Metastable configurations on the Bethe lattice

Andrea Pagnani 1, Giorgio Parisi 2, Mathieu Ratieville 1, 2

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 67 (2003) 026116

We present a general analytic method to compute the number of metastable configurations as a function of the energy for a system of interacting Ising spins on the Bethe lattice. Our approach is based on the cavity method. We apply it to the case of ferromagnetic interactions, and also to the binary and Gaussian spin glasses. Most of our results are obtained within the replica symmetric ansatz, but we illustrate how replica symmetry breaking can be performed.

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