Instability of one-step replica-symmetry-broken phase in satisfiability problems
<|reference_start|>Instability of one-step replica-symmetry-broken phase in satisfiability problems: 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.<|reference_end|>
@article{montanari2003instability,
    title={Instability of one-step replica-symmetry-broken phase in satisfiability
  problems},
    author={Andrea Montanari, Giorgio Parisi and Federico Ricci-Tersenghi},
    journal={J. Phys. A 37, 2073 (2004)},
    year={2003},
    doi={10.1088/0305-4470/37/6/008},
    archivePrefix={arXiv},
    eprint={cond-mat/0308147},
    primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
}