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A Multi-scale Spin-Glass Mean-Field Model

  • Pierluigi ContucciEmail author
  • Emanuele Mingione
Article
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Abstract

In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved by means of lower and upper bounds. The lower bound is obtained with a Ruelle cascade using the interpolation technique, while the upper bound exploits factorisation properties of the equilibrium measure and the synchronisation technique.

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Notes

Acknowledgements

Wewant to thank several useful discussionswithDiegoAlberici, FrancescoGuerra, Jorge Kurchan and especially Dmitry Panchenko whose observation led to a valuable improvement of proposition 5.1. P.C. was partially supported by PRIN project Statistical Mechanics and Complexity (2015K7KK8L), E.M. was partially supported by Progetto Almaidea 2018.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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