Quick answer: The string tension $\sigma$ as shown in that plot (which looks like an older version of Fig. 11 in arXiv:1004.3206) is the dimension-2 coefficient of the linear term in the static potential $V(r)$ (the energy of two infinitely heavy probes separated by spatial distance $r$). So one computes $V(r)$, typically from the exponential decay of rectangular $r\times T$ Wilson loops oriented along the temporal direction, $W(r,T) \propto e^{-V(r)\cdot T}$, and then fits $V(r) = -\frac{C}{r} + A + \sigma r$ to determine $\sigma$.

The stuff above is in continuum language, implicitly working in "lattice units" where the dimensionful lattice spacing is set to $a=1$. Non-zero lattice spacing leads to discretization artifacts in the predictions for the dimensionless combination $a^2 \sigma$, which are removed by extrapolating $a \to 0$. One can play games with lattice perturbation theory to reduce these artifacts.

This is one of the simplest non-trivial calculations one can do in lattice gauge theory, so it should be covered comprehensively in the standard textbooks/lecture notes. Silvia Necco's PhD thesis, hep-lat/0306005, might be a good starting point.

This post imported from StackExchange Physics at 2020-11-06 18:49 (UTC), posted by SE-user David Schaich