Numerical Construction of the Aizenman-Wehr Metastate

A. Billoire, L. A. Fernandez, A. Maiorano, E. Marinari, V. Martin-Mayor, J. Moreno-Gordo, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo
Phys. Rev. Lett. 119, 037203 – Published 21 July 2017
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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=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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  • Received 27 March 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.037203

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

A. Billoire1, L. A. Fernandez2,3, A. Maiorano4,3, E. Marinari4,5,6, V. Martin-Mayor2,3, J. Moreno-Gordo2,3, G. Parisi4,5,6, F. Ricci-Tersenghi4,5,6, and J. J. Ruiz-Lorenzo7,3

  • 1Institute de Physique Théorique, CEA Saclay and CNRS, 91191 Gif-sur-Yvette, France
  • 2Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
  • 3Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
  • 4Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Rome, Italy
  • 5Nanotec, Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy
  • 6Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Rome, Italy
  • 7Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain

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Issue

Vol. 119, Iss. 3 — 21 July 2017

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