  We present a non-perturbative study of the running coupling constant in the
Twisted Polyakov Loop (TPL) scheme. We investigate how the systematic and
statistical errors can be controlled {\it via} a feasibility study in SU(3)
pure Yang-Mills theory. We show that our method reproduces the perturbative
determination of the running coupling in the UV. In addition, our numerical
result agrees with the theoretical prediction of this coupling constant in the
IR. We also present our preliminary results for $N_f=12$ QCD, where an IR fixed
point may be present.
