期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 2021, 期 7, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/ac0900
关键词
slow relaxation; glassy dynamics; ageing; extreme value statistics
资金
- Brazilian funding agency CNPq
We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick model with finite number of degrees of freedom, identifying three time regimes of relaxation influenced by eigenvalue distribution and initial states effects.
We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick (p = 2) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes: a first algebraic one controlled by the decay of the eigenvalue distribution of the random exchange interaction matrix at its edge in the infinite size limit; a faster algebraic one determined by the distribution of the gap between the two extreme eigenvalues; and a final exponential one determined by the minimal gap sampled in the disorder average. We also analyse the finite size effects on the relaxation from initial states which are almost projected on the saddles of the potential energy landscape, and we show that for deviations scaling as N (-nu ) from perfect alignment the system escapes the initial configuration in a time-scale scaling as ln N after which the dynamics no longer 'self-averages' with respect to the initial conditions. We prove these statements with a combination of analytic and numerical methods.
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