Journal of Statistical Physics

, Volume 111, Issue 3, pp 505-533

First online:

Two Solutions to Diluted p-Spin Models and XORSAT Problems

  • M. MézardAffiliated withLaboratoire de Physique Théorique et Modèles Statistiques, Université Paris Sud
  • , F. Ricci-TersenghiAffiliated withDipartimento di Fisica and INFM, Università di Roma “La Sapienza,”
  • , R. ZecchinaAffiliated withInternational Center for Theoretical Physics

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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 glass satisfiability leaf removal cavity method