arXiv subjects
Publications and source records attributed to C. Legeland.
We report a method to select optimal smearing parameters before production runs and discuss the advantages of this selection for the determination of the string tension.
We determine the critical couplings and the critical exponents of the finite temperature transition in SU(2) and SU(3) pure gauge theory in (2+1) dimensions. We also measure Wilson loops at $T=0$ on a wide range of $β$ values using APE smearing to improve the signal. We extract the string tension $σ$ from a fit to large distances, including a string fluctuation term. With these two entities we calculate $T_c/\sqrtσ$.
The pressure and the energy density of the $SU(3)$ gauge theory are calculated on lattices with temporal extent $N_τ= 4$, 6 and 8 and spatial extent $N_σ=16$ 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 $N_τ= 8$ 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 $T_c/\sqrtσ = 0.629(3)$. 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 $T\simeq 5T_c$. For the spatial string tension we find $\sqrt{σ_s}/T = 0.566(13) g^2(T)$ with $g^2(5T_c) \simeq 1.5$.
Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of the $SU(3)$ gauge theory on lattices with temporal extent $N_τ= 4$, 6 and 8 and spatial extent $N_σ=16$ and 32. The results are extrapolated to the continuum limit. We find a deviation from ideal gas behaviour of (15-20)\%, depending on the quantity, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature on lattices with temporal extent $N_τ= 8$ and 12 and the string tension on $32^4$ lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrtσ = 0.629(3)$.
We compute heavy quark potentials in pure gauge $SU(3)$ at high temperatures in $2+1$ dimensions and confront them with expectations emerging from perturbative calculations.