Abstract
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 $t^2 \langle E\rangle|_{t=t_0} = 0.1$. This reference value 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.
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