Interactions of several replicas in the random field Ising model

The replicated field theory of the random field Ising model involves the co uplings of replicas of different indices. The resulting correlation functio ns involve a superposition of different types of long distance behaviours. However the n = 0 limit allows one to discuss the renormalization group pro perties in spite of this phenomenon. The attraction of pairs of replicas is enhanced under renormalization flow and no stable fixed point is found. Co nsequently, an instability occurs in the paramagnetic region, before one re aches the Curie line, signalling the onset of replica symmetry breaking.