Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses

Sompolinsky, Haim; Zippelius, Annette

doi:10.1103/physrevb.25.6860

Cited by 490 publications

(408 citation statements)

References 47 publications

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“…We thus obtain the susy form of the well-known single spin equation for fully connected models: averages of Ψ are taken with a Gaussian weight (apart from the soft-spin v term), to be determined self-consistently through Q sp . It is the equation of a single degree of freedom evolving through a Langevin equation with a retarded interaction and a colored noise, which are to be expressed self-consistently in terms of the correlation and the response of the process [43]. In the dilute case, one can also follow this idea, but the self consistency equations cannot be written solely in terms of the two point function.…”

Section: Functional Formalismmentioning

confidence: 99%

On the Stochastic Dynamics of Disordered Spin Models

Semerjian

Cugliandolo

Montanari

2004

Journal of Statistical Physics

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In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spinglasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs.

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Section: Functional Formalismmentioning

confidence: 99%

On the Stochastic Dynamics of Disordered Spin Models

Semerjian

Cugliandolo

Montanari

2004

Journal of Statistical Physics

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“…Here we have to take into account the time t w at which the measurement is performed, and consider ω −1 o ≪ t c ≪ t w . Then, a similar calculation yields for the energy of the oscillator 14) where the average x 2 tw is taken on a comparatively short time stretch after t w . This definition of the frequency-and waiting-time-dependent correlation C O (ω o , t w ) and out-ofphase susceptibility χ ′′ O (ω o , t w ) closely follows the actual experimental procedure for their measure: one considers a time window around t w consisting of a few cycles (so that phase and amplitude can be defined) and small enough respect to t w so that the measure is "as local as possible in time".…”

Section: Frequency Dependent Thermometers That Measure Effectivementioning

confidence: 99%

Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

1997

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We show that, in nonequilibrium systems with small heat flows, there is a time-scale dependent effective temperature which plays the same role as the thermodynamical temperature, in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy systems that age after cooling and show that they exhibit very similar behavior provided that time dependences are expressed in terms of the correlations of the system. We substantiate our claims with examples taken from solvable models with nontrivial low-temperature dynamics, but argue that they have a much wider range of validity. We suggest experimental checks of these ideas. 75.40.Gb, 75.10.Nr, Typeset using REVT E X 1

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“…Extrapolating at low temperature, one can estimate the point where the entropy vanishes to be in the range 0.3рT c р0. 6. This range of temperatures should not be considered as more than a mere indication of what could happen.…”

Section: Thermodynamicsmentioning

confidence: 99%

“…The natural separation of the variables among ''quenched'' and ''annealed'' allows for the successful use of powerful techniques such as the replica method for static dynamics 5 and functional methods in dynamics. 6 In fact, a satisfactory mean-field theory of disordered systems for static 5 as well as for equilibrium 6 and off-equilibrium dynamics exists. 7,8 Recently, examples of mean-field deterministic models with glassy behavior very similar to the one of disordered systems have been displayed.…”

Section: Introductionmentioning

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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Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses

Cited by 490 publications

References 47 publications

On the Stochastic Dynamics of Disordered Spin Models

On the Stochastic Dynamics of Disordered Spin Models

Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

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

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