AbstractIt is shown that below a critical dimensiondc= 4 higher‐order random‐field cumulants contribute to the divergent part of the free energy. They renormalize the standard diagrammatic expansion into the most divergent terms in weak random fields in such a way that the perturbative effective dimensionality in the scaling region of thed<4 model is two. It is argued that any dimensional reduction based on a diagrammatic expansion is doubtful in lower dimensi