Alternative solutions to diluted p-spin models and XORSAT problems

Marc Mézard 1, Federico Ricci-Tersenghi 2, Riccardo Zecchina 3

Journal of Statistical Physics 111 (2003) 505-533

We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of the phase diagram: location of the phase transitions (static and dynamic), together with a description of the clustering phenomenon taking place in configurational space. We use two alternative methods: the cavity approach and a rigorous derivation.

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