Numerical construction of the Aizenman-Wehr metastate

Abstract

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a "dispersed" metastate, supported on many thermodynamic states.

5 pages, 5 figures

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• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Spin-glass dynamics: experiment, theory and simulation
• On the superposition principle and non-linear response in spin glasses
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Deepening the knowledge of Spin Glasses: Metastate, Off-equilibrium phenomena and Temperature Chaos