Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model

Cugliandolo, Leticia F.; Kurchan, Jorge

doi:10.1103/physrevlett.71.173

Cited by 991 publications

(1,754 citation statements)

References 16 publications

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“…Although the existence of an effective temperature can be rationalized using theoretical frameworks of disordered LETTERS spin-glass models 4 , we find that the scaling forms of the correlations and responses are not consistent with such models. On the basis of invariance properties under time reparametrization, spin-glass models predict a general scaling form C ag (t , t w ) = C ag (h(t )/h(t w )), where h(t ) is a generic monotonic function 2 .…”

Section: Scaling Ansatz For the Global Correlations And Responsesmentioning

confidence: 86%

“…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 .…”

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confidence: 99%

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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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Section: Scaling Ansatz For the Global Correlations And Responsesmentioning

confidence: 86%

mentioning

confidence: 99%

Dynamic particle tracking reveals the ageing temperature of a colloidal glass

Wang

Makse

2006

Nature Phys

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“…2͒. The resulting plot, t w independent for large t w , 36 can be fitted with two straight lines, yielding X͓C͔. In Fig.…”

Section: A Strong Rejuvenation?mentioning

confidence: 93%

“…to the real part of the susceptibility: ͑ =2 / t 0 , t w ͒ Ϸ͓1−C͑t w , t w + t 0 , ͔͒ / T. Yet, off equilibrium, FDT needs to be generalized replacing T by T / X͓C͔ (X͓C͔ is a smooth function 36 of C͑t w , t w + t 0 ͒). Hence one assumes [24][25][26]34 to be in pseudoequilibrium regime ͑ t w ӷ 1 thus X͓C͔ =1͒, which is not always true.…”

Section: Models and Simulationsmentioning

confidence: 99%

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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“…Determination of X, the fluctuation dissipation ratio (FDR), or of an "effective temperature" T ef f = T /X, was the aim of many recent theoretical studies, following the seminal works of L. F. Cugliandolo and J. Kurchan. 12,13 In mean field models, a generalization of FDT was predicted on the basis of the "weak ergodicity breaking" scenario. 14 It was conjectured that, in the asymptotic limit of large times, when stationary and non-stationary timescales are well separated, the FDR would depend on time only through the correlation function: X(t ′ , t) = X(C(t ′ , t)) for t ′ (and t > t ′ ) → ∞.…”

Section: Generalized Fluctuation Dissipation Relationmentioning

confidence: 99%

Experimental investigation of the fluctuation dissipation relation in a spin glass

Hérisson

Ocio

2003

SPIE Proceedings

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We present the first experimental determination of the time auto-correlation of magnetization in the nonstationary regime of a spin glass, and its quantitative comparison with the corresponding response, the magnetic relaxation function. These measurements were performed in a new experimental setup working as an absolute thermometer. Clearly, we observe a non-linear fluctuation-dissipation relation between correlation and relaxation, i.e. an effective temperature higher than the bath temperature in the aging regime. According to theoretical developments on mean field models, and lately on short range ones, in the limit of very large waiting times, the relation between relaxation and correlation in the aging regime becomes temperature independent for a given system. A scaling procedure allows us to extrapolate to the limit of long waiting times by separating stationary and non-stationary regimes and to check the validity of the temperature independence of the fluctuation dissipation relation in the non-stationary regime.

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Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model

Cited by 991 publications

References 16 publications

Dynamic particle tracking reveals the ageing temperature of a colloidal glass

Dynamic particle tracking reveals the ageing temperature of a colloidal glass

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

Experimental investigation of the fluctuation dissipation relation in a spin glass

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