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arXiv:cond-mat/9505149 · Journal of Physics A Mathematical and General

On the dynamics of a spherical spin-glass in a magnetic field

Leticia F. Cugliandolo, David S. Dean

Published Sep 7, 1995• 38 citations
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Abstract

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.

DOI
10.1088/0305-4470/28/17/001

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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.
Using Sherrington-Kirkpatric (SK) model we investigated the nonequilibrum properties of spin glass by dynamical Monte Carlo simulation. Our results revealed that the susceptibility in the weak field shows a cusp near the glass transition, while the specific heat shows a more broad transition. The aging and zero-field colding memory effect is also reproduced in our simulation, and the phenomena can be explained by energy relaxation. Our simulation also reveals that homogeneous SK model can not reproduce the exchange bias effect observed in the experiment.
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.
We present a numerical study of the non-equilibrium dynamics of the Sherrington-Kirkpatrick model. We analize the overlap distribution between the configurations visited at the time t and in particular its scaling behaviour with the size of the system. We find two different non-equilibrium dynamical regimes. The first is a proper Out of Equilibrium Regime, that is the relevant regime for the dynamics of an infinite system. The second is an Intermediate Regime that separates the Out of Equilibrium Regime from equilibrium. After studying the crossover beetween the two regimes, we focus on the Out of Equilibrium Regime and we reveal some of the geometrical features of phase space. According to recent analitical work, we find that the asymptotic out of equilibrium energy density is the equilibrium one. The same happens to the staggered-magnetisation, suggesting there is a deep geometrical similarity between equilibrium and out of equilibrium configurations. A procedure, that we call clonation, shows that the dynamics follows sort of canyons, as opposed to a system of independent traps.
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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