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

@article{Montanari2003InstabilityOO,
  title={Instability of one-step replica-symmetry-broken phase in satisfiability problems},
  author={Andrea Montanari and Giorgio Parisi and Federico Ricci-Tersenghi},
  journal={CoRR},
  year={2003},
  volume={cond-mat/0308147}
}
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 Montanari and Ricci-Tersenghi (2003 Eur. Phys. J. B 33 339) to more general combinatorial problems. It turns out that 1RSB is always unstable at sufficiently small clause density α or high energy. In… CONTINUE READING
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