Out of Equilibrium Dynamics in Spin-Glasses and Other Glassy Systems

Bouchaud, Jean‐Philippe; Cugliandolo, Leticia F.; Kurchan, Jorge; Mézard, Marc

doi:10.1142/9789812819437_0006

Cited by 492 publications

(866 citation statements)

References 108 publications

(239 reference statements)

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“…The existence of more than one time sector is a necessary ͑but not sufficient͒ requirement for dynamic ultrametricity. 2 Some indications of the presence of more than one time sector in the dynamics of the EA model in three-dimensions were found in Ref. 44.…”

Section: E Results For T W ͻmentioning

confidence: 90%

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Rejuvenation and memory in model spin glasses in three and four dimensions

2005

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We numerically study aging for the Edwards-Anderson model in three and four dimensions using different temperature-change protocols. In D = 3, time scales a thousand times larger than in previous work are reached with the Spin Update Engine ͑SUE͒ machine. Deviations from cumulative aging are observed in the nonmonotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the D = 3 site-diluted ferromagnetic Ising model ͑without chaos͒. However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.

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Section: E Results For T W ͻmentioning

confidence: 90%

“…2 Spin glasses age, 3 as shown by the thermoremanent magnetization: consider a spin glass that has spent a time t w below its glass temperature T c in the presence of a magnetic field. Let t be the time elapsed since the magnetic field was switched off.…”

Section: Introductionmentioning

confidence: 99%

Rejuvenation and memory in model spin glasses in three and four dimensions

2005

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“…Analytical extensions of the mode-coupling theory for supercooled liquids to the low-temperature regime of glasses allow for the interpretation of the ageing of global correlation and response functions 2,5 . In these frameworks, the evolution of C(t , t w ) and χ(t , t w ) are separated into a stationary part (short time) and an ageing part (long time):…”

Section: Correlations and Responsesmentioning

confidence: 99%

“…Theories originally developed in the field of spin glasses 6 attempt to develop a common framework for the understanding of ageing. For example, the structural glass and spin-glass transitions have been coupled by the low-temperature extension of the modecoupling theory 4,5,7 . More generally, this approach is related to analogous ideas developed in the field of granular matter such as compactivity [8][9][10][11] , and the inherent structure formalisms 12 , adapted to the energy landscape of glasses 13 .…”

mentioning

confidence: 99%

Dynamic particle tracking reveals the ageing temperature of a colloidal glass

Wang

Makse

2006

Nature Phys

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T he glass transition 1 is considered to be one of the most fundamental problems in statistical physics. Despite decades of effort, a general consensus on the validity of a universal theory for the large variety of glass systems is lacking 2,3 -partly because of difficulties encountered in the experimental testing of the theoretical predictions 4,5 . Here, we present experiments on a colloidal glass made of micrometresized particles in a fluid. We investigate the autocorrelation and response function to monitor the ageing of a colloidal glass. At equilibrium, all the observables are stationary, whereas in the out-of-equilibrium glassy state they have an explicit dependence on the age of the system. We find that the transport coefficients scale with the ageing time as a power law, a signature of the slow relaxation. Nevertheless, our analysis reveals that the glassy system has thermalized at a constant temperature independent of the age and warmer than the bath, reflecting the structural rearrangements of cage dynamics. Furthermore, we find a universal scaling law to describe the global and local fluctuations of the observables.Increasing the volume fraction of a colloidal system slows down the brownian dynamics of its constitutive particles, implying a limiting density, φ g , above which the system can no longer be equilibrated with its bath 1 . Hence, the thermal system falls out of equilibrium on the timescale of the experiment and thus undergoes a glass transition 2 . Even above φ g the particles continue to relax, but the nature of the relaxation is very different to that in equilibrium. This phenomenon of a structural slow evolution beyond the glassy state is known as 'ageing' 3 . The system is no longer stationary and the relaxation time is found to increase with the age of the system, t w , as measured from the time of sample preparation.This picture applies not only to structural glasses such as colloids, silica and polymer melts, but also to spin glasses, ferromagnetic coarsening, elastic manifolds in quenched disorder and jammed matter such as grains and emulsions 2,4,5 . Theories originally developed in the field of spin glasses 6 attempt to develop a common framework for the understanding of ageing. For example, the structural glass and spin-glass transitions have been coupled by the low-temperature extension of the modecoupling theory 4,5,7 . More generally, this approach is related to analogous ideas developed in the field of granular matter such as compactivity [8][9][10][11] , and the inherent structure formalisms 12 , adapted to the energy landscape of glasses 13 .One of the important features of this scenario is a separation of timescales where the observables are equilibrated at different temperatures, even though the system is far from equilibrium. Although theoretical results have flourished, the difficulties in the experimental testing of the fundamental predictions of the theories have hampered the development of an understanding of ageing in glasses [14][15][16][17][18] . Experiments so f...

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“…(2) is like the equation of motion where the right hand side is like the force acting on a fluid element. In constructing this model, we were motivated by the works [10,11] in which random coupling models involving an infinite component order parameter have been shown to be exactly analyzed by mean-field-type concepts. We will thus eventually take N and M infinite with the ratio δ * ≡ M/N kept finite.…”

Section: Modelmentioning

confidence: 99%

Kinetically driven glassy transition in an exactly solvable toy model with a reversible mode coupling mechanism and trivial statics

Kim¹,

Kawasaki²

2002

J. Phys.: Condens. Matter

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Abstract. We propose a toy model with reversible mode coupling mechanism and with trivial Hamiltonian (and hence trivial statics). The model can be analyzed exactly without relying upon uncontrolled approximation such as the factorization approximation employed in the current MCT. We show that the model exhibits a kinetically driven transition from an ergodic phase to nonergodic phase. The nonergodic state is the nonequilibrium stationary solution of the Fokker-Planck equation for the distribution function of the model.

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Out of Equilibrium Dynamics in Spin-Glasses and Other Glassy Systems

Cited by 492 publications

References 108 publications

Rejuvenation and memory in model spin glasses in three and four dimensions

Rejuvenation and memory in model spin glasses in three and four dimensions

Dynamic particle tracking reveals the ageing temperature of a colloidal glass

Kinetically driven glassy transition in an exactly solvable toy model with a reversible mode coupling mechanism and trivial statics

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