Abstract
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.
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Mézard, M., Ricci-Tersenghi, F. & Zecchina, R. Two Solutions to Diluted p-Spin Models and XORSAT Problems. Journal of Statistical Physics 111, 505–533 (2003). https://doi.org/10.1023/A:1022886412117
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DOI: https://doi.org/10.1023/A:1022886412117