Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 515–542 | Cite as

The Marginally Stable Bethe Lattice Spin Glass Revisited

Article

Abstract

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been studied only using an approximation where marginal stability is not present, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a marginally stable solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non-perturbative approach to the Bethe lattice spin glass problem using approximations that should be hopefully consistent with marginal stability.

Keywords

Spin glasses Bethe lattices Replicas 

Notes

Acknowledgements

It is a pleasure to thank Dmitry Panchenko for many discussions and clarifications. I would like also to thank Valerio Astuti, Silvio Franz, Carlo Lucibello, Federico Ricci-Tersenghi, and Pierfrancesco Urbani for a critical reading of the manuscript. This work has been supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (Grant Agreement No. [694925]).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Dipartimento di Fisica, INFN, Sezione di Roma I, CNR-NANOTEC UOS RomaUniversità di Roma La SapienzaRomaItaly

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