1. The values of string tension for \(N_{\tau}=8,10\) does not agree well with the predictions from dimensionally reduced theory. We are looking to first stablize values of pseudo potentials by varying [tmin:tmax] and finding the best possible fit.
2. Even after stablizing the potentials we could not find the agreement (within error bounds) with predictions from dimensionally reduced theory.
3. We then compared the potentials for same values of inverse gauge coupling \(\beta\) with that of zero temperature results.
4. The pseudo potentials (finite temperature results of spatial potential) must match with potentials at zero temperature for very small distances (since the notion of temperature is applicable after certain distances). But we see some shift in potential which suggest that our results are not right. However with rise in distance we see clear more slope (string tension) for non zero temperature case.

I have been skeptic of my work (as it is easiest to fool self), so I am on an adventure to check all of my analysis steps.

1. We tried for three level hyp smearing while ignoring smearing of fictitious time links. We realised that it can be done in two ways:
   1. Including thin/original fictitious time links while smearing other links.
   2. Including fat fictitious time links while smearing other links; but not doing smearing of fictitious time links in final level.

The results of both the approaches were similar and incorrect in the sense that the ratio of wilson loops were appraoching plateau from below. So we are ignoring this procedure.

1. I have also checked that no links are smeared in fictitious time (ex_dir) direction by using the method HypSmear_ExDir_checker() and also by calculating polyakov loop in fictitious time direction before and after smearing. It was found that the polyakov loop like quantity does not change in two level and three level hyp smearing which we tried.
2. Now I need to see if the smearing procedure is working fine, I am planning to replace all links with Identity matrices and print the link at a given site in some direction and see if the calculation matches with calculation done by hand or another program. But if we replace each link with Identity matrix which is easily done by gauge.one(); we find that the hyp smearing does not change anyting and each link remains Identity matrix even after any number of hyp smearing. \[ \overline{v}=Proj_{su_3}[(1-\alpha)I+(\alpha)I]=I \]
3. We also tried checking if the ratio of wilson loops starts from above in three level hyp smearing 1(b), but it turns out that ratio again starts from below and reaches a plateau.
4. We will try to calculate the pseudo potential and string tension from smear all case(which will depend on smear steps), and find string tension for nt8,nt10.
5. We will also find pseudo potential for zero temperature configuration synced. Since the potential shall match for all values of beta for zero temperature. and match with all zero temperature potential.
6. We have also compared the results of all zero temperature potentials with that of one of zero temperature (\(\beta=6.354\)) on \(32\times32\times32\times32\) lattice. It suggest that the two level hyp smearing is accurate, which can be seen in below plot.