Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields

Abstract

The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf , which comes as a direct consequence of λAT = 0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T * which does not coincide with the spin-glass transition temperature Tf (i.e., T * > Tf for a given applied random field). Thus, the maximum value of χ3 at T * reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1−xF4 compound.