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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 | Abstract: | The 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 | Services: | Forum | Review | PDF | Favorites |
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