Alternative solutions to diluted p-spin models and XORSAT problems

2002/07/31 by M. Mezard, F. Ricci-Tersenghi, R. Zecchina
Physics and Astronomy · Computer Science · #cond-mat.dis-nn #cond-mat.stat-mech #cs.DM

paper · pdf

published as J. Stat. Phys. 111, 505 (2003) · 14 pages, 14 figures. v3: small errors corrected, simpler notation used

arxiv created 2002/09/19 · arxiv updated 2009/11/30

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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