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

Crisanti, A.; Ritort, Fèlix

doi:10.1088/0305-4470/36/21/201

Cited by 352 publications

(612 citation statements)

References 349 publications

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“…[39][40][41] Evidences of this have been found not only in numerical simulations of the 3D EAB model 42,43 but also in recent experiments, 44 which lends strong support for the RSB picture. But it has also been found 5 that when the system is separated into RL and FL the physical behavior of these components is very different from the one observed for the whole system.…”

Section: Discussionmentioning

confidence: 61%

Ground-state topology of the Edwards-Anderson±Jspin glass model

et al. 2010

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In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.

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Section: Discussionmentioning

confidence: 61%

Ground-state topology of the Edwards-Anderson±Jspin glass model

et al. 2010

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“…For instance, the spatio-temporal relaxation in classical glassy systems (or even non-disordered coarsening systems [40][41][42]) is very different from an equilibrium one with, e.g., breakdown of stationarity (aging effects) and other peculiar features. Still, the FDRs show that the dynamics can be interpreted as taking place in different temporal regimes each of them in equilibrium at a different value of an effective temperature with good thermal properties [12][13][14][15]. Similar results were found in quantum dissipative glassy models of mean-field type [43].…”

mentioning

confidence: 64%

“…(16) and (18) can be used to define a single "macroscopic" temperature (or maybe a few), at least long after the quench and in the stationary regime. This approach turned out to be particularly fruitful for understanding the physics of the thermalization of classical dissipative systems with slow dynamics [13,14]. In particular, clarifying the relation between this temperature and the one defined from one-time observables [29][30][31] via Eq.…”

Section: B Dynamic Correlations and Response Functionsmentioning

confidence: 99%

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Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

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“…As for bulk systems, 22,23 surface autocorrelation and autoresponse functions can be combined to yield the surface fluctuation-dissipation ratio 13…”

Section: ͑7͒mentioning

confidence: 99%

Local aging phenomena close to magnetic surfaces

Baumann

Pleimling

2007

Phys. Rev. B

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Surface aging phenomena are discussed for semi-infinite systems prepared in a fully disordered initial state and then quenched to or below the critical point. In addition to solving exactly the semi-infinite Ising model in the limit of large dimensions, we also present results of an extensive numerical study of the nonequilibrium dynamical behavior of the two-dimensional semi-infinite Ising model undergoing coarsening. The studied models reveal a simple aging behavior where some of the nonequilibrium surface exponents take on values that differ from their bulk counterparts. For the two-dimensional semi-infinite Ising model we find that the exponent b 1 that describes the scaling behavior of the surface autocorrelation vanishes. These simulations also reveal the existence of strong finite-time corrections that to some extent mask the leading scaling behavior of the studied two-time quantities.

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

Cited by 352 publications

References 349 publications

Ground-state topology of the Edwards-Anderson±Jspin glass model

Ground-state topology of the Edwards-Anderson±Jspin glass model

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Local aging phenomena close to magnetic surfaces

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