Journal of Statistical Physics, Vol. 47, Nos. 5/6, 1987. p. 931-938.
Within the perturbation diagrammatic expansion we discuss the origin of differences in determinations of the lower critical dimension of the random-field Ising model and show that below four dimensions metastability and hysteresis occur. We also explain the occurrence of a quasicritical d = 2 behavior at weak random fields, which is responsible for local stability of the ordered state above two dimensions.