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

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 ${\lambda }_{\mathrm{AT}}$ (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 ${\chi }_{\mathrm{SG}}$, which presents a term inversely proportional to the replicon ${\lambda }_{\mathrm{AT}}$. As a result of a relation between ${\chi }_{\mathrm{SG}}$ and ${\chi }_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of ${\lambda }_{\mathrm{AT}}=0$ at $T_f$. However, our results show that, in the presence of random fields, ${\chi }_3$ presents a rounded maximum at a temperature $T^{\ast }$, which does not coincide with the spin-glass transition temperature $T_f$ (i.e., $T^{\ast }>T_f$ for a given applied random field). Thus, the maximum value of ${\chi }_3$ at $T^{\ast }$ 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 ${\lambda }_{\mathrm{AT}}$, 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.

accepted for publication in PRB

References in corpus (5)

• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• Quantum and Classical Glass Transitions in $LiH{o}_x{Y}_{1-x}{F}_4$
• Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system

Cited by in corpus (5)

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• Ising spin glass in a random network with a gaussian random field
• Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism
• Specific heat and non-linear susceptibility in spin glasses with random fields
• Unfolding of phases and multicritical points in the Classical Anisotropic van Hemmen Spin Glass Model with Random Field