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The stability of the random field Ising model (RFIM) against spin glass (SG)fluctuations, as investigated by M\'ezard and Young, is naturally expressed viaLegendre transforms, stability being then associated with the non-negativenessof eigenvalues of the inverse of a generalized SG susceptibility matrix. It isfound that the signal for the occurrence of the SG transition will manifestitself in free-energy {\sl fluctuations\/} only, and not in the free energyitself. Eigenvalues of the inverse SG susceptibility matrix is then approachedby the Rayleigh Ritz method which provides an upper bound. Coming from theparamagnetic phase {\sl on the Curie line,\/} one is able to use a virial-likerelationship generated by scaling the {\sl single\/} unit length $ (D<6; $ inhigher dimension a new length sets in, the inverse momentum cut off).Instability towards a SG phase being probed on pairs of {\sl distinct\/}replicas, it follows that, despite the repulsive coupling of the RFIM theeffective pair coupling is {\sl attractive\/} (at least for small values of theparameter $ g\bar \Delta , $ $ g $ the coupling and $ \bar \Delta $ theeffective random field fluctuation). As a result, \lq\lq bound states\rq\rq\associated with replica pairs (negative eigenvalues) provide the instabilitysignature. {\sl Away from the Curie line\/}, the attraction is damped out tillthe SG transition line is reached and paramagnetism restored. In $ D<6, $ theSG transition always precedes the ferromagnetic one, thus the domain indimension where standard dimensional reduction would apply (on the Curie line)shrinks to zero.Comment: te

Random Field Ising Model: Dimensional Reduction or Spin-Glass Phase?