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Numerical construction of the Aizenman-Wehr metastate

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arxiv 1704.01390 v1 pith:6DTOVNVS submitted 2017-04-05 cond-mat.dis-nn cond-mat.stat-mech

Numerical construction of the Aizenman-Wehr metastate

classification cond-mat.dis-nn cond-mat.stat-mech
keywords metastatenumericalthermodynamicconstructionlimitstatesaizenman-wehranalysis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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