Scaling of the critical temperature and quark potential with a renormalization group improved SU(3) gauge action

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 t...

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region...

We present an overview of the construction and testing of actions for SU(3) gauge theory which are approximate fixed points of renormalization group equations (at $\beta\rightarrow \infty$). Such actions are candidates for use in numerical simulations on coarse lattices.

The potential between a static quark and antiquark in pure SU(3) Yang-Mills theory is evaluated non-perturbatively through computations on the lattice in the region from short to intermediate distances (0.05 fm < r < 0.8 fm). In the high energy regime the results are compared with the parameter-free prediction of perturbation theory obtained by solving the Renormalization Group equation at two and three loops. The choice of the renormalization scheme to define a running coupl...

We have calculated the $q\bar q$ potential over a wide range of lattice separations on a $48^3\cdot56$ lattice at $\beta = 2.85$. We are able to investigate both long-range and (by correcting for the effects of lack of rotational invariance) short-range potentials. From the former we estimate the string tension and from the latter we are able to investigate asymptotic scaling. Fitting to this enables us to give an estimate for the $\Lambda$-parameter of pure-gauge SU(2).

The scaling behavior of pure gauge SU(3) in the region $\beta=5.85 - 7.60$ is examined by a Monte Carlo Renormalization Group analysis. The coupling shifts induced by factor 2 blocking are measured both on 32$^4$ and 16$^4$ lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all of the deviation. It can be accounted for by a suitable change of coupling con...

We present the equation of state (pressure, trace anomaly, energy density and entropy density) of the SU(3) gauge theory from lattice field theory in an unprecedented precision and temperature range. We control both finite size and cut-off effects. The studied temperature window ($0.7... 1000 T_c$) stretches from the glueball dominated system into the perturbative regime, which allows us to discuss the range of validity of these approaches. From the critical couplings on fine...

We construct a few parameter approximate fixed point action for SU(2) pure gauge theory and subject it to scaling tests, via Monte Carlo simulation. We measure the critical coupling for deconfinement for lattices of temporal extent $N_t=2$, 3, 4, the torelon mass at fixed physical volume, and the string tension (and heavy quark potential) from Wilson loops. We calculate the topological susceptibility using inverse blocking and show that it scales over the observed range of la...

Heavy quark potentials are investigated at high temperatures. The temperature range covered by the analysis extends from $T$ values just below the deconfinement temperature up to about $4 T_c$ in the deconfined phase. We simulated the pure gauge sector of QCD on lattices with temporal extents of 4, 6 and 8 with spatial volumes of $32^3$. On the smallest lattice a tree level improved action was employed while in the other two cases the standard Wilson action was used. Below $T...

We study the effective string corrections to the inter-quark potential at finite temperature by simulating the SU(2) lattice gauge theory in four dimensions. We provide the first numerical evidence that the logarithmic correction to the potential, which was recently proposed to be a signature of the effective string at finite temperature, is universal also in (3+1)D gauge theory, thus extending previous results limited to the (2+1)D case.