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29 March 2024
 
  » arxiv » 1606.1186

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Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields
C. V. Morais ; F. M. Zimmer ; M. J. Lazo ; S. G. Magalhães ; F.D. Nobre ;
Date 3 Jun 2016
AbstractThe behavior of the nonlinear susceptibility $chi_3$ 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 $lambda_{ m AT}$ (replicon) on the random fields is analyzed. Particularly, in absence of random fields, the temperature $T_f$ can be traced by a divergence in the spin-glass susceptibility $chi_{ m SG}$, which presents a term inversely proportional to the replicon $lambda_{ m AT}$. As a result of a relation between $chi_{ m SG}$ and $chi_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of $lambda_{ m AT}=0$ at $T_f$. However, our results show that, in the presence of random fields, $chi_3$ 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 $chi_3$ at $T^*$ reflects the effects of the random fields in the paramagnetic phase, instead of the non-trivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that $chi_3$ still maintains a dependence on the replicon $lambda_{ m AT}$, 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$_x$Y$_{1-x}$F$_4$ compound.
Source arXiv, 1606.1186
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