Fluctuation-dissipation ratio in three-dimensional spin glasses

Franz, Silvio; Rieger, Heiko

doi:10.1007/bf02184881

Cited by 95 publications

(142 citation statements)

References 17 publications

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“…In the case of the 3d ea model the numerical results were interpreted as supporting the existence of a curve with non-constant slope below q ea [57]. Similar conclusions were drawn from the experimental work presented in [58].…”

Section: Behavior Of Global Two-time Quantitiessupporting

confidence: 80%

Spatially heterogeneous ages in glassy systems

et al. 2003

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We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution in these systems: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators obtained for a given noise realization. We explain why the noise-averaged correlators describe the fingerprint of quenched disorder when it exists, while the coarse-grained correlators are linked to noise-induced mesoscopic fluctuations. We predict constraints on the distribution of the fluctuations of the coarse-grained quantities. In particular, we show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. A symmetry of the underlying theory, namely invariance under reparametrizations of the time coordinates, underlies these results. We establish a connection between the probabilities of spatial distributions of local coarse-grained quantities and the theory of dynamic random manifolds. We define, and discuss the behavior of, a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We characterize the fluctuations in the system in terms of their fractal properties. For concreteness, we present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.

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Section: Behavior Of Global Two-time Quantitiessupporting

confidence: 80%

Spatially heterogeneous ages in glassy systems

et al. 2003

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“…The obtain the effective temperature it is sometimes useful to construct the so-called fluctuation-dissipation (FD) plots [23,24,25,8]. The FD plots for the homogeneous model can be worked out as follows (the same construction holds for the GOM).…”

Section: The Homogeneous Potential Modelmentioning

confidence: 99%

Spontaneous Relaxation in Generalized Oscillator Models with Glassy Dynamics

Ritort

2004

J. Phys. Chem. B

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In this paper we introduce the generalized oscillator model (GOM) as a family of exactly solvable models useful to investigate theoretical aspects related to the statistical description of the aging state. GOMs are defined by a potential function V (x) and characterized by a zero-temperature relaxation determined by entropy barriers and partial equilibration. Analytic expressions for the effective temperature can be derived using a fluctuation theorem valid in the aging regime without the need to solve the dynamical equations for correlations and responses. Two classes of models are investigated in detail: the homogeneous potential model with V (x) = (k/2p)x 2p (p being a positive integer) and the wedge potential model (V (x) = k|x|) where V (x) has a singularity at the ground state coordinate x = 0. For the latter, we present some numerical simulations that reinforce the validity of the main analytical results. GOMs offer a conceptual framework to develop a statistical description of the spontaneous relaxation process that has been recently proposed [4] to be at the root of the intermittency phenomenon observed in glasses and colloids.

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“…For a discussion of the behavior of this quantity in the Edwards-Anderson model, as well as for a qualitative discussion of its behavior in a different glassy scenario, see Ref. 43. The response function is measured from simulations of ''zero-field-cooled experiments.''…”

Section: X͑tt W ͒ϭX"c͑ Tt W ͒… ͑13͒mentioning

confidence: 99%

Fragile-glass behavior of a short-rangep-spin model

1996

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We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory. ͓S0163-1829͑96͒04137-9͔

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Fluctuation-dissipation ratio in three-dimensional spin glasses

Cited by 95 publications

References 17 publications

Spatially heterogeneous ages in glassy systems

Spatially heterogeneous ages in glassy systems

Spontaneous Relaxation in Generalized Oscillator Models with Glassy Dynamics

Fragile-glass behavior of a short-rangep-spin model

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