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تسجيل مستخدم جديدThemodynamics for pure SU($2$) gauge theory using gradient flow
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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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We present the scale-setting function and the equation of state of the pure SU(2) gauge theory using the gradient flow method. We propose a reference scale t0 for the SU(2) gauge theory satisfying $t^2langle E rangle|_{t=t_0} = 0.1$. This reference v
alue is fixed by a natural scaling-down of the standard t0-scale for the SU(3) gauge theory based on the 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.
A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed temperature ar
e calculated directly on 32^3 x (6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor (T_{mu nu}^R(x)) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t-dependence of the flowed data.
We study energy gap (latent heat) between the hot and cold phases at the first order phase transition point of the SU(3) gauge theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the energy gap b
y a method using the Yang-Mills gradient flow and compare it with that by the conventional derivative method.
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 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.
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