Is mean-field theory valid for spin glasses?

Dipolar and Dzyaloshinsky-Moriya (DM) interactions are studied as candidates for producing long-range interactions in metallic spin glasses, with the aim of understanding the mean-field behaviour observed in some systems. It is shown that while the dipolar interactions is effectively short-ranged, the DM interaction, mediated either by non-magnetic impurities with strong spin-orbit coupling to the conduction electrons, or by the magnetic ions themselves, does lead to a quasi-long-range interaction which varies as R -3 over tens of lattice spacings. However, the magnitude of this effect seems to be too small to account for the experimental results. Both dipolar and DM interactions lead, in an otherwise isotropic Heisenberg spin glass, to phase transition behaviour characteristic of an Ising spin glass.