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

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

2003-08-07

arxiv.org/abs/cond-mat/0308147v1

J. Phys. A 37, 2073 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

26 pages, 7 eps figures

Scientific paper

10.1088/0305-4470/37/6/008

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.

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