  In a previous article we have shown, within the replica formalism, that the
conventional picture of the random field Ising model breaks down, by the effect
of singularities in the interactions between fields involving several replicas,
below dimension eight. In the zero-replica limit several coupling constants
have thus to be considered, instead of just one. As a result we had found that
there is no stable fixed point in the vicinity of dimension six. It is natural
to reconsider the problem in a dynamical framework, which does not require
replicas, although the equilibrium properties should be recovered in the large
time limit. Singularities in the zero-replica limit are a priori not visible in
a dynamical picture. In this note we show that in fact new interactions are
also generated in the stochastic approach. Similarly these interactions are
found to be singular below dimension eight. These critical singularities
require the introduction of a time origin $t_0$ at which initial data are
given. The dynamical properties are thus dependent upon the waiting time. It is
shown here that one can indeed find a complete correspondence between the
equilibrium singularities in the $n=0$ limit, and the singularities in the
dynamics when the initial time $t_0$ goes to minus infinity, with $n$ replaced
by $-\frac{1}{t_0}$. There is thus complete coherence between the two
approaches.
