Random field Ising model: dimensional reduction or spin-glass phase?

Details Random field Ising model: dimensional reduction or spin-glass phase? Random field Ising model: dimensional reduction or spin-glass phase?

1995-01-17

arxiv.org/abs/cond-mat/9501069v1

Physics

Condensed Matter

tex

Scientific paper

10.1051/jp1:1995178

The stability of the random field Ising model (RFIM) against spin glass (SG) fluctuations, as investigated by M\'ezard 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 {\sl fluctuations\/} only, and not in the free energy itself. Eigenvalues of the inverse SG susceptibility matrix is then approached by the Rayleigh Ritz method which provides an upper bound. Coming from the paramagnetic phase {\sl on the Curie line,\/} one is able to use a virial-like relationship generated by scaling the {\sl 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 {\sl distinct\/} replicas, it follows that, despite the repulsive coupling of the RFIM the effective pair coupling is {\sl attractive\/} (at least for small values of the parameter $ g\bar \Delta , $ $ g $ the coupling and $ \bar \Delta $ the effective random field fluctuation). As a result, \lq\lq bound states\rq\rq\ associated with replica pairs (negative eigenvalues) provide the instability signature. {\sl 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.

Affiliated with

Also associated with

No associations

Rating

Random field Ising model: dimensional reduction or spin-glass phase? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random field Ising model: dimensional reduction or spin-glass phase?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random field Ising model: dimensional reduction or spin-glass phase? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-573180