Different scenarios for critical glassy dynamics

Ciuchi, S.; Crisanti, A.

doi:10.1209/epl/i2000-00215-y

Cited by 13 publications

(23 citation statements)

References 30 publications

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“…These are more involved than those of the spherical case because spin variables cannot be integrated away and hence will not be reported here. However, near the critical point the dynamical equations can be written in the MCT form (157), (147) …”

Section: The Sherrington-kirkpatrick Model the Sherrington-kirkpatrimentioning

confidence: 99%

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Crisanti

Ritort

2003

J. Phys. A: Math. Gen.

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353

595

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Abstract. This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies.It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.

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Section: The Sherrington-kirkpatrick Model the Sherrington-kirkpatrimentioning

confidence: 99%

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Crisanti

Ritort

2003

J. Phys. A: Math. Gen.

Self Cite

353

595

View full text Add to dashboard Cite

show abstract

“…7,22 For this reason the solution of maximal complexity is also called the "dynamic solution" as opposed to the "static solution" discussed so far which, on the contrary, has vanishing complexity.…”

Section: 49mentioning

confidence: 99%

Spherical2+pspin-glass model: An analytically solvable model with a glass-to-glass transition

Crisanti

Leuzzi

2006

Phys. Rev. B

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We present the detailed analysis of the spherical s + p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2 + p model with p ≥ 4 for which a very rich phase diagram occurs, including, next to the paramagnetic and the glassy phase represented by the one step replica symmetry breaking ansatz typical of the spherical p-spin model, other two amorphous phases. Transitions between two contiguous phases can also be of different kind. The model can thus serve as mean-field representation of amorphous-amorphous transitions (or transitions between undercooled liquids of different structure). The model is analytically solvable everywhere in the phase space, even in the limit where the infinite replica symmetry breaking ansatz is required to yield a thermodynamically stable phase.PACS numbers: 75.10. Nr, 11.30.Pb, 05.50.+q Spin glasses have become in the last thirty years the source of ideas and techniques now representing a valuable theoretical background for "complex systems", with applications not only to the physics of amorphous materials, but also to optimization and assignment problems in computer science, to biology, ethology, economy and finance. These systems are characterized by a strong dependence from the details, such that their behavior cannot be rebuilt starting from the analysis of a 'cell' constituent but an approach involving the collective behavior of the whole system becomes necessary. One of the feature usually expressed is the existence of a large number of stable and metastable states, or, in other words, a large choice in the possible realizations of the system and a rather difficult (and therefore slow) evolution through many, details-dependent, intermediate steps, hunting its equilibrium state or optimal solution.Mean-field models have largely helped in comprehending many of the mechanisms yielding such complicated structure and also have produced new theories (or combined among each other old concepts pertaining to other fields) such as, e.g., the spontaneous breaking of the replica symmetry and the ultrametric structure of states.Among mean-field models spherical models are analytically solvable even in the most complicated cases. Up to now only spherical models with one step Replica Symmetry Breaking (1RSB) phases were studied, mainly due to their relevance for the fragile glass transition.

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“…[21], where the statics was solved. The equilibrium dynamics was recently worked out [22]. It consists in a slight modification of the spherical p-spin model.…”

Section: A Modelmentioning

confidence: 99%

Dynamic ultrametricity in spin glasses

Barrat

Kurchan

2000

Phys. Rev. E

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We investigate the dynamics of spin glasses from the 'rheological' point of view, in which aging is suppressed by the action of small, non-conservative forces. The different features can be expressed in terms of the scaling of relaxation times with the magnitude of the driving force, which plays the role of the critical parameter. Stated in these terms, ultrametricity loses much of its mystery and can be checked rather easily. This approach also seems a natural starting point to investigate what would be the real-space structures underlying the hierarchy of time scales. We study in detail the appearance of this many-scale behavior in a mean-field model, in which dynamic ultrametricity is clearly present. A similar analysis is performed on numerical results obtained for a 3D spin glass: In that case, our results are compatible with either that dynamic ultrametricity is absent or that it develops so slowly that even in experimental time-windows it is still hardly observable.

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Different scenarios for critical glassy dynamics

Cited by 13 publications

References 30 publications

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Spherical2+pspin-glass model: An analytically solvable model with a glass-to-glass transition

Dynamic ultrametricity in spin glasses

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