  We analyse numerically the critical behavior of an absorbing phase transition
in a conserved lattice gas in an external field. The external field is realized
as a spontaneous creation of active particles which drives the system away from
criticality. Nevertheless, the order parameter obeys certain scaling laws for
sufficiently small external fields. These scaling laws are investigated and the
corresponding exponents are determined in various dimensions ($D=2,3,4,5$). At
the so-called upper critical dimension $D_{\text c}=4$ one has to modify the
usual scaling laws by logarithmic corrections.
