Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

Araújo, João M. de; Nobre, Fernando D.; Costa, F. A. da

doi:10.1103/physreve.61.2232

Cited by 9 publications

(13 citation statements)

References 61 publications

(93 reference statements)

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“…For continuous transitions, For the particular case σ = 0, i.e., the bimodal probability distribution for the fields [25], (1) 0 (σ) as a collapse of two tricritical points. Such an unusual critical point is a characteristic of some infinite-range-interaction spin-glasses in the presence of random magnetic fields [25,26], and to our knowledge, it has never been found in other magnetic models. ¿From (1) 0 (σ)/σ decreases.…”

Section: Standart Calculations Lead Tomentioning

confidence: 72%

“…The model is considered in the limit of infinite-range interactions, and the probability distribution for the random magnetic fields is a double Gaussian, which consists of a sum of two independent Gaussian distributions. Such a distribution interpolates between the bimodal and the simple Gaus-sian distributions, which are known to present distinct low-temperature critical behavior, within the mean-field limit [24,25,26,27]. It is argued that this distribution is more appropriate for a theoretical description of diluted antiferromagnets than the bimodal and Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

“…In what concerns Fe x Mg 1−x Cl 2 , one gets an ISG-like behavior for x < 0.55, whereas for 0.7 < x < 1.0 one has a typical RFIM with a first-order transition turning into a continuous one due to a change in the random fields [14,18,19]. Even though a lot of experimental data is available for these systems, they still deserve an appropriate understanding, with only a few theoretical models proposed for that purpose [20,21,22,23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

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Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

Crokidakis

Nobre²

2008

Phys. Rev. E

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The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.

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Section: Standart Calculations Lead Tomentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

Crokidakis

Nobre²

2008

Phys. Rev. E

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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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“…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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Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

Cited by 9 publications

References 61 publications

Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

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

Spin-1 Hopfield model under a random field

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