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

Abstract

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 the Binder cumulant, the two-point finite-size correlation length, and the susceptibility 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. Based on our numerical data, we present analytical expressions for the phase boundaries of both models.