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