Frustrated Blume-Emery-Griffiths model

Schreiber, Gerald

doi:10.1007/s100510050789

Cited by 21 publications

(16 citation statements)

References 25 publications

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“…If the interactions matrix J is taken from the Gaussian ensemble, one then obtains a reentrant spin-glass phase. [6][7][8][9][10][11] In this paper, the inverse freezing problem is addressed in the context of mean-field models of structural glasses by using the above mechanism of entropy-driven reentrance. Several reasons make such a problem interesting.…”

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confidence: 99%

Inverse freezing in mean-field models of fragile glasses

Sellitto

2006

Phys. Rev. B

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A disordered spin model suitable for studying inverse freezing in fragile glass-forming systems is introduced. The model is a microscopic realization of the "random first-order" scenario in which the glass transition can be either continuous or discontinuous in thermodynamic sense. The phase diagram exhibits a first-order transition line between two fluid phases terminating at a critical point. When the interacting degrees of freedom are entropically favored, an inverse static glass transition and a double inverse dynamic freezing appear.

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confidence: 99%

Inverse freezing in mean-field models of fragile glasses

Sellitto

2006

Phys. Rev. B

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“…First, in the absence of biquadratic interactions (K ij = 0 for every pair (i, j)), we have a conventional spin-1 spin-glass model. The properties of this model are quite analogous to those of the Sherrington-Kirkpatrick model [5][6][7][8][9][26][27][28]; the system presents a continuous transition from a paramagnetic to a low-temperature spin-glass phase where the ergodicity is also broken [27]. On the other hand, if J ij = 0 for every pair (i, j), the system becomes equivalent to the discrete quadrupolar-glass model investigated in Ref.…”

Section: The Model and Its Free-energy Densitymentioning

confidence: 68%

“…[1][2][3] ). Recently, much effort has been dedicated to understanding the phase behavior of spin-1 Ising glasses [5][6][7][8][9], as promising models to describe real systems which present multicritical phenomena. Other models which can be mapped onto spin-1 Ising glasses were also studied recently [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Effects of random biquadratic couplings in a spin-1 spin-glass model

2000

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A spin-1 model, appropriated to study the competition between bilinear (J ij S i S j ) and biquadratic (K ij S 2 i S 2 j ) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replicasymmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.

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“…[22,23] for what concerns the lattice gas version of the model, and in Refs. [24,25,26,27] for the spin-1 model. For sake of completeness we also report the study [28] where, together with the random magnetic interaction, also a random biquadratic interaction is considered.…”

Section: 14mentioning

confidence: 99%

Thermodynamic properties of a full-replica-symmetry-breaking Ising spin glass on lattice gas: The random Blume-Emery-Griffiths-Capel model

Crisanti

Leuzzi

2004

Phys. Rev. B

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The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.Since its discovery, the spin glass (SG) phase has played and still plays a fundamental role in the investigation and understanding of many basic properties of disordered and complex systems. The analysis of the mean-field approximation of theoretical models displaying such a phase has revealed different possible scenarios, including different kinds of transition from the paramagnetic phase to the SG phase, as well as different kinds of SG phases. Most of the work, however, has been concentrated on just two scenarios.In order of appearance in literature the first scenario is described by a Full Replica Symmetry Breaking (FRSB) solution characterized by a continuous order parameter function, 1 which continuously grows from zero by crossing the transition. The prototype model is the Sherrington-Kirkpatrick (SK) model, 2 a fully connected Ising-spin model with quenched random magnetic interactions.The second scenario, initially introduced by Derrida by means of the Random Energy Model (REM), 3 provides a transition with a jump in the order parameter to a stable low temperature phase in which the replica symmetry is spontaneously broken only once. The order parameter is a step function taking two values q min and the so-called Edwards-Anderson order parameter, 4 q EA , (else said self-overlap), with q min < q EA . In the paramagnetic phase they are both equal to zero. At the transition, q EA grows to a value larger than q min . No discontinuity appear, however, in the thermodynamic functions. Actually, at the transition to the one step Replica Symmetry Breaking (1RSB) SG phase, the Edwards-Anderson order parameter q EA can either grow continuously from zero or jump discontinuously to a finite value. The first case of this second scenario includes Potts-glasses with three or four states, 5 the spherical p-spin spin-glass model in strong magnetic field 6 and some inhomogeneous spherical p-spin model with a mixture of p = 2 and p > 3 interactions.7,8 The latter case includes, instead, Potts-glasses with more than four states 5 , quadrupolar glass models, 5,9 p-spin interaction spin-glass models with p...

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Frustrated Blume-Emery-Griffiths model

Cited by 21 publications

References 25 publications

Inverse freezing in mean-field models of fragile glasses

Inverse freezing in mean-field models of fragile glasses

Effects of random biquadratic couplings in a spin-1 spin-glass model

Thermodynamic properties of a full-replica-symmetry-breaking Ising spin glass on lattice gas: The random Blume-Emery-Griffiths-Capel model

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