Replica symmetry breaking in random-field systems

Elusive spin-glass phase in the random field Ising model

We show rigorously that the spin-glass susceptibility in the random field Ising model is always bounded by the ferromagnetic susceptibility, and therefore that no spin-glass phase can be present at equilibrium out of the ferromagnetic critical line. When the magnetization is, however, fixed to values smaller than the equilibrium value, a spin-glass phase can exist, as we show explicitly on the Bethe lattice.

Effects of random fields in an antiferromagnetic Ising spin glass

The effects of random fields on the two-sublattice infinite-ranged Ising spin-glass model are investigated. This model is expected to be appropriate as a mean-field description of antiferromagnetic spin glasses such as FexMn1-xTiO3. Within replica-symmetric calculations, we study the influence of Gaussian and bimodal random fields on the phase transitions and phase diagrams. It is shown that, in the presence of random fields, the first-order transitions are weakened and may become continuous. Also, the antiferromagnetic phases are always destroyed by sufficiently strong random fields. A qualitative comparison with existing experimental results and the limitations of the present calculations are discussed.