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

摘要

The behavior of the nonlinear susceptibility X_3 and its relation to the spin-glass transition temperature T_f 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 λ_(AT) (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature T_f can be traced by a divergence in the spin-glass susceptibility X_(SG), which presents a term inversely proportional to the replicon λ_(AT). As a result of a relation between X_(SG) and X_3, the latter also presents a divergence at T_f, which comes as a direct consequence of λ_(AT) = 0 at T_f. However, our results show that, in the presence of random fields, X_3 presents a rounded maximum at a temperature T~* which does not coincide with the spin-glass transition temperature T_f (i.e., T~* ＞ T_f for a given applied random field). Thus, the maximum value of X_3 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 X_3 still maintains a dependence on the replicon λ_(AT), 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 LiHo_xY_(1-x)F_4 compound.