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arXiv:cond-mat/9307001 · Physical review. B, Condensed matter

Evidence of aging in spin-glass mean-field models

Leticia F. Cugliandolo, Jorge Kurchan B, Félix Ritort

Published Mar 1, 1994• 81 citations
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Abstract

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

DOI
10.1103/physrevb.49.6331

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We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.
We present a numerical study of the nonequilibrium dynamics of the Sherrington-Kirkpatrick model. We analyze the behavior of the system for different system sizes N and time scales t, in order to identify the correct out-of-equilibrium regime. We find evidence of aging behavior in the dynamics of the system, compatible with a weak-ergodicity breaking scenario. In addition, we obtain a pictorial characterization of the out-of-equilibrium phase space that presents some analogies with the hierarchy of states found in equilibrium.
The relaxational modes and aging of the Glauber dynamics of the mean-field spin-glass model, SK model, are studied by a numerical diagonalization technique and Monte Carlo simulations. We found that the aging process of the model is understood as hierarchical growth of quasi-equilibrium domain in the phase-space. The fascinating features of aging effects of spin-glasses revealed by experiments 1) have arose much theoretical interest in recent years, which includes various phenomenologies 2) 3) , analytic predictions 4) and numerical simulations. 5) 6) In order to seek for concrete information to provide theoretical base, we study the relaxational
In this work we study, by means of numerical simulations, the out-of-equilibrium dynamics of the one-dimensional Edwards–Anderson model with long-range interactions of the form ± Jr-α. In the limit α → 0 we recover the well known Sherrington–Kirkpatrick mean-field version of the model, which presents a very complex dynamical behavior. At the other extreme, for α → ∞ the model converges to the nearest-neighbor one-dimensional system. We focus our study on the dependence of the dynamics on the history of the sample (aging phenomena) for different values of α. The model is known to have mean-field exponents already for values of α = 2/3. Our results indicate that the crossover to the dynamic mean-field occurs at a value of α < 2/3.
We present results of a Monte Carlo study of the equilibrium dynamics of the one dimensional long-range Ising spin glass model. By tuning a parameter , this model interpolates between the mean field Sherrington–Kirkpatrick model and a proxy of the finite dimensional Edward-Anderson model. Activated scaling fits for the behavior of the relaxation time as a function of the number of spins N (Namely ) give values of that are not stable against inclusion of subleading corrections. Critical scaling ( ) gives more stable fits, at least in the non mean field region. We also present results on the scaling of the time decay of the critical remanent magnetization of the Sherrington–Kirkpatrick model, a case where the simulation can be done with quite large systems and that shows the difficulties in obtaining precise values for dynamical exponents in spin glass models.
We carry out an analysis of the effect of a quenched magnetic field on the dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We show that there is a characteristic time introduced by the presence of the field. First, for times sufficiently small the dynamic scenario of the zero field case-with aging effects-is reproduced. Second, for times larger than the characteristic time one sees equilibrium dynamics. This dynamical behaviour is reconciled with the geometry of the energy landscape of the model. We compare this behaviour with experimental observations at a finite applied field.
Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without random magnetic anisotropy by dynamical Monte Carlo simulations. In the isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observed in the mean-field model. In the anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.