Is dynamic ultrametricity observable in spin glasses?

Abstract

We investigate the dynamics of spin glasses from the `rheological' point of view, in which aging is suppressed by the action of small, non-conservative forces. The different features can be expressed in terms of the scaling of relaxation times with the magnitude of the driving force, which plays the role of the critical parameter. Stated in these terms, ultrametricity loses much of its mystery and can be checked rather easily. This approach also seems a natural starting point to investigate what would be the real-space structures underlying the hierarchy of time scales. We study in detail the appearance of this many-scale behavior in a mean-field model, in which dynamic ultrametricity is clearly present. A similar analysis is performed on numerical results obtained for a 3D spin glass: In that case, our results are compatible with either that dynamic ultrametricity is absent or that it develops so slowly that even in experimental time-windows it is still hardly observable.

16 pages, Revtex, 12 eps figures

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• Quasi-equilibrium interpretation of aging dynamics
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Cited by in corpus (14)

• Theoretical perspective on the glass transition and amorphous materials
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study
• Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws
• Aging Dynamics of the Heisenberg Spin Glass
• Dynamical ultrametricity in the critical trap model
• Real space application of the mean-field description of spin glass dynamics
• Effective temperatures from the fluctuation-dissipation measurements in soft glassy materials
• Cluster formation in complex multi-scale systems
• Spin Glasses on the Hypercube
• Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice
• Dynamic ultrametricity in finite dimensional spin glasses
• A consequence of local equilibration and heterogeneity in glassy materials
• Controlling the Glass Transition through Active Fluctuating Interactions