Alternative solutions to diluted p-spin models and XORSAT problems

Details Alternative solutions to diluted p-spin models and XORSAT problems Alternative solutions to diluted p-spin models and XORSAT problems

2002-07-04

arxiv.org/abs/cond-mat/0207140v3

J. Stat. Phys. 111, 505 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 14 figures. v3: small errors corrected, simpler notation used

Scientific paper

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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