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

Diluted antiferromagnets in a field seem to be in a different universality class than the random-field Ising model