One-step replica-symmetry-breaking solution of the Sherrington–Kirkpatrick model under a Gaussian random field

Magalhães, S. G.; Morais, C. V.; Nobre, Fernando D.

doi:10.1088/1742-5468/2011/07/p07014

Cited by 12 publications

(17 citation statements)

References 22 publications

(44 reference statements)

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“…When D = 0, the results are similar to those ones found recently for the SK model with a random field (see Ref. 19 ). For ∆ = 0, the PM/SG phase transition is trivially induced.…”

Section: Resultssupporting

confidence: 90%

“…In this model, the spins can assume values S = ±1, 0, D is a crystal lattice field and the spin-spin coupling J ij and the random field h i follow Gaussian distributions. In the case of a random field following a Gaussian distribution, it is necessary to use the replica symmetry breaking in order to obtain the SG solution 19 . The free energy is obtained and consequently, the SG order parameters.…”

Section: Introductionmentioning

confidence: 99%

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Inverse freezing in the Ghatak-Sherrington model with a random field

et al. 2012

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The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from GS model without RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

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“…When D = 0, the results are similar to those ones found recently for the SK model with a random field (see Ref. 19 ). For ∆ = 0, the PM/SG phase transition is trivially induced.…”

Section: Resultssupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Inverse freezing in the Ghatak-Sherrington model with a random field

et al. 2012

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“…For example, the Sherrington-Kirkpatrick (SK) model [15] was combined with RFs following distinct types of disorder. Specifically, the SK model with a Gaussian RF exhibits phase diagrams, in which the SG phase decreases with the RF, at least in the mean field * Electronic address: carlosavjr@gmail.com theory [14]. It should be emphasized that this result was obtained within the one-step replica-symmetry-breaking (1S-RSB) approximation for the SG solution.…”

Section: Introductionmentioning

confidence: 81%

“…For instance, several studies display broad divergences even for the RFIM phase diagram structure [4,[7][8][9]. On the other hand, the effect of RFs on the SG phase has also been investigated [10][11][12][13][14]. In this case, random bond (RB) interaction models with an additional magnetic RF have been considered extensively.…”

Section: Introductionmentioning

confidence: 99%

Spin-1 Hopfield model under a random field

et al. 2014

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The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three state Hopfield model under a Gaussian Random Field. In order to control the nontrivial disorder, the Hebb interaction is used. It provides a way to control the system frustration by means of the parameter a = p N , varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replicasymmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, anisotropy constant and the Random Field.

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“…One possible consequence of the transverse field, induced longitudinal RF, is that the Almeida-Thouless (AT) line 22 can be sup-pressed, as suggested by numerical simulations in shortrange-interaction SGs 23 . However, previous studies using mean-field Parisi's framework have shown that the SK model with a RF does preserve the AT line [24][25][26][27][28] . Consequently, assuming that Parisi's mean-field theory is a valid framework to describe the SG problem with a transverse field, induced longitudinal RF, one can also raise the question of how the behavior of χ 3 can be related with the AT line, when a RF is present in the SK model?…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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The behavior of the nonlinear susceptibility χ3 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-symmetrybreaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analysed. Particularly, in absence of random fields, the temperature T f can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at T f , which comes as a direct consequence of λAT = 0 at T f . However, our results show that, in the presence of random fields, χ3 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 χ3 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 χ3 still maintains a dependence on the replicon λAT, 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 LiHoxY1−xF4 compound.

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One-step replica-symmetry-breaking solution of the Sherrington–Kirkpatrick model under a Gaussian random field

Cited by 12 publications

References 22 publications

Inverse freezing in the Ghatak-Sherrington model with a random field

Inverse freezing in the Ghatak-Sherrington model with a random field

Spin-1 Hopfield model under a random field

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

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