we can take the average of string tension at small R and large R when the pattern is linear, but as we increase the temperature the curvature starts to appear. As we increase the temperature the curve can not fitted by \(c-\alpha/r\), and one has to use \(log(r)\) to fit. The value of alpha is accurate with high temperature curve of string tension vs R(due to presence of many points at curvature region). Therefore it is very difficult to find the curvature for small temperature region. For more look at Jack Liddle's paper on string tension and dimensional reduction in 2+1 flavour QCD.
we can also use the two loop ratio to find potential for larger value of R instead of Creutz ratio, as we have seen that 2 loop ratio is more accurate at larger R and for shorter R Creutz ratio is more appropriate to find plateau for large Z.
can we define the over smearing by change of sign of alpha after some smearing steps. We have seen that from smearing 1-5 the string tension decreases from small R to large R. But it increases for smearing steps 5 to 25 as we move form small R to large R (which can be seen in comprehensive exam report).
To find the plateau for give R, we can also use exponential fitting for some values of R. All of these tricks can be useful to find the values of potential at larger values of R. For Creutz ratio method of potential, we can fit with \(c-exp(-ax)\).
The value of \(T_c\) in paper of peter is chiral phase transition for physical values of quark masses, which is \(T_c=156 MeV\).
The ratio of \(m_u/m_s=m_d/m_s\) can be found from directory names of peter's configurations.
The mass gap is same as confinement problem in QCD as the mass gap is difference in ground state and first excited state in QCD, the first excited state of QCD does not consist of free quarks but a bound state making mesons or baryons.