  Through a finite size renormalization group technique we calculate the
running coupling constant for quenched SU(2) with a few percent error over a
range of energy varying by a factor thirty. The definition is based on ratio of
correlations of Polyakov loops with twisted boundary conditions. The
extrapolation to the continuum limit is governed by corrections due to lattice
artifacts which are proportional to the square of the lattice spacing and
appears rather smooth.
