Publication: Numerical construction of the Aizenman-Wehr metastate
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Publication Date
2017-07-21
Authors
Billoire,, A.
Maiorano, A.
Marinari, E.
Moreno Gordo, J.
Parisi, G.
Ricci-Tersenghi, F.
Ruiz Lorenzo, J. J.
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American Physical Society
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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 ¼ 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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© 2017 American Physical Society. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant No. 694925). We were partially supported by MINECO (Spain) through Grants No. FIS2012-35719-C02-01, No. FIS2013-42840-P, No. FIS2015-65078-C2, and No. FIS2016-76359-P (contract partially funded by FEDER), and by the Junta de Extremadura (Spain) through Grant No. GRU10158 (partially funded by FEDER). Our simulations were carried out at the BIFI supercomputing center (using the Memento and Cierzo clusters), at the TGCC supercomputing center in Bruyères-le-Châtel (using the Curie computer, under Grant No. 2015-056870 made by GENCI), and at the ICCAEx supercomputer center in Badajoz (GrInFishpc and ICCAExhpc). We thank the staff at the BIFI, TGCC, and ICCAEx supercomputing centers for their assistance.