Aging, rejuvenation and memory phenomena in spin glasses

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and of real space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.Comment: submitted for the Proceedings of Stat Phys 22, Bangalore (India

The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking

We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian quenched random couplings. Our results clearly support the existence of replica symmetry breaking in the thermodynamical limit.Comment: 8 pages, 13 postscript figure

Fluctuation-dissipation ratio of a spin glass in the aging regime

We present the first experimental determination of the time autocorrelation $C(t',t)$ of magnetization in the non-stationary regime of a spin glass. Quantitative comparison with the response, the magnetic susceptibility $\chi(t',t)$, is made using a new experimental setup allowing both measurements in the same conditions. Clearly, we observe a non-linear fluctuation-dissipation relation between $C$ and $\chi$, depending weakly on the waiting time $t'$. Following theoretical developments on mean-field models, and lately on short range models, it is predicted that in the limit of long times, the $\chi(C)$ relationship should become independent on $t'$. A scaling procedure allows us to extrapolate to the limit of long waiting times.Comment: 4 pages, 3 figure

Real spin glasses relax slowly in the shade of hierarchical trees

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview of the important experimental results which could be understood within the mean-field solution. The existence of a true phase transition and the particular behaviour of the susceptibility below the freezing temperature, predicted by the theory, are clearly confirmed by the experimental results. The behaviour of the complex order parameter and of the Fluctuation Dissipation ratio are in good agreement with results of spontaneous noise measurements. The very particular ultrametric symmetry, the key feature of the theory, provided us with a simple description of the rejuvenation and memory effects observed in experiment. Finally, going a step beyond mean-field, the paper shortly discusses new analyses in terms of correlated domains characterized by their length scales, as well as new experiments on superspin glasses which compare well with recent theoretical simulations.Comment: To appear in the proceedings of "Wandering with Curiosity in Complex Landscapes", a scientific conference in honour of Giorgio Parisi for his 60th birthday, Roma, September 8-10 2008 (submitted for the special issue of the Journal of Statistical Physics, 2009

Off Equilibrium Study of the Fluctuation-Dissipation Relation in the Easy-Axis Heisenberg Antiferromagnet on the Kagome Lattice

Violation of the fluctuation-dissipation theorem (FDT) in a frustrated Heisenberg model on the Kagome lattice is investigated using Monte Carlo simulations. The model exhibits glassy behaviour at low temperatures accompanied by very slow dynamics. Both the spin-spin autocorrelation function and the response to an external magnetic field are studied. Clear evidence of a constant value of the fluctuation dissipation ratio and long range memory effects are observed for the first time in this model. The breakdown of the FDT in the glassy phase follows the predictions of the mean field theory for spin glasses with one-step replica symmetry breaking.Comment: 4 pages, 4 figure

On the definition of a unique effective temperature for non-equilibrium critical systems

We consider the problem of the definition of an effective temperature via the long-time limit of the fluctuation-dissipation ratio (FDR) after a quench from the disordered state to the critical point of an O(N) model with dissipative dynamics. The scaling forms of the response and correlation functions of a generic observable are derived from the solutions of the corresponding Renormalization Group equations. We show that within the Gaussian approximation all the local observables have the same FDR, allowing for a definition of a unique effective temperature. This is no longer the case when fluctuations are taken into account beyond that approximation, as shown by a computation up to the first order in the epsilon-expansion for two quadratic observables. This implies that, contrarily to what often conjectured, a unique effective temperature can not be defined for this class of models.Comment: 32 pages, 5 figures. Minor changes, published versio

Extended droplet theory for aging in short-ranged spin glasses and a numerical examination

We analyze isothermal aging of a four dimensional Edwards-Anderson model in detail by Monte Carlo simulations. We analyze the data in the view of an extended version of the droplet theory proposed recently (cond-mat/0202110) which is based on the original droplet theory plus conjectures on the anomalously soft droplets in the presence of domain walls. We found that the scaling laws including some fundamental predictions of the original droplet theory explain well our results. The results of our simulation strongly suggest the separation of the breaking of the time translational invariance and the fluctuation dissipation theorem in agreement with our scenario.Comment: 27 pages, 39 epsfiles, revised versio

Chirality scenario of the spin-glass ordering

Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.Comment: Submitted to J. Phys. Soc. Japan "Special Issue on Frustration

MISA [Material gráfico]

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