Alternative solutions to diluted p-spin models and XORSAT problems

@article{Mzard2002AlternativeST,
  title={Alternative solutions to diluted p-spin models and XORSAT problems},
  author={Marc M{\'e}zard and Federico Ricci-Tersenghi and Riccardo Zecchina},
  journal={CoRR},
  year={2002},
  volume={cond-mat/0207140}
}
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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