Alternative solutions to diluted p-spin models and XORSAT problems

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.

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

Cited by in corpus (8)

• The random K-satisfiability problem: from an analytic solution to an efficient algorithm
• Statistical physics of inference: Thresholds and algorithms
• Focused Local Search for Random 3-Satisfiability
• Relaxation and Metastability in the RandomWalkSAT search procedure
• The Phase Diagram of 1-in-3 Satisfiability Problem
• The large deviations of the whitening process in random constraint satisfaction problems
• Research on Solution Space of Bipartite Graph Vertex-Cover by Maximum Matchings
• Duality approach to quantum annealing of the 3-XORSAT problem