We show by numerical simulations that the correlation function of the random
field Ising model (RFIM) in the critical region in three dimensions has very
strong fluctuations and that in a finite volume the correlation length is not
self-averaging. This is due to the formation of a bound state in the underlying
field theory. We argue that this non perturbative phenomenon is not particular
to the RFIM in 3-d. It is generic for disordered systems in two dimensions and
may also happen in other three dimensional disordered systems