{Scale setting of $\mathrm{SU}(N)$ Yang{\textendash}Mills theories via Twisted Gradient Flow}

We present preliminary results for the scale setting of $\mathrm{SU}(N)$ Yang--Mills theories using twisted boundary conditions and the gradient-flow scale $\sqrt{t_0}$. The end goal of this study is to determine the $\mathrm{SU(N)}$ $\Lambda$-parameter through the \emph{step-scaling} method. The scale $\sqrt{t_0}$, being defined from the flowed action density of the gauge fields, is correlated with their topological charge and thus could be affected by \emph{topological freezing}. We deal with this problem with the Parallel Tempering on Boundary Conditions algorithm, which we found to be effective for the same numerical setup in a previous work.