Journal of Statistical Physics

, Volume 111, Issue 3, pp 505–533

Two Solutions to Diluted p-Spin Models and XORSAT Problems

  • M. Mézard
  • F. Ricci-Tersenghi
  • R. Zecchina

DOI: 10.1023/A:1022886412117

Cite this article as:
Mézard, M., Ricci-Tersenghi, F. & Zecchina, R. Journal of Statistical Physics (2003) 111: 505. doi:10.1023/A:1022886412117


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.

Spin glasssatisfiabilityleaf removalcavity method

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • M. Mézard
    • 1
  • F. Ricci-Tersenghi
    • 2
  • R. Zecchina
    • 3
  1. 1.Laboratoire de Physique Théorique et Modèles StatistiquesUniversité Paris SudOrsayFrance
  2. 2.Dipartimento di Fisica and INFMUniversità di Roma “La Sapienza,”Roma (Italy)
  3. 3.International Center for Theoretical PhysicsTriesteItaly