Variation of lattice spacing with Smearing

The value of Wilson loop defines static potential, compare the plots with fixed length , see how the value of Wilson loop is varying with smearing. The Wilson loop must be same for fixed length(as it is observable). You will find that the smearing steps decrease lattice spacing.

Find corresponding \(\beta\) values for HISQ action from that of \(P_4\) action.

Below, the values for P4 action and \(N_{\tau}=8\) is given.
We first will find temperature for corresponding beta for P4 action, from temperature we can find the lattice spacing of P4 action. Once we found the lattice spacing for P4 action, we can just find beta for HISQ action.

\(\beta_{P4}\) T \(a_{P4}\) \(\beta_{HISQ}\)