Random fields Hrf, which are generated in diluted antiferromagnets by uniform fields H, have been studied using optical birefringence. Their effects on the critical behavior of the magnetic specific heat Cm of d=3 and d=2 Ising systems differ dramatically. For d=3 (Fe0.6Zn0.4F2), the phase transition appears sharper and more divergent for H≠0 than it does at H=0. For d=2 (Rb2Co0.85Mg0.15Fe4), the sharp peak in Cm at H=0 immediately rounds in small fields, indicating the phase transition is destroyed in Hrf. From these studies we conclude that 2≤dl<3, where dl is the lower critical dimensionality of the random field Ising model (RFIM). Moreover, all of the observed crossover and scaling behavior (e.g., shift of TC and decrease of Cm peak height with H at d=2, crossover exponents), are exactly as predicted. The new critical behavior in Hrf for d=3 (logarithmic divergence of Cm with reduced temperature) shows that d̄≂2, where d̄ is the new effective space dimensionality of the RFIM; hence d̄≂d−1, in disagreement with early perturbation theory and supersymmetry predictions of d̄=d−2. Recent neutron scattering results support all of the above conclusions. The above, and magnetization and computer simulation studies, strongly suggest the early interpretation given to the domains seen in field-cooled experiments on d=3 systems, as evidence that dl≥3, is in error. Rather, it appears that the ground state has long-range antiferromagnetic order, corresponding to that obtained by zero-field cooling.