Specific heat and non-linear susceptibility in spin glasses with random fields

Abstract

We study magnetic properties of spin glass SG systems under a random field (RF), beased on the suggestion that RFs can be induced by a weak transverse field in the compound LiHo${}_x$Y${}_{1-x}$F${}_4$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $\Delta$. We adopt the one-step replica symmetry breaking (RSB) approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat $C_m$, nonlinear susceptibility ${\chi }_3$ and phase diagrams for different disorder configurations. In the absence of RF, the ${\chi }_3$ exhibits a divergence at $T_f$, while the $C_m$ shows a broad maximum at a temperature $T^{\ast \ast }$ around 30$\%$ above $T_f$, as expected for conventional SG systems. The presence of RF changes this scenario. The $C_m$ still shows the maximum at $T^{\ast \ast }$ that is weakly dependent on $\Delta$. However, the $T_f$ is displaced to lower temperatures, enhancing considerable the ration $T^{\ast \ast }/T_f$. Furthermore, the divergence in ${\chi }_3$ is replaced by a rounded maximum at a temperature $T^{\ast }$, which becomes increasingly higher than $T_f$ as $\Delta$ enhances. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>T^{\ast \ast }$; (ii) a region with formation of short-range order with frozen spins ($T^{\ast }<T<T^{\ast \ast }$); (iii) a region with slow growth of free-energy barriers slowing down the spin dynamics before the SG transition ($T_f<T<T^{\ast }$) suggesting an intermediate Griffiths phase before the SG state. Our results reproduce qualitatively some findings of LiHo${}_x$Y${}_{1-x}$F${}_4$ as the rounded maximum of ${\chi }_3$ behavior triggered by RF.

9 pages, 6 figures

References in corpus (6)

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• 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
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• Specific Heat of the Dilute Ising Magnet LiHo${}_x$Y${}_{1-x}$F${}_4$
• Nonlinear susceptibility of a quantum spin glass under uniform transverse and random longitudinal magnetic fields