  Lattice studies of the infrared regime of gauge theories are complicated by
the required extensive limits, the performed gauge fixing and the demand for
high statistics. Using a general power counting scheme for the infrared limit
of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions we show that
the infrared behavior of Greens functions is both qualitatively and
quantitatively similar in two, three and four spacetime dimensions. Therefore,
lower dimensional lattice simulations can serve as a simplified laboratory to
analyze the presently applied approximations and to obtain first results for
higher correlation functions.
