Jochen Fingberg

Scaling and Asymptotic Scaling in the SU(2) Gauge Theory

Abstract We determine the critical couplings for the deconfinement phase transition in SU(2) gauge theory on Nτ × Nσ3 lattices with Nτ = 8 and 16 and Nσ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio Tc/√σ in the entire coupling regime s = 2.30−2.75, while the individual quantities still exhibit large scaling violations. We find Tc/√σ = 0.69(2). We also discuss in detail the extrapolation of T c /Λ MS and √σ/Λ MS to the continuum limit. Our result, which is consistent with the above ratio, is T c /Λ MS =1.23(11) and √σ/Λ MS =1.79(12) . We also comment upon corresponding results for SU(3) gauge theory and four-flavour QCD.

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.

Spatial string tension in the deconfined phase of (3+1)-dimensional SU(2) gauge theory

We present results of a detailed investigation of the temperature dependence of the spatial string tension in SU(2) gauge theory. We show, for the first time, that the spatial string tension is scaling on the lattice and thus is non-vanishing in the continuum limit. It is temperature independent below Tc and rises rapidly above. For temperatures larger than 2Tc we find a scaling behaviour consistent with sigma_s(T) = 0.136(11) g^4(T) T^2, where g(T) is the 2-loop running coupling constant with a scale parameter determined as Lambda_T = 0.076(13) Tc.

Finite size scaling analysis of su(2) lattice gauge theory in (3+1) dimensions

Abstract We have calculated the order parameter, the susceptibility and the normalized fourth cumulant g r with high precision on N σ 3 ×4 lattices ( N σ =8,12,18 and 26) for SU(2) gauge theory at finite temperature. The finite size scaling analysis of these quantities confirms that the critical exponents of SU(2) gauge theory are the same as those of the three-dimensional Ising model, the infinite volume value for the critical coupling is 4/ g c 2 ( N τ = 4) = 2.2985 ±0.0006. With direct scaling fits we determine β / ν and γ / ν and find excellent agreement with the hyperscaling relation.

The onset of deconfinement in SU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeNσ3×4,Nσ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε−3P)/T4. It increases sharply just aboveTc, peaks atT/Tc=1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveTc, the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.

Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

Near the deconfinement transition of SU(2) gauge theory the finite-size scaling behaviour of the order parameter, the susceptibility and the normalized fourth cumulant gr is studied on Nσ3 × Nτ lattices with Nτ = 4 and 6 and Nσ = 8, 12, 18, 24or 26. For that purpose we have calculated new high-statistics data for Nτ = 6 and re-evaluated previous results obtained for Nτ = 4. In both cases we used the density of states method. We determine the critical coupling and with a new way of phenomenological renormalization the critical exponents. For Nτ = 6 we find that 4/gc,∞2 = 2.4265(30). Using the results for the criitical temperature obtained for different Nτ we examine the approach to asymptotic scaling.

The onset of intermittent behaviour in the Ising model

Abstract We study the development of intermittent behaviour near the critical point of the two-dimensional Ising model for lattices of size 32 × 32 to 256 × 256. Using Monte Carlo simulation, we calculate both standard and factorial moments. Our results approach the values of the intermittency indices calculated analytically for an infinite system.

Critical exponents of the chiral transition in strong coupling QCD

We study the critical behaviour of the chiral phase transition of SU(3) lattice QCD with one species of staggered fermions in the strong coupling limit. We find a second-order phase transition which seems to be controlled by an effective action which is in the same universality class as three-dimensional O(2) spin models. In particular, we find for the exponent-delta, 0.18 < 1/delta < 0.25, in good agreement with the three-dimensional O(2) value, 1/delta = 0.21.

Polyakov loop distributions near deconfinement inSU(2) lattice gauge theory

The distribution function of the Polyakov loop is investigated on a 163×3 lattice in the neighbourhood of the deconfinement transition ofSU(2) gauge theory. We find, that well above the transition the distribution is a Gaussian; when the coupling approaches the critical point it is modified due to phase flip attempts of the system. Corresponding distributions for the plaquettes remain, however, Gaussian. For one coupling close to the transition we study the distributions on 83, 123 and 183×4 lattices and show that strong finite size effects are present. Using the maximum values of the Gaussian parts of the distributions we construct a more physical (and therefore scaling) order parameter whose critical exponent is in excellent agreement with the universality hypothesis.

Efficient calculation of critical parameters in SU (2) gauge theory

Abstract We show how the critical point and the ratio γ ν of critical exponents of the finite temperature deconfinement transition of SU (2) gauge theory may be determined simply from the expectation value of the square of the Polyakov loop. In a similar way we estimate the ratio (α−1) ν . The method is based on a consistent application of finite size scaling theory to results obtained with the density of state technique. It may also be used in other lattice theories at second order transitions.