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

Bjoern Ahrens, Jianping Xiao, Alexander K. Hartmann, Helmut G. Katzgraber

Published 2013-02-11, updated 2013-11-13Version 2

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.