Numéro |
J. Phys. I France
Volume 5, Numéro 8, August 1995
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Page(s) | 987 - 1001 | |
DOI | https://doi.org/10.1051/jp1:1995178 |
J. Phys. I France 5 (1995) 987-1001
Random Field Ising Model: Dimensional Reduction or Spin-Glass Phase?
C. De Dominicis1, H. Orland1 and T. Temesvari21 CEA, Service de Physique Théorique, CE-Saclay, 91191 Gif-sur-Yvette Cedex, France
2 Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Hungary
(Received 23 December 1994, received in final form and accepted 9 May 1995)
Abstract
The stability of the random field Ising model (RFIM) against spin glass (SG) fluctuations, as
investigated by Mézard and Young, is naturally expressed via Legendre transforms, stability being
then associated with the non-negativeness of eigenvalues of the inverse of a generalized SG
susceptibility matrix. It is found that the signal for the occurrence of the SG transition will
manifest itself in free-energy fluctuations only, and in the free energy itself. Eigenvalues
of the inverse SG susceptibility matrix are then investigated by the Rayleigh Ritz method which
provides an upper bound. Coming from the paramagnetic phase on the Curie line, one is able to
use a virial-like relationship generated by the single unit length (
D<6; in higher dimension
a new length sets in, the inverse momentum cut off). Instability towards a SG phase being probed on
pairs of distinct replicas, it follows that, despite the repulsive coupling of the RFIM the
effective pair coupling is attractive (at least for small values of the parameter
the coupling and
the effective random field fluctuation). As
a result, "bound states" associated with replica pairs (negative eigenvalues) provide the
instability signature. Away from the Curie line, the attraction is damped out till the SG
transition line is reached and paramagnetism restored. In
D<6, the SG transition always precedes
the ferromagnetic one, thus the domain in dimension where standard dimensional reduction would apply
(on the Curie line) shrinks to zero.
© Les Editions de Physique 1995