  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 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, so that the issue cannot be decided on the basis of
numerical simulations.
