  We perform large-scale Monte Carlo simulations using the Machta-Newman-Chayes
algorithms to study the critical behavior of both the diluted antiferromagnet
in a field with 30% dilution and the random-field Ising model with Gaussian
random fields for different field strengths. Analytical calculations by Cardy
[Phys. Rev. B 29, 505 (1984)] predict that both models map onto each other and
share the same universality class in the limit of vanishing fields. However, a
detailed finite-size scaling analysis of both the Binder cumulant and the
two-point finite-size correlation length suggests that even in the limit of
small fields, where the mapping is expected to work, both models are not in the
same universality class. Therefore, care should be taken when interpreting
(experimental) data for diluted antiferromagnets in a field using the
random-field Ising model. Based on our numerical data, we present analytical
expressions for the phase boundaries of both models.
