Critical scaling in random-field systems: 2 or 3 independent exponents?

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole (d, N) domain of the d-dimensional random-field O(N) model (RFO(N) M) and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random-field Ising model are extremely close to the predictions of the two-exponent scaling in d = 3 and d = 4, so that the issue cannot be decided only on the basis of numerical simulations in these spatial dimensions. Copyright (C) EPLA, 2013