Scaling behavior of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension

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.