Crossover from stationary to aging regime in glassy dynamics

Abstract

We study the non-equilibrium dynamics of the spherical p-spin models in the scaling regime near the plateau and derive the corresponding scaling functions for the correlators. Our main result is that the matching between different time regimes fixes the aging function in the aging regime to $h(t)=\exp (t^{1-\mu })$. The exponent $\mu$ is related to the one giving the length of the plateau. Interestingly $1-\mu$ is quickly very small when one goes away from the dynamic transition temperature in the glassy phase. This gives new light on the interpretation of experiments and simulations where simple aging was found to be a reasonable but not perfect approximation, which could be attributed to the existence of a small but non-zero stretching exponent.

7 pages+2 figures

References in corpus (12)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Memory and Chaos Effects in Spin Glasses
• Time and length scales in supercooled liquids
• Phase space geometry and slow dynamics
• Full dynamical solution for a spherical spin-glass model
• Dynamic criticality in glass-forming liquids
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Large times off-equilibrium dynamics of a particle in a random potential
• Brownian Dynamics simulations of aging colloidal gels
• The dynamics of the spherical p-spin model: from microscopic to asymptotics
• Time reparametrization group and the long time behaviour in quantum glassy systems
• Aging and effective temperatures in the low temperature mode-coupling equations

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• From sub-aging to hyper-aging in structural glasses
• Ageing in bosonic particle-reaction models with long-range transport
• Critical Off-Equilibrium Dynamics in Glassy Systems
• Nonequilibrium dynamics in an amorphous solid
• Correlators in phase-ordering from Schrödinger-invariance