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Register a new userEquation of state for pure SU(3) gauge theory with RG improved action
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We present results for the equation of state for pure SU(3) gauge theory obtained with a renormalization-group (RG) improved action. The energy density and pressure are calculated on a $16^3times 4$ and a $32^3times 8$ lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4%.
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We present results for the equation of state for pure SU(3) gauge theory obtained on anisotropic lattices with the anisotropy $xi equiv a_s/a_t = 2$. The pressure and energy density are calculated on $N_t / xi = 4, 5$ and 6 lattices with the integral method. They are found to satisfy the leading $1/N_t^2$ scaling from our coarsest lattice $N_t/xi=4$. This enables us to carry out well controlled continuum extrapolations. We find that the pressure and energy density agree with those obtained using the isotropic plaquette action, but have smaller and more reliable errors.
The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $beta=6.287$--$7.500$ corresponding to the lattice spacing $a= 0.013$--$0.061,mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s= 64$, $96$, $128$ ($N_{tau}=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33 le N_s/N_{tau} le 8$. Double extrapolation, $arightarrow 0$ (the continuum limit) followed by $trightarrow 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.
We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.
We compute the Euclidean correlators of the stress tensor in pure $SU(3)$ Yang-Mills theory at finite temperature at zero and finite spatial momenta with lattice simulations. We perform continuum extrapolations using $N_tau=10,12,16,20$ lattices with renormalized anisotropy 2. We use these correlators to estimate the shear viscosity of the gluon plasma in the deconfined phase. For $T=1.5T_c$ we obtain $eta/s=0.17(2)$.
We study the equation of state of pure SU($2$) gauge theory using Monte Carlo simulations. The scale-setting of lattice parameters has been carried by using the gradient flow. We propose a reference scale $t_0$ for the SU($2$) gauge theory satisfying $t^2 langle E rangle|_{t=t_0} =0.1$, which is fixed by a natural scaling-down of the standard $t_0$-scale for the SU($3$) case based on perturbative analyses. We also show the thermodynamic quantities as a function of $T/T_c$, which are derived by the energy-momentum tensor using the small flow-time expansion of the gradient flow.
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