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We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range 6.3 ≤ β ≤ 7.5 with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.

Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices