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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2004

Instability of one-step replica-symmetry-broken phase in satisfiability problems

Résumé

We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general combinatorial problems. It turns out that 1RSB is always unstable at sufficiently small clauses density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT is unstable at zero energy for alpha< alpha_m, with alpha_m\\approx 4.153. On the other hand, the SAT-UNSAT phase transition seems to be correctly described within 1RSB.

Dates et versions

hal-00008647 , version 1 (13-09-2005)

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Andrea Montanari, Giorgio Parisi, Federico Ricci-Tersenghi. Instability of one-step replica-symmetry-broken phase in satisfiability problems. Journal of Physics A: Mathematical and Theoretical, 2004, 37, pp.2073. ⟨hal-00008647⟩
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