RANDOM-FIELD ISING-MODEL - DIMENSIONAL REDUCTION OR SPIN-GLASS PHASE

The stability of the random field Ising model (RFIM) against spin glas s (SG) fluctuations, as investigated by Mezard and Young, is naturally expressed via Legendre transforms, stability being then associated wi th the non-negativeness of eigenvalues of the inverse of a generalized SG susceptibility matrix. It is found that the signal for the occurre nce of the SG transition will manifest itself in free-energy fluctuati ons only, and not in the free energy itself. Eigenvalues of the invers e SG susceptibility matrix are then investigated by the Rayleigh Ritz method which provides an upper bound. Coming from the paramagnetic pha se on the Curie Line, one is able to use a virial-like relationship ge nerated by scaling the single unit length (D < 6; in higher dimension a new length sets in, the inverse momentum cut off). Instability towar ds a SG phase being probed on pairs of distinct replicas, it follows t hat, despite the repulsive coupling of the RFIM the effective pair cou pling is attractive (at least for small values of the parameter g<(Del ta)over bar>, g the coupling and <(Delta)over bar> the effective rando m field fluctuation). As a result, ''bound states'' associated with re plica pairs (negative eigenvalues) provide the instability signature. Away from the Curie line, the attraction is damped out till the SG tra nsition line is reached and paramagnetism restored. In D < 6, the SG t ransition always precedes the ferromagnetic One, thus the domain in di mension where standard dimensional reduction would apply (on the Curie line) shrinks to zero.