Running coupling constant and correlation length from Wilson loops

We consider a definition of the QCD running coupling constant alpha(mu) related to Wilson loops of size rXt with arbitrary fixed t/r. The schemes defined by these couplings are very close to the <(MS)over bar> scheme (i.e. the one-loop perturbative correction to the coupling is small) for all values of t/r; in the t/r --> infinity limit, the ''q (q) over bar force'' scheme is recovered, where the coupling constant is related to the quark-antiquark force. We discuss the possibility of applying finite-size scaling techniques to the Monte Carlo evaluation of alpha(mu) up to very large momentum scales. We propose a definition of correlation length, also related to Wilson loops, which should make such a computation feasible.