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Numerical Construction of the Aizenman-Wehr Metastate
A Billoire1, L A Fernandez2,3, A Maiorano3,4
1Institute de Physique Théorique, CEA Saclay and CNRS, 91191 Gif-sur-Yvette, France.
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.
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