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We calculate the step scaling function, the lattice analog of the renormalization group $beta$-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step scaling function, making numerical simulations particularly challenging. We present a detailed analysis including the study of systematic effects of our extensive data set generated with twelve dynamical flavors using the Symanzik gauge action and three times stout smeared Mobius domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $beta$ function for a scale change $s=2$ on up to five different lattice volume pairs. Our preferred analysis is fully $O(a^2)$ Symanzik improved and uses Zeuthen flow combined with the Symanzik operator. We find an infrared fixed point within the range $5.2 le g_c^2 le 6.4$ in the $c=0.250$ finite volume gradient flow scheme. We account for systematic effects by calculating the step-scaling function based on alternative flows (Wilson or Symanzik) as well as operators (Wilson plaquette, clover) and also explore the effects of the perturbative tree-level improvement.
We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $tilde g_c^2(L)$ we determine the
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
We present details of a lattice study of infrared behaviour in SU(3) gauge theory with twelve massless fermions in the fundamental representation. Using the step-scaling method, we compute the coupling constant in this theory over a large range of sc
We summarize the results recently reported in Ref.[1] [A. Deuzeman, M.P. Lombardo, T. Nunes da Silva and E. Pallante,The bulk transition of QCD with twelve flavors and the role of improvement] for the SU(3) gauge theory with Nf=12 fundamental flavors
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 $beta=6.287$-