 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 ≈ 2 it has reached only about 70% of the limit.

Symmetric Hadron Pairs at Large Transverse Momenta as a Test of Hard Scattering Models

The inclusive cross section of hadron pairs produced back-to-back with large transverse momenta is examined in the parton model. It is shown quantitatively that this cross section is determined directly by the hard scattering subprocesses, without being influenced by the internal momentum of the constituents, even for transverse momenta of the order of 2–3 GeV/c. The predictions of the phenomenological quark-quark scattering model and of the quantum chromodynamics model for the back-to-back cross section are compared with recent Fermi-lab data. Predictions are made for the corresponding cross section at ISR-energies.