We present rigorous upper and lower bounds for the zero-momentum gluon propagator $D(0)$ of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in $SU(2)$ gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find $D(0)=0$, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of São Paulo.

• Received 21 December 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.241601