Journal of Statistical Physics

, Volume 111, Issue 1–2, pp 1–34 | Cite as

The Cavity Method at Zero Temperature

  • Marc Mézard
  • Giorgio Parisi
Article

Abstract

In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a lattice with a local tree like structure, which is the proper generalization of the usual Bethe lattice to frustrated problems. The computation is done explicitly in the formalism equivalent to “one step replica symmetry breaking;” we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three. The main assumptions underlying the one step cavity approach, namely the existence of many local ground states, are explicitely stated and discussed: some of the main obstacles towards a rigorous study of the problem with the cavity method are outlined.

Spin glass Bethe lattice cavity method 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Marc Mézard
    • 1
  • Giorgio Parisi
    • 2
  1. 1.Laboratoire de Physique Théorique et Modèles StatistiquesUniversité Paris SudOrsay CedexFrance
  2. 2.Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFMUniversità di Roma “La Sapienza,”RomeItaly

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