The cavity method at zero temperature

Marc Mézard 1, Giorgio Parisi 2

Journal of Statistical Physics 111 (2003) 1-34

In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a Bethe lattice. 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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM,
    Università degli studi di Roma I - La Sapienza